HIGHWAY CAPACITY MANUAL Special Report 209 Third Edition
TRANSPORTATION RESEARCH BOARD National Research Council Washington, D.C. 1998
1998 TRANSPORTATION RESEARCH BOARD EXECUTIVE COMMITTEE OFFICERS Chairwoman: Sharon D. Banks, General Manager, AC Transit Vice Chairman: Wayne Shackelford, Commissioner, Georgia Department of Transportation Executive Director: Robert E. Skinner, Jr., Transportation Research Board
MEMBERS Thomas F. Barry, Jr., Secretary of Transportation, Florida Department of Transportation Brian J. L. Berry, Lloyd Viel Berkner Regental Professor, University of Texas at Dallas Sarah C. Campbell, President, TransManagement, Inc. E. Dean Carlson, Secretary, Kansas Department of Transportation Joanne F. Casey, President, Intermodal Association of North America John W. Fisher, Director, ATLSS Engineering Research Center, and Professor of Civil and Environmental Engineering, Lehigh University Gorman Gilbert, Director, Institute for Transportation Research and Education, North Carolina State University Delon Hampton, Chairman and CEO, Delon Hampton & Associates, Chartered Lester A. Hoel, Hamilton Professor, Department of Civil Engineering, University of Virginia James L. Lammie, Director, Parsons Brinckerhoff, Inc. Thomas F. Larwin, General Manager, San Diego Metropolitan Transit Development Board Bradley L. Mallory, Secretary of Transportation, Commonwealth of Pennsylvania Jeffrey J. McCaig, President and CEO, Trimac Corporation Joseph A. Mickes, Chief Engineer, Missouri Department of Transportation Marshall W. Moore, Director, North Dakota Department of Transportation Andrea Riniker, Executive Director, Port of Tacoma John M. Samuels, Vice President—Operations Planning and Budget, Norfolk Southern Corporation Les Sterman, Executive Director, East-West Gateway Coordinating Council James W. van Loben Sels, Director, California Department of Transportation (Past Chairman, 1996) Martin Wachs, Director, University of California Transportation Center, and Professor of Civil Engineering and City and Regional Planning, University of California David L. Winstead, Secretary, Maryland Department of Transportation David N. Wormley, Dean of Engineering, Pennsylvania State University (Past Chairman, 1997) Mike Acott, President, National Asphalt Pavement Association (ex officio) Joe N. Ballard (Lt. Gen., U.S. Army), Chief of Engineers and Commander, U.S. Army Corps of Engineers (ex officio) Andrew H. Card, Jr., President and CEO, American Automobile Manufacturers Association (ex officio) Kelley S. Coyner, Acting Administrator, Research and Special Programs Administration, U.S. Department of Transportation (ex officio) Mortimer L. Downey, Deputy Secretary, Office of the Secretary, U.S. Department of Transportation (ex officio) Francis B. Francois, Executive Director, American Association of State Highway and Transportation Officials (ex officio) David Gardiner, Assistant Administrator, Office of Policy, Planning and Evaluation, Environmental Protection Agency (ex officio) Jane F. Garvey, Administrator, Federal Aviation Administration, U.S. Department of Transportation (ex officio) John E. Graykowski, Acting Administrator, Maritime Administration, U.S. Department of Transportation (ex officio) Robert A. Knisely, Deputy Director, Bureau of Transportation Statistics, U.S. Department of Transportation (ex officio) Gordon J. Linton, Administrator, Federal Transit Administration, U.S. Department of Transportation (ex officio) Ricardo Martinez, Administrator, National Highway Traffic Safety Administration, U.S. Department of Transportation (ex officio) Walter B. McCormick, President and CEO, American Trucking Associations, Inc. (ex officio) William W. Millar, President, American Public Transit Association (ex officio) Jolene M. Molitoris, Administrator, Federal Railroad Administration, U.S. Department of Transportation (ex officio) Karen Borlaug Phillips, Senior Vice President, Policy, Legislation, and Economics, Association of American Railroads (ex officio) Valentin J. Riva, President, American Concrete Pavement Association (ex officio) George D. Warrington, Acting President and CEO, National Railroad Passenger Corporation (ex officio) Kenneth R. Wykle, Administrator, Federal Highway Administration, U.S. Department of Transportation (ex officio) Updated December 1997
Transportation Research Board Special Report 209 Subscriber Categories IA planning and administration IIA highway and facility design IVA highway operations, capacity, and traffic control VI public transit Transportation Research Board publications are available by ordering individual publications directly from the TRB Business Office, through the Internet at http://www.nas.edu/trb/index.html, or by annual subscription through organization or individual affiliation with TRB. Affiliates and library subscribers are eligible for substantial discounts. For further information, contact the Transportation Research Board Business Office, National Research Council, 2101 Constitution Avenue, N.W., Washington, D.C. 20418 (telephone 202-334-3214; fax 202-334-2519; or e-mail
[email protected]). NOTICE The project that is the subject of this report was approved by the Governing Board of the National Research Council, whose members are drawn from the councils of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. The members of the committee responsible for the report were chosen for their special competence and with regard for appropriate balance. This report has been reviewed by a group other than the authors according to procedures approved by a Report Review Committee consisting of members of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine.
©1985, 1992, 1994, 1998 by the Transportation Research Board All rights reserved. First edition 1950 Third edition 1985 Printed in the United States of America First printing, August 1985 Second printing, December 1985 Third printing, June 1987 Fourth printing, June 1993 Fifth printing, October 1994 Sixth printing, April 1998
Library of Congress Cataloging in Publication Data National Research Council. Transportation Research Board. Highway capacity manual. 3rd ed. ©1998. p. cm. — (Special report ; 209) Includes index. ISBN 0-309-06450-3 1. Highway capacity—Handbooks, manuals, etc. I. Series: Special report (National Research Council (U.S.) Transportation Research Board); 209. HE336.H48H54 1998 ISSN 0360-859X 98-5965 388.3’ 14—dc21 CIP
The Transportation Research Board is a unit of the National Research Council, which serves the National Academy of Sciences and the National Academy of Engineering. The Board’s mission is to promote innovation and progress in transportation by stimulating and conducting research, facilitating the dissemination of information, and encouraging the implementation of research results. The Board’s varied activities annually draw on approximately 4,000 engineers, scientists, and other transportation researchers and practitioners from the public and private sectors and academia, all of whom contribute their expertise in the public interest. The program is supported by state transportation departments, federal agencies including the component administrations of the U.S. Department of Transportation, and other organizations and individuals interested in the development of transportation. The National Research Council was organized by the National Academy of Sciences in 1916 to associate the broad community of science and technology with the Academy’s purpose of furthering knowledge and advising the federal government. Functioning in accordance with general policies determined by the Academy, the Council has become the principal operating agency of both the National Academy of Sciences and the National Academy of Engineering in providing services to the government, the public, and the scientific and engineering communities. The Council is administered jointly by both the Academies and the Institute of Medicine.
Contents
Foreword................................................................................................................................................. Contributors and Acknowledgments .............................................................................................. Figures, Photographs, and Tables.....................................................................................................
v vii xv
PART I PRINCIPLES OF CAPACITY Chapter 1
Introduction, Concepts, and Applications.............................................................................
1-1
Chapter 2
Traffic Characteristics ...........................................................................................................
2-1
Chapter 3
Basic Freeway Sections.........................................................................................................
3-1
Chapter 4
Weaving Areas ......................................................................................................................
4-1
Chapter 5
Ramps and Ramp Junctions ..................................................................................................
5-1
Chapter 6
Freeway Systems ...................................................................................................................
6-1
PART II FREEWAYS
PART III RURAL AND SUBURBAN HIGHWAYS Chapter 7
Multilane Rural and Suburban Highways ............................................................................
7-1
Chapter 8
Two-Lane Highways .............................................................................................................
8-1
Chapter 9
Signalized Intersections.........................................................................................................
9-1
Chapter 10
Unsignalized Intersections..................................................................................................... 10-1
Chapter 11
Arterial Streets....................................................................................................................... 11-1
Chapter 12
Transit Capacity..................................................................................................................... 12-1
Chapter 13
Pedestrians ............................................................................................................................. 13-1
Chapter 14
Bicycles.................................................................................................................................. 14-1
PART IV URBAN STREETS
APPENDIX A Glossary ................................................................................................................................. A-1 Symbols ................................................................................................................................. A-5 INDEX
iii
Updated December 1997
Foreword The Highway Capacity Manual (HCM) continues to provide a resource for technical information that is used by transportation planners, designers, and operators. The materials contained in the HCM represent a collection of state-of-the-art techniques for estimating capacity and determining level of service for many transportation facilities and modes. These techniques have been developed and enhanced through funded research projects and through review of the research results by the Committee on Highway Capacity and Quality of Service. The contents of this edition of the HCM represent the consensus view of the committee as to the best available techniques for determining capacity. However, this manual does not establish a legal standard for highway design or construction. Throughout the manual, sound engineering judgment supplemented by field observations is encouraged. Throughout previous editions of the manual, many transportation professionals have contributed to the development of highway capacity analysis techniques. These efforts were documented in the 1994 update to the manual and are repeated here to recognize the accomplishments of these professionals. The first Highway Capacity Manual was published in 1950 as a joint venture between the Highway Research Board’s Committee on Highway Capacity and the Bureau of Public Roads. O. K. Normann served as committee chairman and William Walker as secretary. This edition, the first international document on the broad subject of capacity, provided definitions of key terms, a compilation of maximum observed flows, and the initial fundamentals of capacity. Analytical procedures were included for uninterrupted-flow facilities, signalized intersections, weaving sections, and ramps. The second edition of the manual was published in 1965 by the Highway Research Board and authored by the Committee on Highway Capacity. It was dedicated to O. K. Normann, who had provided leadership to the committee from its inception in 1944 until his death in 1964. Carl C. Saal had become committee chairman and Arthur A. Carter, Jr., continued to serve as secretary. During the final stages of the preparation of the manual, a five-person task group was assigned by the Bureau of Public Roads to work full time on the project. The 1965 manual was a significant extension of the 1950 edition and is most noted for its introduction of the level-of-service concept. The third edition of the manual was published in 1985 by the Transportation Research Board and authored by the Committee on Highway Capacity and Quality of Service chaired by Carlton C. Robinson, with Charles W. Dale as secretary. Credit is also due Robert C. Blumenthal and James H. Kell, who served as committee chairmen and provided leadership between the publication of the 1965 and the 1985 editions. Again, the breadth and depth of the previous manuals were extended. The 1985 edition is perhaps most noted for the extension into facilities other than highways, refinements to the level-of-service concept, and the accompanying computer software.
When the 1994 update was published by the Transportation Research Board, it provided new analytical procedures in response to the increased levels of research and professional interest in this topic. The committee was chaired by Adolf D. May, with Wayne Kittelson as secretary. This update contained revisions to portions of 8 of the 14 chapters to include current speed-flow relationships, revised capacity values, and new analytical procedures. In addition, greater emphasis was placed on describing the principles of capacity and on defining the capacity and level-of-service terms. v
Updated December 1997
vi
This 1997 update of the HCM has been published to make the most current procedures available to the user community in a timely fashion. It is recognized that the relatively short time between updates of the manual causes some difficulty in users’ ability to incorporate the new procedures into their practice; however, the committee has chosen to publish this update to make the results of a significant amount of new research available in a timely manner. The current update includes extensive revisions to Chapters 3, 9, 10, and 11. In addition, Chapters 1, 4, 5, 6, and 7 have been modified to make them consistent with other revised chapters. Chapter 3, Basic Freeway Sections, includes a revised procedure for determining capacity on the basis of density. Capacity values under ideal flow conditions now vary by free-flow speed. This chapter also provides a ‘‘preview’’ of the proposed format for the HCM 2000 that is currently being developed. Your comments on this format are requested. Chapter 9, Signalized Intersections, includes findings from recent research on actuated traffic signals. The delay equation is modified to account for signal coordination, oversaturation, variable length analysis periods, and the presence of initial queues at the beginning of an analysis period. The level-of-service measure has been changed from average stopped delay to total (control) delay. Adjustments have been made to the permitted left-turn movement model and to the left-turn equivalency table. Chapter 10, Unsignalized Intersections, has been completely revised to incorporate the results of a nationwide research project in the United States at two-way and four-way stop-controlled intersections. Modified delay formulas and new level-of-service thresholds are provided for both two-way and four-way stop-controlled intersections. In addition, the impact on capacity at a two-way stop-controlled intersection due to the presence of an upstream traffic signal can be determined. Procedures are provided to account for flared approaches, upstream signals, pedestrian crossings, and two-stage gap acceptance (where vehicles seek refuge in a median before crossing a second stream of traffic). Chapter 11, Arterial Streets, incorporates the changes to the Signalized Intersections chapter that affect Chapter 11. In addition, a new arterial classification is established for high-speed facilities. The delay equation is modified to take into account the effect of upstream signalized intersections on platoon arrivals. Despite the extensive improvements incorporated into the 1997 update of the HCM, plans are under way for a complete revision of the HCM in 2000. The content, format, and delivery system for HCM 2000 will be made more accessible to users in both paper and multimedia (CD-ROM) formats. Ongoing research in freeway weaving, freeway systems, two-lane highways, transit capacity, bicycle and pedestrian capacity, interchange ramp terminals, and enhanced procedures for transportation planning will be included in HCM 2000. This 1997 update and the upcoming HCM 2000 will represent a major milestone in the ongoing efforts of researchers and practitioners to provide a practical guide for capacity analysis techniques for all who use them. The efforts of the funding agencies, research institutions, the academic community, and users from the public and private sectors are gratefully acknowledged. The Highway Capacity and Quality of Service Committee invites your comments and suggestions regarding this 1997 update as we enhance our ability to design, operate, and plan for improved transportation facilities. For the Committee on Highway Capacity and Quality of Service John D. Zegeer Chairman
Updated December 1997
Contributors and Acknowledgments This report is the result of the coordinated efforts of many individuals, research organizations, and government agencies. Although responsibility for the content of the Highway Capacity Manual lies with the Committee on Highway Capacity and Quality of Service, its preparation was accomplished through the efforts of the following groups and individuals:
TRB COMMITTEE ON HIGHWAY CAPACITY AND QUALITY OF SERVICE Committee Members as of February 1, 1985 Carlton C. Robinson, Chairman, Highway Users Federation for Safety and Mobility Charles W. Dale, Secretary, Federal Highway Administration Donald S. Berry, Evanston, Illinois Robert C. Blumenthal, Blumenthal Associates (Chairman, 1971–1977) James B. Borden, California Department of Transportation Fred W. Bowser, Pennsylvania Department of Transportation V. F. Hurdle, University of Toronto, Canada James H. Kell, JHK & Associates (Chairman, 1977–1983) Frank J. Koepke, Northwestern University Jerry Kraft, New Jersey Turnpike Authority Walter H. Kraft, Edwards & Kelcey, Inc. Joel P. Leisch, Jack E. Leisch & Associates Adolf D. May, Jr., University of California William R. McShane, Polytechnic Institute of New York Carroll J. Messer, Texas A&M University System Guido Radelat, Federal Highway Administration Hubert M. Shaver, Jr., Virginia Department of Highways and Transportation Alexander Werner, Alberta Transportation Department, Canada Robert H. Wortman, University of Arizona David K. Witheford, Transportation Research Board Staff Representative
Other Committee Members During 1985 Manual Preparation Period Brian L. Allen, McMaster University George W. Black, Jr., Gwinnett County, Georgia Arthur A. Carter, Jr., Federal Highway Administration Joseph W. Hess, Bethesda, Maryland Jack A. Hutter, Jack E. Leisch & Associates Thomas D. Jordan, Skycomp Data Corporation Paul D. Kiser, City of Salt Lake Herbert S. Levinson, University of Connecticut Louis E. Lipp, Colorado Department of Highways Edward B. Lieberman, KLD Associates, Inc. Louis J. Pignataro, Polytechnic Institute of New York Frederick D. Rooney, California Department of Transportation Stephen E. Rowe, Los Angeles Department of Transportation vii
Updated December 1997
viii John L. Schlaefli, TRACOR, Inc. Gerald W. Skiles, Cambria, California Jeffrey M. Zupan, New Jersey Transit Committee Members as of December 1, 1994 Adolf D. May, Jr., Chairman, University of California Wayne K. Kittelson, Secretary, Kittelson & Associates, Inc. Rahmi Akcelik, Australian Road Research Board Ltd. James A. Bonneson, University of Nebraska Werner Brilon, Ruhr University, Germany Kenneth G. Courage, University of Florida Rafael E. DeArazoza, Florida Department of Transportation Richard G. Dowling, Dowling Associates Daniel B. Fambro, Texas A&M University System Ronald K. Giguere, Federal Highway Administration Mariano Gullo´n Lo¨w, Centro de Estudios de Carreteras, Madrid, Spain Fred L. Hall, McMaster University, Canada Douglas W. Harwood, Midwest Research Institute Michael D. Kyte, University of Idaho Joel P. Leisch, Glenview, Illinois Douglas S. McLeod, Florida Department of Transportation John F. Morrall, University of Calgary, Canada Barbara K. Ostrom, Berkeley, California Ronald C. Pfefer, Northwestern University James L. Powell, DeLeuw, Cather & Co. William R. Reilly, Catalina Engineering Roger P. Roess, Polytechnic University Nagui M. Rouphail, North Carolina State University Ronald C. Sonntag, Wisconsin Department of Transportation Alex Sorton, Northwestern University Dennis W. Strong, Strong Concepts Stan Teply, University of Alberta, Canada Pierre Yves Texier, INRETS, France Rod J. Troutbeck, Queensland University of Technology, Australia Thomas Urbanik II, Texas A&M University System John D. Zegeer, Barton-Aschman Associates, Inc. Richard Cunard, Transportation Research Board Staff Representative Dan Rosen, NCHRP Staff Representative Committee Members as of December 31, 1997 John D. Zegeer, Chairman, Kittelson & Associates, Inc. Richard G. Dowling, Secretary, Dowling Associates, Inc. James A. Bonneson, Texas A&M University System Werner Brilon, Ruhr University of Bochum, Germany Robert W. Bryson, City of Milwaukee Kenneth G. Courage, University of Florida Alan R. Danaher, Kittelson & Associates, Inc. Rafael E. DeArazoza, Florida Department of Transportation Lily Elefteriadou, Pennsylvania State University Daniel B. Fambro, Texas A&M University System Ronald K. Giguere, Federal Highway Administration Albert L. Grover, Albert Grover & Associates, Inc. Mariano Gullo´n Lo¨w, Centro de Estudios de Carreteras, Madrid, Spain Fred L. Hall, McMaster University, Canada Douglas W. Harwood, Midwest Research Institute Chris Hoban, The World Bank Wayne K. Kittelson, Kittelson & Associates, Inc. Michael D. Kyte, University of Idaho Adolf D. May, Jr., University of California Douglas S. McLeod, Florida Department of Transportation Barbara K. Ostrom, EBA Engineering, Inc. Updated December 1997
ix James L. Powell, DeLeuw, Cather & Company Nagui M. Rouphail, North Carolina State University Erik O. Ruehr, Valley Research and Planning Associates Rikke Rysgaard, Danish Road Directorate James M. Schoen, Catalina Engineering, Inc. Alex Sorton, Northwestern University Dennis W. Strong, Strong Concepts Stan Teply, University of Alberta, Canada Rod J. Troutbeck, Queensland University of Technology, Australia Richard Cunard, Transportation Research Board Staff Representative Ray Derr, NCHRP Staff Representative The work of the following individuals in subcommittees of the Committee on Highway Capacity and Quality of Service contributed immeasurably to the effectiveness of the committee in accomplishing its goals: Subcommittee Members as of February 1, 1985 Charles M. Abrams, JHK & Associates Frank E. Barker, Chicago Transit Authority Seth S. Barton, New Jersey Department of Transportation Richard Bowman, Beiswenger Hoch & Associates, Inc. John P. DiRenzo, Peat, Marwick, Mitchell & Co. Paul Eng-Wong, Snavely King & Associates Thomas C. Ferrara, California State University A. Reed Gibby, California State University William Haussler, Edwards & Kelcey, Inc. Joseph W. Hess, Bethesda, Maryland Paul P. Jovanis, Northwestern University Joseph M. Kaplan, National Safety Council (Los Angeles Chapter) Wayne K. Kittelson, CH2M Hill Herbert S. Levinson, University of Connecticut C. John MacGowan, National Highway Traffic Safety Administration Ralph J. Meller, St. Louis, Missouri David R. Merritt, Federal Highway Administration Panos G. Michalopoulos, University of Minnesota Timothy R. Neuman, Jack E. Leisch & Associates Martin R. Parker, Jr., M.R. Parker & Associates, Inc. Ronald C. Pfefer, Northwestern University William R. Reilly, JHK & Associates Roger P. Roess, Polytechnic Institute of New York Richard Rogers, California Department of Transportation Frederick D. Rooney, California Department of Transportation Gilbert T. Satterly, Jr., Purdue University Frederick S. Scholz, Roger Creighton Associates, Inc. Steven R. Shapiro, Goodell-Grivas, Inc. Joseph H. Sinnott, System Design Concepts, Inc. Alex Sorton, Northwestern University Frank C. Tecca, Municipality of Anchorage, Alaska Linda Turnquist, California Department of Transportation Kenneth H. Voigt, Southeastern Wisconsin Regional Planning Commission Mark R. Virkler, University of Missouri John D. Zegeer, Barton-Aschman Associates, Inc. Subcommittee Members as of December 1, 1994 Rahmi Akcelik, Australian Road Research Board Ltd. Donald S. Berry, Evanston, Illinois James A. Bonneson, University of Nebraska Ulrich Brannolte, PTV GMBH, Germany Werner Brilon, Ruhr University, Germany Robert W. Bryson, City of Milwaukee Joonho Byun, Federal Highway Administration Michael J. Cassidy, University of California Updated December 1997
x Kenneth G. Courage, University of Florida Rafael E. DeArazoza, Florida Department of Transportation Richard G. Dowling, Dowling Associates Lily Elefteriadou, Germen Associates Daniel B. Fambro, Texas A&M University System Joseph Fazio, Chicago, Illinois Kay Fitzpatrick, Texas A&M University System A. Reed Gibby, California State University Ronald K. Giguere, Federal Highway Administration Glenn M. Grigg, City of Cupertino, California Albert L. Grover, Albert Grover & Associates Mariano Gullo´n Lo¨w, Centro de Estudios de Carreteras, Madrid, Spain Fred L. Hall, McMaster University, Canada Wayne E. Haussler, Edwards & Kelcey, Inc. VanOlin F. Hurdle, University of Toronto, Canada Dane Ismart, Federal Highway Administration Paul P. Jovanis, University of California R. Ian Kingham, Victoria, Canada Wayne K. Kittelson, Kittelson & Associates, Inc. Frank J. Koepke, S/K Transportation Consultants, Inc. Raymond A. Krammes, Texas A&M University System Michael D. Kyte, University of Idaho B. Kent Lall, Portland State University Jim C. Lee, Lee Engineering Joel P. Leisch, Glenview, Illinois Herbert S. Levinson, New Haven, Connecticut Feng-Bor Lin, Clarkson University George F. List, Rensselaer Polytechnic University Charles W. Manning, Roger Creighton Associates, Inc. Joseph F. Marek, Clackamas County, Oregon William R. McGrath, Fort Myers, Florida Douglas S. McLeod, Florida Department of Transportation William R. McShane, Polytechnic University David R. Merritt, Federal Highway Administration Carroll J. Messer, Texas A&M University System Leonard Newman, Emeryville, California Michael P. O’Rourke, Eng-Wong Taub and Associates Barbara K. Ostrom, Berkeley, California Ronald C. Pfefer, Northwestern University James L. Powell, DeLeuw, Cather & Co. William A. Prosser, Federal Highway Administration William R. Reilly, Catalina Engineering Roger P. Roess, Polytechnic University Frederick Rooney, California Department of Transportation Nagui M. Rouphail, North Carolina State University Erik O. Ruehr, JHK & Associates James M. Schoen, Catalina Engineering Alex Skabardonis, University of California Ronald C. Sonntag, Wisconsin Department of Transportation Alex Sorton, Northwestern University Dennis W. Strong, Strong Concepts Stan Teply, University of Alberta, Canada Marian Tracz, Cracow Technical University, Poland Rod J. Troutbeck, Queensland University of Technology, Australia Thomas Urbanik II, Texas A&M University System Mark A. Vandehey, Kittelson & Associates, Inc. R. A. Vincent, Transport Research Laboratory, Great Britain Mark R. Virkler, University of Missouri-Columbia Kenneth H. Voigt, HNTB Corporation Robert H. Wortman, University of Arizona John D. Zegeer, Barton-Aschman Associates, Inc. Updated December 1997
xi Subcommittee Members as of December 31, 1997 Subcommittee on General Concepts and Definitions Barbara K. Ostrom, Chairwoman, EBA Engineering, Inc. Douglas S. McLeod, Florida Department of Transportation Stan Teply, University of Alberta, Canada Thomas Urbanik II, Texas Transportation Institute Subcommittee on Freeways and Multilane Highways Adolf D. May, Jr., Chairman, University of California Michael J. Cassidy, University of California Michael Church, California Department of Transportation Lily Elefteriadou, Pennsylvania State University Joseph Fazio, Illinois Institute of Technology Fred L. Hall, McMaster University, Canada Abdul-Rahman Hamad, H.W. Lochner, Inc. Joel P. Leisch, Private Consultant Barbara K. Ostrom, EBA Engineering, Inc. Ronald C. Pfefer, Northwestern University Traffic Institute William R. Reilly, Catalina Engineering, Inc. Bruce W. Robinson, Kittelson & Associates, Inc. Roger P. Roess, Polytechnic University Fred Rooney, California Department of Transportation Nagui M. Rouphail, North Carolina State University Rikke Rysgaard, Danish Road Directorate James M. Schoen, Catalina Engineering, Inc. Ronald C. Sonntag, Marquette University Andrzej P. Tarko, Purdue University Michelle Thomas, Federal Highway Administration Jose Ulerio, Polytechnic University Thomas Urbanik II, Texas Transportation Institute Subcommittee on Interchange Ramp Terminals James L. Powell, Chairman, DeLeuw, Cather & Company James A. Bonneson, Texas A&M University System Robert W. Bryson, City of Milwaukee Michael Church, California Department of Transportation F. Thomas Creasey, Wilbur Smith & Associates Janice Daniel, Georgia Institute of Technology Michael F. Holling, Transcore B. Kent Lall, Portland State University Joel P. Leisch, Private Consultant Joel K. Marcuson, Sverdrup Civil, Inc. Scott J. Parker, Edwards and Kelcey, Inc. Frederick Rooney, California Department of Transportation Subcommittee on Signalized Intersections Dennis W. Strong, Chairman, Strong Concepts Rahmi Akcelik, ARRB Transport Research, Ltd. Rahim F. Benekohal, University of Illinois Donald S. Berry, Private Consultant Robert W. Bryson, City of Milwaukee Kenneth G. Courage, University of Florida Glenn M. Grigg, Private Consultant Albert L. Grover, Albert Grover & Associates, Inc. David J. P. Hook, Hook Engineering, Inc. John D. Leonard II, Georgia Institute of Technology Feng-Bor Lin, Clarkson College Pawan Maini, University of Colorado at Denver Carroll J. Messer, Texas Transportation Institute Elena Prassas, Polytechnic University Updated December 1997
xii Bruce W. Robinson, Kittelson & Associates, Inc. Roger P. Roess, Polytechnic University Nagui M. Rouphail, North Carolina State University Robert H. Wortman, University of Arizona Subcommittee on Unsignalized Intersections Michael D. Kyte, Chairman, University of Idaho Werner Brilon, Ruhr University of Bochum, Germany Robert W. Bryson, City of Milwaukee Joonho Byun, Federal Highway Administration Mitzi M. Dobersek, Wisconsin Department of Transportation Aimee Flannery, Pennsylvania State University Glenn M. Grigg, Private Consultant Mariano Gullo´n Lo¨w, Centro de Estudios de Carreteras, Madrid, Spain Wayne E. Haussler, Goodkind & O’Dea, Inc. Dane Ismart, Louis Berger & Associates, Inc. R. Ian Kingham, Graeme & Murray Wayne K. Kittelson, Kittelson & Associates, Inc. B. Kent Lall, Portland State University George F. List, Rensselaer Polytechnic Institute Charles Manning, Creighton Manning, Inc. Joseph F. Marek, Clackamas County Department of Transportation Michael P. O’Rourke, Eng-Wong-Taub & Associates, Inc. Erik O. Ruehr, Valley Research and Planning Associates John Sampson, Jeffares & Green, Inc. Zong Zhong Tian, Kittelson & Associates, Inc. Marion Tracz, Cracow Technical University, Poland Rod J. Troutbeck, Queensland University of Technology, Australia Kenneth H. Voigt, HNTB Corporation Andrew Wolfe, Union College Subcommittee on Urban and Suburban Arterials Daniel B. Fambro, Chairman, Texas A&M University System Janice R. Daniel, Georgia Tech University Lily Elefteriadou, Pennsylvania State University Ronald K. Giguere, Federal Highway Administration Joel K. Marcuson, Sverdrup Corporation Douglas S. McLeod, Florida Department of Transportation Alex Sorton, Northwestern University Dennis W. Strong, Strong Concepts Andrzej P. Tarko, Purdue University Mark A. Vandehey, Kittelson & Associates, Inc. Subcommittee on Two-Lane Roads Douglas W. Harwood, Chairman, Midwest Research Institute Jan L. Botha, San Jose State University Albert L. Grover, Albert Grover & Associates, Inc. Mariano Gullo´n Lo¨w, Centro de Estudios de Carreteras, Madrid, Spain Chris Hoban, The World Bank Greg M. Laragan, Idaho Department of Transportation David J. Lovell, University of Maryland, College Park Carroll J. Messer, Texas Transportation Institute John F. Morrall, University of Calgary, Canada William A. Prosser, Federal Highway Administration Guido Radelat, Private Consultant Alex Sorton, Northwestern University Davey Warren, Federal Highway Administration Al Werner, Reid Crowther Consultants, Ltd. Updated December 1997
xiii Subcommittee on Transit Systems Alan R. Danaher, Chairman, Kittelson & Associates, Inc. Tara Bartee, Florida Department of Transportation Howard Benn, Private Consultant William Hoey, Private Consultant Michael D. Kyte, University of Idaho Herbert S. Levinson, Transportation Consultant Pat McLoughlin, Metropolitan Transit Authority, Los Angeles David Miller, Parsons Brinckerhoff Rikke Rysgaard, Danish Road Directorate Kevin St. Jacques, Wilbur Smith & Associates Ken Stanley, Oahu Transit Joe Goodman, Federal Transit Administration Joel Volinski, University of South Florida Subcommittee on Planning Applications Douglas S. McLeod, Chairman, Florida Department of Transportation Jim Altenstadter, PIMA Association of Governments Robert W. Bryson, City of Milwaukee F. Thomas Creasey, Wilbur Smith & Associates Richard G. Dowling, Dowling Associates, Inc. Kurt Eichin, Florida Department of Transportation Abdul-Rahman Hamad, H.W. Lochner, Inc. David Hook, Lee Engineering, Inc. John Karachepone, Kittelson & Associates, Inc. Wayne K. Kittelson, Kittelson & Associates, Inc. William R. McShane, Polytechnic University Barbara K. Ostrom, EBA Engineering, Inc. Erik O. Ruehr, Valley Research and Planning Associates Terrel Shaw, Reynolds, Smith & Hills, Inc. Stan Teply, University of Alberta, Canada
Subcommittee on Pedestrians and Bicycles Alex Sorton, Chairman, Northwestern University Patrick Allen, California Department of Transportation Hein Botma, Delft University of Technology, The Netherlands W. Jeffrey Davis, The Citadel Joseph Fazio, Illinois Institute of Technology Chris Hoban, The World Bank Bruce Landis, Sprinkle Consulting Engineering, Inc. John LaPlante, TY Lin Bascor Joseph S. Milazzo, North Carolina State University John F. Morrall, University of Calgary, Canada Virginia Sisiopiku, Michigan State University Mark R. Virkler, University of Missouri-Columbia Thomas Walsh, City of Madison, Wisconsin Subcommittee on User Liaison and Interpretations Wayne K. Kittelson, Chairman, Kittelson & Associates, Inc. Rafael E. DeArazoza, Florida Department of Transportation Robert S. Foyle, North Carolina State University Ronald K. Giguere, Federal Highway Administration Joel P. Leisch, Private Consultant John D. Leonard II, Georgia Institute of Technology Shahram Malek, Viggen Corporation, Inc. William A. Prosser, Federal Highway Administration Dennis W. Strong, Strong Concepts Rod J. Troutbeck, Queensland University of Technology, Australia Charles E. Wallace, University of Florida Updated December 1997
xiv Subcommittee on Research Coordination Fred L. Hall, Chairman, McMaster University, Canada Jim Clark, Federal Highway Administration Alan R. Danaher, Kittelson & Associates, Inc. Richard G. Dowling, Dowling Associates, Inc. Douglas W. Harwood, Midwest Research Institute John D. Leonard II, Georgia Institute of Technology Pawan Maini, University of Colorado at Denver Larry F. Sutherland, Ohio Department of Transportation Last to be acknowledged among the volunteer contributors to this edition are the unnamed users of draft materials and TRB Circulars published and distributed during the period of the manual’s development. Their interest and support were a constant stimulus to both committee and research activities. Perhaps last in the process, but not least among those who made this document possible, are staff members of the Transportation Research Board. Naomi Kassabian, Norman Solomon, and David Stearman, Editors, worked with the researchers to produce the final manuscript. Other design and production supervision was provided by Nancy A. Ackerman, Director of Reports and Editorial Services. Ray Derr, NCHRP Projects Engineer, and Richard Cunard, Engineer of Traffic and Operations, provided indispensable staff support to the committee and its subcommittees.
Updated December 1997
FIGURES 2–1 2–2 2–3 2–4 2–5 2–6 2–7 2–8(a) 2–8(b) 2–9 2–10 2–11 2–12 2–13 2–14 2–15 2–16 2–17 2–18 2–19 2–20 2–21 2–22 2–23 2–24 2–25 2–26 3-1 3-2 3-3 3-4 3-5 I.3-1 I.3-2 4–1 4–2 4–3 4–4 4–5 4–6 4–7 4–8 4–9 4–10 4–11 4–12 4–13 5–1 5–2 5–3 5–4
Page Typical relationship between time mean and space mean speed...................................................... Generalized relationships among speed, density, and rate of flow on uninterrupted flow facilities ........................................................................................................................................... Conditions at traffic interruption in an approach lane of a signalized intersection......................... Concept of saturation flow rate and lost time ................................................................................... Motor vehicle registrations................................................................................................................. Rural Interstate travel by vehicle type............................................................................................... Annual vehicle miles of travel ........................................................................................................... Examples of monthly traffic volume variations showing monthly variations in traffic for a freeway in Minnesota............................................................................................................................ Examples of monthly traffic volume variations showing relative traffic volume trends by route type on rural roads in Lake County, Illinois ................................................................................. Examples of daily traffic variation by type of route......................................................................... Daily variation in traffic by vehicle type (I-494, 4-lanes, in Minneapolis-St. Paul) ....................... Examples of hourly traffic variations for rural routes in New York State ...................................... Repeatability of hourly traffic variations for four 2-lane arterials in Toronto, Ontario, Canada.... Ranked hourly volumes on Minnesota highways.............................................................................. Ranked hourly volume distribution showing indistinct knee for Kentucky location in 1977......... Relationship between short-term and hourly flows........................................................................... Distribution of power-to-mass ratios of passenger cars .................................................................... On-highway passenger car characteristics ......................................................................................... Nationwide speed trends through 1975 and 1993 ............................................................................. Speed variation by hour of day for I-35W in Minneapolis, weekdays, in relation to volume variations ......................................................................................................................................... Speed variation by hour of day for I-35W, Minneapolis, Saturdays, in relation to volume variations ......................................................................................................................................... Observed speed-flow relationship on a San Diego freeway in 6-min sampling intervals (Interstate Highway 8, 1987)................................................................................................................... Observed speed-flow relationship on an Ontario freeway in 5-min sampling intervals (Queen Elizabeth Way near Toronto, 1987)............................................................................................... Observed speed-flow relationship at Caldecott Tunnel in 15-min sampling intervals (California State Highway 24, 1990)................................................................................................................ Speed-flow relationship for two-lane rural highways ....................................................................... Time headway distribution for Long Island Expressway.................................................................. Comparison of various research results on queue discharge headways ........................................... Example of basic freeway section...................................................................................................... Speed-flow relationships..................................................................................................................... Queue discharge and congested flow................................................................................................. LOS criteria......................................................................................................................................... Worksheet for analysis of basic freeway sections............................................................................. Sample solution for composite grade................................................................................................. Performance curves for standard trucks (200 lb/hp) ......................................................................... Formation of a weaving section......................................................................................................... Measuring length of a weaving section ............................................................................................. Type A weaving areas ........................................................................................................................ Type B weaving areas ........................................................................................................................ Type C weaving areas ........................................................................................................................ Construction and use of weaving diagrams....................................................................................... Weaving flows in a multiple weave formed by a single merge followed by two diverges............ Weaving flows in a multiple weave formed by two merge points followed by a single diverge .. Weaving area for calculation 1 .......................................................................................................... Weaving area and flows for calculation 2......................................................................................... Weaving area for calculation 3 .......................................................................................................... Weaving area for calculation 4 .......................................................................................................... Weaving area for calculation 5 .......................................................................................................... On- and off-ramp influence areas ...................................................................................................... Critical ramp junction values ............................................................................................................. Models for predicting V12 for on-ramps............................................................................................. Models for predicting V12 for off-ramps ............................................................................................ xv
2-4 2-6 2-7 2-8 2-11 2-14 2-14 2-17 2-18 2-19 2-19 2-20 2-20 2-21 2-21 2-22 2-24 2-24 2-25 2-26 2-27 2-29 2-29 2-29 2-30 2-31 2-31 3-2 3-4 3-5 3-10 3-14 3-37 3-38 4-2 4-2 4-3 4-3 4-4 4-10 4-11 4-12 4-12 4-13 4-14 4-16 4-18 5-2 5-3 5-5 5-6
Updated December 1997
xvi FIGURES 5–5 5–6 5–7 5–8 5–9 5–10 5–11 5–12(a) 5–12(b) 5–13 5–14(a) 5–14(b) 5–15 5–16 5–17 5–18 5–19 6–1 6–2 6–3 6–4 6–5 6–6 6–7 6–8 6–9 6–10 6–11 6–12 6–13 6–14 7–1 7–2 7–3 7–4 7–5 7–6 7–7 7–8 7–9 7–10 7–11 7–12 7–13 8–1 8–2 8–3 8–4 8–5(a) 8–5(b) 8–6 8–7 8–8 8–9 9-1 9-2 9-3 9-4
Worksheet for the analysis of ramp-freeway terminals .................................................................... Typical two-lane on-ramp .................................................................................................................. Common geometries for two-lane off-ramps..................................................................................... Major merge areas .............................................................................................................................. Major diverge areas ............................................................................................................................ Worksheet for Calculation 1 .............................................................................................................. Freeway section for Calculation 2 ..................................................................................................... Worksheet for Calculation 2 (first ramp) .......................................................................................... Worksheet for Calculation 2 (second ramp)...................................................................................... Freeway section for Calculation 3 ..................................................................................................... Worksheet for Calculation 3 (first ramp) .......................................................................................... Worksheet for Calculation 3 (second ramp)...................................................................................... Worksheet for Calculation 4 .............................................................................................................. Freeway section for Calculation 5 ..................................................................................................... Equivalent four-lane segment for Calculation 5................................................................................ Worksheet for Calculation 5 .............................................................................................................. Worksheet for Calculation 6 .............................................................................................................. Sample design problem ...................................................................................................................... Likely design for sample problem ..................................................................................................... Consideration of multiple weave........................................................................................................ Consideration of multiple weave........................................................................................................ Graphic representation of overall level of service ............................................................................ Effects of breakdown illustrated ........................................................................................................ Illustration of ramp-metering need..................................................................................................... Plot of cumulative ramp demand and output .................................................................................... Potential for hidden bottlenecks......................................................................................................... Phases of a traffic incident................................................................................................................. Range of observed work zone capacities—work crew at site .......................................................... Cumulative distribution of observed work-zone capacities .............................................................. Sample calculation—queue analysis for a work zone....................................................................... Example for analysis of HOV lane impact........................................................................................ Speed-flow relationships on multilane highways .............................................................................. Density-flow relationships on multilane highways............................................................................ Speed-flow curves with LOS criteria................................................................................................. Example of graphic solution using speed-flow curves...................................................................... Worksheet for operational and design analysis ................................................................................. Worksheet for planning analysis ........................................................................................................ Illustration of solution to Calculation 1—general segment .............................................................. Illustration of solution to Calculation 1—grade segment ................................................................. Illustration of solution to Calculation 2—level segment .................................................................. Illustration of solution to Calculation 2—grade segment ................................................................. Illustration of solution to Calculation 3............................................................................................. Illustration of solution to Calculation 4............................................................................................. Illustration of solution to Calculation 5............................................................................................. Speed-flow and percent time delay-flow relationships for two-lane rural highways ...................... Speed reduction curve for a 200-lb/hp truck..................................................................................... Speed reduction curve for a 300-lb/hp truck..................................................................................... Worksheet for operational analysis of general terrain segments ...................................................... Worksheet for operational analysis of specific grades on two-lane highways (page 1).................. Worksheet for operational analysis of specific grades on two-lane highways (page 2).................. Use of third lane for passing lanes .................................................................................................... Worksheet summarizing solution to calculation 1 ............................................................................ Worksheet summarizing solution to calculation 2 ............................................................................ Worksheet for calculation 4 (pages 1 and 2) .................................................................................... Relationship among actual green, lost-time elements, extension of effective green, and effective green................................................................................................................................. Protected-plus-permitted signal phasing ............................................................................................ Operational analysis procedure .......................................................................................................... Input data needs for each analysis lane group ..................................................................................
Updated December 1997
Page 5-10 5-11 5-11 5-13 5-13 5-15 5-16 5-17 5-18 5-19 5-20 5-21 5-22 5-23 5-24 5-25 5-26 6-3 6-4 6-4 6-5 6-6 6-7 6-8 6-8 6-9 6-9 6-10 6-11 6-13 6-15 7-4 7-5 7-8 7-15 7-17 7-20 7-22 7-23 7-25 7-26 7-27 7-28 7-29 8-4 8-13 8-13 8-15 8-16 8-16 8-19 8-22 8-22 8-25 9-4 9-5 9-9 9-10
xvii FIGURES 9-5 9-6 9-7 9-8(a) 9-8(b) 9-8(c) 9-9 9-10 9-11 9-12 9-13 9-14 9-15 9-16 9-17 9-18 9-19 9-20 9-21 9-22 9-23 9-24 9-25 9-26 9-27 9-28 9-29 9-30(a) 9-30(b) 9-31 9-32 9-33 9-34 9-35 9-36 9-37 9-38 9-39 9-40 9-41 9-42 9-43 9-44 9-45 9-46 9-47 9-48 9-49 9-50 9-51
Typical lane groups for analysis ........................................................................................................ Permitted left turn............................................................................................................................... Through-car equivalents, ELI, for permitted left turns (1 ) ................................................................ Green time adjustments for protected-plus-permitted phasing: standard case and Case 2.............. Green time adjustments for protected-plus-permitted phasing: Cases 3 and 4 ................................ Green time adjustments for protected-plus-permitted phasing: Case 5 ............................................ Critical lane group determination: leading and lagging green phase plan with exclusive left-turn lanes................................................................................................................................................. Critical lane group determination: leading and lagging green phase plan with addition of permitted left turn in Phase 2B ................................................................................................................ Critical lane group determination: complex multiphase signal......................................................... Queue accumulation polygons............................................................................................................ Worksheet information flow............................................................................................................... Input Module Worksheet .................................................................................................................... Volume Adjustment Module Worksheet............................................................................................ Saturation Flow Rate Module Worksheet.......................................................................................... Supplemental Worksheet for Permitted Left Turns: Multilane Approach........................................ Supplemental Worksheet for Permitted Left Turns: Single-Lane Approach.................................... Capacity Analysis Module Worksheet............................................................................................... LOS Module Worksheet..................................................................................................................... Supplemental Uniform Delay Worksheet for Left Turns from Exclusive Lanes with Primary and Secondary Phases..................................................................................................................... Planning Method Input Worksheet .................................................................................................... Planning Method Lane Volume Worksheet....................................................................................... Planning Method Signal Operations Worksheet................................................................................ Planning method worksheet relationships.......................................................................................... Alternative computations using operational analysis ........................................................................ Input Module Worksheet for Calculation 1....................................................................................... Volume Adjustment Module Worksheet for Calculation 1 .............................................................. Saturation Flow Rate Module Worksheet for Calculation 1............................................................. Supplemental left-turn worksheet for EB and WB approaches (multilane)..................................... Supplemental left-turn worksheet for NB and SB approaches (single lane).................................... Capacity Analysis Module Worksheet for Calculation 1.................................................................. LOS Module Worksheet for Calculation 1........................................................................................ Saturation Flow Adjustment Module Worksheet with no lane utilization factor for Calculation 1 ................................................................................................................................... LOS Module Worksheet with no lane utilization factor for Calculation 1...................................... LOS Module Worksheet with timing modifications for Calculation 1 ............................................ Input Module Worksheet for Calculation 2....................................................................................... Volume Adjustment Module Worksheet for Calculation 2 .............................................................. Saturation Flow Rate Module Worksheet for Calculation 2............................................................. Lane Volume Worksheet for Calculation 2....................................................................................... Signal Operations Worksheet for Calculation 2 ................................................................................ Supplemental left-turn worksheet for Calculation 2.......................................................................... Capacity Analysis Module Worksheet for Calculation 2.................................................................. LOS Module Worksheet for Calculation 2........................................................................................ Supplemental Uniform Delay Worksheet for Calculation 2 ............................................................. Capacity Analysis Module Worksheet for protected-only phasing for Calculation 2 ..................... LOS Module Worksheet for protected-only phasing for Calculation 2 ........................................... Queue accumulation polygons for protected and protected-plus-permitted phasing for Calculation 2 ................................................................................................................................... Supplemental Worksheet for Permitted Left Turns: permitted-plus-protected (lagging) left-turn phasing for Calculation 2 ............................................................................................................... Capacity Analysis Module Worksheet for permitted-plus-protected (lagging) left-turn phasing for Calculation 2 ............................................................................................................................. Supplemental Uniform Delay Worksheet for permitted-plus-protected (lagging) left-turn phasing for Calculation 2....................................................................................................................... LOS Module Worksheet for permitted-plus-protected (lagging) left-turn phasing for Calculation 2 ...................................................................................................................................
Page 9-13 9-19 9-20 9-23 9-24 9-25 9-25 9-26 9-27 9-31 9-35 9-36 9-39 9-40 9-41 9-42 9-44 9-47 9-49 9-51 9-52 9-53 9-54 9-59 9-61 9-62 9-63 9-64 9-65 9-66 9-67 9-68 9-68 9-69 9-70 9-71 9-71 9-72 9-73 9-74 9-75 9-75 9-76 9-76 9-77 9-77 9-78 9-78 9-79 9-79 Updated December 1997
xviii FIGURES 9-52 9-53 9-54 9-55 9-56 9-57 9-58 9-59 9-60 9-61 9-62 9-63 9-64 9-65 9-66 9-67 9-68 9-69 9-70 9-71 9-72 9-73 9-74 9-75 I.9-1 II.9-1 II.9-2 II.9-3 II.9-4 II.9-5 II.9-6 II.9-7 II.9-8 II.9-9 II.9-10 II.9-11 II.9-12 III.9-1 III.9-2 III.9-3 IV.9-1 VI.9-1 VI.9-2 VI.9-3 VI.9-4 VI.9-5 10-1 10-2 10-3 10-4 10-5 10-6 10-7
Page Queue accumulation polygons for protected and permitted-plus-protected phasing for Calculation 2 ............................................................................................................................................... Input Module Worksheet for Calculation 3....................................................................................... Volume Adjustment Module Worksheet for Calculation 3 .............................................................. Saturation Flow Rate Module Worksheet for Calculation 3............................................................. Supplemental Worksheet for Permitted Left Turns for Calculation 3.............................................. Capacity Analysis Module Worksheet for Calculation 3.................................................................. LOS Module Worksheet for Calculation 3........................................................................................ Supplemental Uniform Delay Worksheet for Calculation 3 ............................................................. LOS Module Worksheet with revised signal timing for Calculation 3............................................ Planning Method Input Worksheet for Calculation 4 ....................................................................... Lane Volume Worksheet for Calculation 4....................................................................................... Signal Operations Worksheet for Calculation 4 ................................................................................ Lane Volume Worksheet for Calculation 4 with geometric modifications...................................... Signal Operations Worksheet for Calculation 4 with geometric modifications............................... LOS Module Worksheet for Calculation 4........................................................................................ Planning Method Input Worksheet for Calculation 5 ....................................................................... Lane Volume Worksheet for Calculation 5....................................................................................... Signal Operations Worksheet for Calculation 5 ................................................................................ Lane Volume Worksheet with additional EB right-turn lane for Calculation 5 .............................. Signal Operations Worksheet with additional EB right-turn lane for Calculation 5 ....................... Lane Volume Worksheet with NB and SB split-phase operation for Calculation 5 ....................... Signal Operations Worksheet with NB and SB split-phase operation for Calculation 5 ................ Lane Volume Worksheet with added NB and SB left-turn lanes for Calculation 5 ....................... Signal Operations Worksheet with added NB and SB left-turn lanes for Calculation 5 ................ Left-turn bay length versus turning volume ...................................................................................... Phase plans for pretimed and traffic-actuated control....................................................................... Dual-ring concurrent phasing scheme with assigned movements .................................................... Worksheet 1: traffic-actuated control input data ............................................................................... Queue accumulation polygon illustrating two methods of green time computation........................ Convergence of green time computation by elimination of green time deficiency......................... Queue accumulation polygon for permitted left turn from exclusive lane ...................................... Queue accumulation polygon for permitted left turn from shared lane ........................................... Queue accumulation polygon for protected-plus-permitted left-turn phasing with exclusive leftturn lane .......................................................................................................................................... Queue accumulation polygon for permitted-plus-protected left-turn phasing with exclusive leftturn lane .......................................................................................................................................... Worksheet 2: traffic-actuated timing computations........................................................................... Traffic-actuated control data for multiphase example....................................................................... LOS results for multiphase example.................................................................................................. Field intersection control delay worksheet ........................................................................................ Sample application of intersection control delay worksheet............................................................. Sample application with residual queue at end ................................................................................. Field Saturation Flow Rate Study Worksheet ................................................................................... Case III: supplemental delay with initial oversaturation demand clearing in T. [Supplemental delay per vehicle (d3) in seconds = 1,800Qbt/cT.]............................................................................. Case IV: supplemental delay with initial oversaturation demand decreasing in T. [Supplemental delay per vehicle (d3) in seconds = 3,600Qb/c − 1,800T[1 − Min(1, X).].................................... Case V: supplemental delay with initial oversaturation demand increasing in T. [Supplemental delay per vehicle (d3) in seconds = 3,600Qb/c.] ............................................................................ Demand profile for multiple-period analysis (15-min periods) ........................................................ Delay model components for multiple-period analysis..................................................................... Traffic streams at TWSC intersection: (a) four-leg intersection; (b) T-intersection........................ Definition and computation of conflicting volumes.......................................................................... Potential capacity, two-lane roadway................................................................................................. Potential capacity, four-lane roadway................................................................................................ Adjustment to major left-turn, minor-through impedance factor (3) ............................................... Platoon dispersion from upstream signalized intersections............................................................... Upstream signalized intersection........................................................................................................
Updated December 1997
9-80 9-81 9-82 9-82 9-83 9-83 9-84 9-85 9-85 9-86 9-87 9-88 9-89 9-90 9-90 9-91 9-92 9-92 9-93 9-93 9-94 9-94 9-95 9-95 9-98 9-100 9-100 9-104 9-107 9-109 9-110 9-110 9-111 9-111 9-112 9-114 9-114 9-118 9-120 9-121 9-123 9-139 9-139 9-139 9-141 9-143 10-6 10-8 10-12 10-13 10-14 10-17 10-17
xix FIGURES 10-8 10-9
10-10 10-11 10-12 10-13 10-14 10-15 10-16 10-17 10-18 10-19 10-20 10-21 10-22 10-23 10-24 10-25 10-26 10-27 10-28 10-29 10-30 10-31 10-32 10-33 10-34 10-35 10-36 10-37 10-38 10-39 10-40 10-41 10-42 10-43 11-1 11-2 11-3 11-4 11-5 11-6 11-7 11-8 11-9 11-10 11-11 11-12 11-13 11-14 11-15 11-16 11-17 11-18 11-19 11-20 11-21
Platoon dispersion model [adapted from Bonneson and Fitts (12)]................................................. Various platoon overlap cases: best case—platoons completely overlap so unplatooned period is maximum; worst case—platoons alternate so unplatooned period is minimum; average case—one-half of subordinate platoon is subsumed by dominant platoon .................................. Intersection with two-stage gap acceptance process ......................................................................... Capacity approximation at intersections with flared minor-street approach .................................... Estimation of 95th-percentile queue length ....................................................................................... Average control delay......................................................................................................................... Queue-versus-delay relationship......................................................................................................... TWSC intersection capacity and LOS computational procedures .................................................... Traffic volumes for Sample Calculation A1...................................................................................... Traffic volumes for Sample Calculation A2...................................................................................... Traffic volumes for Sample Calculation A3...................................................................................... Traffic volumes for Sample Calculation A5...................................................................................... Traffic volumes for Sample Calculation A6...................................................................................... Definition of intersection approaches ................................................................................................ Saturation headway conditions for Vehicle 2.................................................................................... Case 1: vehicles on subject approach only........................................................................................ Case 2: vehicles on subject and opposing approaches...................................................................... Case 3: vehicles on subject and conflicting approaches ................................................................... Case 4: vehicles on subject and two other approaches..................................................................... Case 5: vehicles on all approaches .................................................................................................... Two-phase operation analogy............................................................................................................. Four-phase operation analogy ............................................................................................................ Configuration for Formulation 1 ........................................................................................................ Configuration for Formulation 2 ........................................................................................................ Flow for AWSC procedures............................................................................................................... Traffic volumes for Sample Calculation B1...................................................................................... Traffic volumes for Sample Calculation B2...................................................................................... Traffic volumes for Sample Calculation B3...................................................................................... Traffic volumes for Sample Calculation B4...................................................................................... Basic roundabout ................................................................................................................................ Analysis of one roundabout leg ......................................................................................................... Roundabout approach capacity........................................................................................................... Flow stream definitions ...................................................................................................................... Traffic volumes for Sample Calculation C1...................................................................................... Worksheet for Sample Calculation C1 .............................................................................................. Sample Calculation C1 capacity and volume analysis...................................................................... Typical time-space trajectories of vehicles on one-lane arterial segment ........................................ Arterial LOS method .......................................................................................................................... Design categories ................................................................................................................................ Types of segments .............................................................................................................................. Worksheet for summary of arterial intersection delay estimates...................................................... Worksheet for computation of arterial level of service .................................................................... Speed profile by arterial section ........................................................................................................ Arterial LOS calculation process ....................................................................................................... Calculation 2, description: using worksheet for summary of arterial intersection delay estimates Calculation 2, description: using worksheet for summary of arterial level of service .................... Calculation 2, solution: using worksheet for summary of arterial intersection delay estimates ..... Calculation 2, solution: using worksheet for computation of arterial level of service.................... Speed profile for Calculation 2, southbound traffic.......................................................................... Calculation 3, description: using worksheet for summary of arterial intersection delay estimates Calculation 3, solution: using worksheet for summary of arterial intersection delay estimates ..... Calculation 3, solution: using worksheet for computation of arterial level of service.................... Speed profile for Calculation 3, northbound traffic .......................................................................... Sample calculation speed as a function of arterial flow rate............................................................ Calculation 5 speed as a function of arterial flow rate on two different segment lengths.............. Calculation 6, solution: using worksheet for computation of arterial level of service.................... Speed profile for Calculation 6 ..........................................................................................................
Page 10-18
10-19 10-20 10-21 10-22 10-24 10-26 10-28 10-47 10-49 10-50 10-54 10-56 10-59 10-59 10-60 10-60 10-60 10-61 10-61 10-61 10-62 10-62 10-63 10-68 10-76 10-78 10-79 10-80 10-82 10-83 10-84 10-85 10-87 10-88 10-89 11-3 11-5 11-7 11-9 11-13 11-14 11-15 11-17 11-18 11-18 11-21 11-22 11-23 11-24 11-25 11-26 11-27 11-28 11-28 11-30 11-31 Updated December 1997
xx FIGURES 11-22 11-23 11-24 11-25 11-26 11-27 11-28 11-29 11-30 11-31 12–1 12–2 12–3 12–4 13–1 13–2 13–3 13–4 13–5 13–6 13–7 13–8 13–9 13–10 13–11 13–12 13–13 13–14 13–15 13–16 13–17 13–18 13–19 13–20 13–21 14–1
Calculation 7, solution: using worksheet for summary of arterial intersection delay estimates ..... Calculation 7, solution: using worksheet for computation of arterial level of service.................... Speed profile for Calculation 7 .......................................................................................................... Arterial geometry for Calculation 10................................................................................................. Calculation 10, solution: using worksheet for summary of arterial intersection delay estimates ... Calculation 10, solution: using worksheet for computation of arterial level of service.................. Arterial geometry for Calculation 11................................................................................................. Calculation 11, solution: using worksheet for summary of arterial intersection delay estimates ... Calculation 11, solution: using worksheet for computation of arterial level of service.................. Speed profile for Calculation 11, eastbound traffic .......................................................................... Example of freeway person-capacity ................................................................................................. The two-dimensional nature of transit level of service as related to transit capacity ..................... Bus stop capacity related to dwell times and loading positions....................................................... Typical CBD busway line-haul passenger volumes .......................................................................... Relationships between pedestrian speed and density ........................................................................ Relationships between pedestrian flow and space............................................................................. Relationships between pedestrian speed and flow ............................................................................ Relationships between pedestrian speed and space........................................................................... Preemption of walkway width............................................................................................................ Typical free-flow walkway speed distribution .................................................................................. Cross-flow traffic—probability of conflict ........................................................................................ Illustration of walkway levels of service........................................................................................... Minute-by-minute variations in pedestrian flow................................................................................ Relationship between platoon flow and average flow ...................................................................... Levels of service for queuing areas ................................................................................................... Pedestrian movements at a street corner............................................................................................ Worksheet for walkway analysis........................................................................................................ Illustration of solution to walkway problem...................................................................................... Intersection corner geometrics and pedestrian movements............................................................... Intersection corner condition 1—minor street crossing .................................................................... Intersection corner condition 2—major street crossing..................................................................... Worksheet for crosswalk analysis ...................................................................................................... Worksheet for street corner analysis.................................................................................................. Worksheet for street corner analysis of sample calculation.............................................................. Worksheet for crosswalk analysis of sample calculation.................................................................. Illustration of right-turn conflicts with bicycles and pedestrians......................................................
Page 11-32 11-33 11-34 11-34 11-35 11-36 11-37 11-38 11-39 11-40 12-5 12-7 12-22 12-27 13-4 13-4 13-4 13-5 13-5 13-7 13-8 13-9 13-10 13-11 13-12 13-13 13-15 13-16 13-17 13-18 13-19 13-20 13-21 13-23 13-25 14-2
PHOTOGRAPHS Vehicles shying away from both roadside and median barriers ............................................................................ Ideal conditions of lane width and lateral clearance .............................................................................................. Formation of large gaps in front of slow-moving trucks climbing the grade ....................................................... Formation of large gaps in front of trucks or other heavy vehicles on relatively level terrain ........................... LOS A ...................................................................................................................................................................... LOS B....................................................................................................................................................................... LOS C....................................................................................................................................................................... LOS D ...................................................................................................................................................................... LOS E....................................................................................................................................................................... LOS F ....................................................................................................................................................................... Divided multilane highway in a rural environment................................................................................................ Divided multilane highway in a suburban environment......................................................................................... Undivided multilane highway in a rural environment............................................................................................ Undivided multilane highway in a suburban environment..................................................................................... Bridge pier in center of normally undivided suburban multilane highway........................................................... Inadequate shoulder and obstructions on roadway ................................................................................................. Ideal divided multilane highway ............................................................................................................................. Undivided multilane highway with no obstructions ............................................................................................... Typical views of two-lane two-way highways in rural environments................................................................... Typical use of paved shoulders—slow-moving vehicle uses shoulder of a two-lane rural highway, permitting faster vehicles to pass .......................................................................................................................................... Updated December 1997
3-6 3-6 3-7 3-8 3-12 3-12 3-12 3-13 3-13 3-13 7-3 7-3 7-3 7-3 7-11 7-11 7-11 7-11 8-3 8-19
xxi PHOTOGRAPHS Design categories: top left, typical high speed design; top right, typical suburban design; bottom left, typical intermediate design; bottom right, typical urban design .................................................................................... TABLES 1–1 1–2 1–3 1–4 2–1 2–2 2–3 2–4 2–5 2–6 2–7 2–8 2–9 2–10 2–11 2–12 2–13 2–14 3-1 3-2 3-3 3-4 3-5 3-6 3-7 3-8 3-9 4–1 4–2 4–3 4–4 4–5 4–6 4–7 5–1 5–2 5–3 5–4 5–5 5–6 6–1 6–2 6–3 7–1 7–2 7–3 7–4 7–5 7–6 7–7 7–8 7–9 7–10 7–11 8–1 8–2
Organization of manual ...................................................................................................................... Primary measures of effectiveness for level of service definition.................................................... Adjustment factors used for analyses ................................................................................................ Analysis techniques ............................................................................................................................ Maximum annual average daily traffic reported on selected Interstate routes (1990) .................... Reported maximum one-way hourly volumes on selected freeways................................................ Reported maximum lane volumes on selected freeways .................................................................. Reported maximum one-way volumes for selected multilane highways ......................................... Reported maximum volumes on selected two-lane rural highways ................................................. Reported maximum one-way volumes on selected urban arterials .................................................. Directional distribution characteristics............................................................................................... Observed values of K and D on selected freeways and expressways .............................................. Lane distribution by vehicle type....................................................................................................... National spot speed trends for 55-mph facilities............................................................................... Average speed by day vs. night and lane in mph ............................................................................. Average speed by lane in mph........................................................................................................... Observed saturation flow rates at signalized intersections................................................................ Capacity by facility type .................................................................................................................... LOS criteria for basic freeway sections............................................................................................. Passenger-car equivalents on extended general freeway segments .................................................. Passenger-car equivalents for trucks and buses on specific upgrades.............................................. Passenger-car equivalents for recreational vehicles on specific upgrades........................................ Passenger-car equivalents for trucks and buses on specific downgrades......................................... Adjustment factors for lane width...................................................................................................... Adjustment factors for right-shoulder lateral clearance .................................................................... Adjustment factors for number of lanes ............................................................................................ Adjustment factors for interchange density ....................................................................................... Configuration type vs. minimum number of required lane changes ................................................ Parameters affecting weaving area operation .................................................................................... Constants of prediction for weaving intensity factor, W................................................................... Criteria for unconstrained vs. constrained operation of weaving areas............................................ Limitations on weaving sections ........................................................................................................ Level-of-service criteria for weaving areas ....................................................................................... Results of weaving analysis: Sample Calculation 6.......................................................................... Capacity values for merge and diverge areas.................................................................................... Level-of-service criteria for ramp-freeway junction areas of influence ........................................... Models for prediction of density in ramp influence areas ................................................................ Models for prediction of speed in ramp influence areas .................................................................. Determination of V5 for right-hand ramps on 10-lane freeways....................................................... Approximate capacity of ramp roadways .......................................................................................... Measured average work-zone capacities............................................................................................ Summary of observed capacities for some typical operations.......................................................... Capacity of long-term construction sites with portable concrete barriers ........................................ Level-of-service criteria for multilane highways............................................................................... Adjustment for median type............................................................................................................... Adjustment for lane width.................................................................................................................. Adjustment for lateral clearance ........................................................................................................ Access-point density adjustment ........................................................................................................ Number of access points for general development environments .................................................... Passenger-car equivalents on extended general multilane highway segments ................................. Passenger-car equivalents for trucks and buses on uniform upgrades ............................................. Passenger-car equivalents for recreational vehicles on uniform upgrades ....................................... Passenger-car equivalents for trucks on downgrades ........................................................................ Service flow rates in vehicles per lane for use in planning analysis ............................................... Level-of-service criteria for general two-lane highway segments .................................................... Level-of-service criteria for specific grades ......................................................................................
Page 11-7
1-2 1-5 1-8 1-9 2-12 2-13 2-14 2-15 2-15 2-16 2-22 2-23 2-23 2-25 2-27 2-28 2-32 2-34 3-11 3-16 3-17 3-18 3-18 3-21 3-21 3-22 3-22 4-4 4-5 4-7 4-8 4-8 4-9 4-19 5-7 5-7 5-8 5-8 5-12 5-14 6-10 6-11 6-12 7-8 7-10 7-10 7-10 7-10 7-11 7-12 7-13 7-13 7-14 7-19 8-5 8-6 Updated December 1997
xxii TABLES 8–3 8–4 8–5 8–6 8–7 8–8 8–9 8–10 8–11 8–12 9-1 9-2 9-3 9-4 9-5 9-6 9-7 9-8 9-9 9-10 9-11(a) 9-11(b) 9-12 9-13 9-14 9-15 9-16 9-17 9-18 I.9-1 II.9-1 III.9-1 VI.9-1 10-1 10-2 10-3 10-4 10-5 10-6 10-7 10-8 10-9 10-10 10-11 10-12 10-13 10-14 10-15 10-16 10-17 10-18 10-19 10-20 10-21 10-22 10-23 10-24 10-25
Page Peak-hour factors for two-lane highways based on random flow .................................................... Adjustment factors for directional distribution on general terrain segments ................................... Adjustment factors for the combined effect of narrow lanes and restricted shoulder width .......... Average passenger-car equivalents for trucks, RVs, and buses on two-lane highways over general terrain segments....................................................................................................................... Values of v/c ratio vs. speed, percent grade, and percent no passing zones for specific grades.... Adjustment factor for directional distribution on specific grades .................................................... Passenger-car equivalents for specific grades on two-lane rural highways, E and Eo..................... Maximum AADTs vs. level of service and type of terrain for two-lane rural highways ............... Spacing of passing lanes on two-lane highways ............................................................................... Length of turnouts on two-lane highways ......................................................................................... Level-of-service criteria for signalized intersections......................................................................... Relationship between arrival type and platoon ratio (Rp) ................................................................. Default values for use in operational and planning analyses............................................................ Default lane utilization adjustment factors ........................................................................................ Adjustment factor for average lane width (fw)................................................................................... Adjustment factor for heavy vehicles (fHV)........................................................................................ Adjustment factor for approach grade (fg) ......................................................................................... Adjustment factor for parking (fp)...................................................................................................... Adjustment factor for bus blockage (fbb)............................................................................................ Adjustment factor for area type (fa) ................................................................................................... Adjustment factor for right turns (fRT): formulas............................................................................... Adjustment factor for right turns: factors .......................................................................................... Adjustment factor for left turns (fLT).................................................................................................. Progression adjustment factor (PF).................................................................................................... Recommended k values for lane groups under actuated and pretimed control................................ Intersection status criteria for signalized intersection planning analysis.......................................... Shared-lane left-turn adjustment computations for planning-level analysis..................................... Phase plan summary for planning analysis........................................................................................ Service flow rate solutions for Calculation 6 .................................................................................... Left-turn bay length adjustment factors............................................................................................. Comparison of traffic-actuated controller settings for multiphase example..................................... Acceleration-deceleration delay correction factor ............................................................................. Selection of delay model variables by case....................................................................................... Critical gaps tc and follow-up times tf for passenger cars at TWSC intersections .......................... Relative pedestrian-vehicle hierarchy ................................................................................................ Pedestrian impedance factors ............................................................................................................. Platoon dispersion factor, a (12, 1) ................................................................................................... Proportion of study period for each flow regime for average case.................................................. Proportion of study period unblocked for each minor movement for average case........................ Level-of-service criteria...................................................................................................................... Example left-turn delay calculation ................................................................................................... Impedance and capacity calculations ................................................................................................. Delay, queue length, and level of service.......................................................................................... Impedance and capacity calculations ................................................................................................. Conflicting flows ................................................................................................................................ Lane usage by approach ..................................................................................................................... Critical gap and follow-up time by movement.................................................................................. Impedance and capacity calculations ................................................................................................. Delay, queue length, and level of service.......................................................................................... Upstream signal parameters................................................................................................................ Computation 1: queue clearance time (A5a) ..................................................................................... Computation 2: proportion of TWSC intersection time blocked (A5b)........................................... Computation 3: platoon events and proportion unblocked (A5c)..................................................... Computation 4 (single-stage process) (A5d) ..................................................................................... Computation 5 (single-stage process) (A5e)...................................................................................... Impedance and capacity calculations ................................................................................................. Delay, queue length, and level of service.......................................................................................... Lane usage by approach .....................................................................................................................
Updated December 1997
8-7 8-9 8-9 8-9 8-10 8-11 8-12 8-14 8-20 8-21 9-7 9-11 9-12 9-12 9-14 9-14 9-14 9-15 9-15 9-15 9-15 9-16 9-17 9-29 9-29 9-32 9-54 9-57 9-96 9-98 9-115 9-119 9-140 10-11 10-15 10-15 10-18 10-19 10-19 10-25 10-26 10-48 10-49 10-49 10-50 10-50 10-51 10-51 10-52 10-52 10-52 10-53 10-53 10-54 10-54 10-54 10-54 10-54
xxiii TABLES 10-26 10-27 10-28 10-29 10-30 10-31 10-32 10-33 10-34 10-35 10-36 10-37 10-38 10-39 10-40 10-41 10-42 10-43 10-44 10-45 10-46 10-47 10-48 10-49 10-50 10-51 10-52 10-53 10-54 11-1 11-2 11-3 11-4 11-5 11-6 11-7 11-8 11-9 11-10 11-11 11-12 12–1 12–2 12–3 12–4 12–5 12–6 12–7 12–8 12–9 12–10 12–11 12–12 12–13 12–14
Shared-lane capacities......................................................................................................................... Delay, queue length, and level of service.......................................................................................... Two-stage gap acceptance: Step 3 ..................................................................................................... Two-stage gap acceptance: Step 4 ..................................................................................................... Shared-lane capacities......................................................................................................................... Flared minor-street approach calculations ......................................................................................... Delay, queue length, and level of service.......................................................................................... Probability of degree-of-conflict case ................................................................................................ Degree-of-conflict cases for two-lane approach intersections .......................................................... Degree-of-conflict cases for three-lane approach intersections ........................................................ Number of vehicles by approach for degree-of-conflict cases, multilane AWSC intersections (two-lane approach intersections)................................................................................................... Occupied lane combinations for degree-of-conflict cases, multilane AWSC intersections (twolane approach intersections) ........................................................................................................... Level-of-service criteria...................................................................................................................... Geometry group .................................................................................................................................. Saturation headway adjustment factors by geometry group ............................................................. Probability of aj .................................................................................................................................. Saturation headway values by case and geometry group.................................................................. Departure headways............................................................................................................................ Capacity, delay, and level of service ................................................................................................. Saturation headways ........................................................................................................................... Departure headways............................................................................................................................ Service times....................................................................................................................................... Capacity, delay, and level of service ................................................................................................. Saturation headway............................................................................................................................. Degrees of utilization and departure headways................................................................................. Service times....................................................................................................................................... Capacity, delay, and level of service ................................................................................................. Critical gap and follow-up time ......................................................................................................... Effects of changes in critical gap and move-up time........................................................................ Arterial levels of service .................................................................................................................... Aid in establishing arterial classification........................................................................................... Arterial classification according to functional and design categories .............................................. Segment running time per mile.......................................................................................................... Relationship between arrival type and platoon ratio (Rp) ................................................................. Uniform delay (d1) progression adjustment factor (PF).................................................................... Recommended k-values for lane groups under actuated and pretimed control................................ Recommended I-values for lane groups with upstream signals........................................................ Computations for Sample Calculation 4 ............................................................................................ Computations for Sample Calculation 5 ............................................................................................ Input data for Sample Calculation 10 ................................................................................................ Input data for Sample Calculation 11 ................................................................................................ Peak-hour use of public transport by persons entering or leaving the central business district ..... Important terms in transit capacity .................................................................................................... Factors that influence transit capacity................................................................................................ Characteristics of typical transit vehicles—United States and Canada ............................................ Passenger loading standards and levels of service for bus transit vehicles ..................................... Passenger loading standards and levels of service for urban rail vehicles ...................................... Typical space requirements for seated and standing passengers ...................................................... Passenger car equivalency of urban buses at signalized intersections ............................................. Passenger boarding and alighting times related to service conditions ............................................. Typical bus passenger boarding and alighting service times for selected bus types and door configurations.................................................................................................................................. Suggested bus flow service volumes for planning purposes ............................................................ Suggested bus passenger service volumes for planning purposes .................................................... Observed peak-hour passenger volumes on U.S. and Canadian rapid transit systems.................... Observed peak-hour passenger volumes on street car and light rail systems in United States and Canada......................................................................................................................................
Page 10-55 10-55 10-56 10-57 10-57 10-58 10-58 10-64 10-65 10-65 10-65 10-66 10-67 10-68 10-68 10-69 10-75 10-78 10-78 10-79 10-79 10-79 10-79 10-80 10-80 10-80 10-80 10-84 10-89 11-4 11-8 11-8 11-9 11-11 11-11 11-12 11-12 11-27 11-29 11-34 11-37 12-3 12-3 12-6 12-8 12-8 12-9 12-9 12-11 12-12 12-13 12-13 12-14 12-15 12-16 Updated December 1997
xxiv TABLES 12–15 12–16 12–17 12–18 12–19 12–20 12–21 12–22 12–23 12–24 12–25 12–26 12–27 12–28 12–29 12–30 12–31 12–32 12–33 12–34 12–35 12–36 12–37 I.12–1 I.12–2 I.12–3 I.12–4 I.12–5 I.12–6 I.12–7 II.12–1 II.12–2 II.12–3 III.12–1 III.12–2 III.12–3 III.12–4 13–1 13–2 13–3 14–1 14–2
Typical rail transit capacities.............................................................................................................. Estimated maximum capacity of bus stops........................................................................................ Levels of service for bus stops .......................................................................................................... Typical service levels, single stop, no passing.................................................................................. Efficiency of multiple linear bus berths ............................................................................................ Estimated capacity of on-line bus stops by number of berths.......................................................... Bus berth passenger capacity equations and illustrative examples................................................... Maximum load point hourly passengers per effective berth at the busiest station—uninterrupted flow conditions................................................................................................................................ Maximum load point hourly passengers per effective berth at busiest station—interrupted flow conditions ........................................................................................................................................ Illustrative bus capacity guidelines for CBD busways...................................................................... Busway service volumes at maximum load points ........................................................................... Typical arterial street bus service volumes at maximum load point ................................................ Berth requirements at bus stops ......................................................................................................... Significant examples of bus priority treatments—United States and Canada.................................. Summary of illustrative planning guidelines for bus priority treatments......................................... Summary and applications of transit capacity equations .................................................................. Basic transit capacity variables .......................................................................................................... Summary and applications of transit capacity figures and tables..................................................... Guidelines for application—planning parameters.............................................................................. Person-capacity of a freeway lane for varying bus volumes ............................................................ Anticipated peak-hour buses at transit center.................................................................................... Bus berth requirements, year-1985 .................................................................................................... Bus berth requirements, year-2000 .................................................................................................... Reported theoretical bus lane capacities ............................................................................................ Observed peak-hour bus volumes on streets and freeways .............................................................. Observed bus volumes on urban limited access facilities 1972–1976 conditions ........................... Peak-hour bus volumes on urban arterials, 1972–1976 conditions .................................................. Observed bus volumes on urban arterials, 1978–1984 ..................................................................... Observed passengers at major bus terminals..................................................................................... Observed peak bus berth volumes and flow rates at bus terminals ................................................. Observed peak-hour passenger volumes on streetcar and LRT lines—Europe ............................... Rapid transit car and train capacities................................................................................................. Theoretical rail rapid transit equations .............................................................................................. Typical CBD service times per passenger......................................................................................... Observed rail transit station dwell times, 1980 ................................................................................. Bus boarding and alighting times in selected urban areas................................................................ Means and variances of observed passenger service time distributions........................................... Observed pedestrian flow rates in urban areas.................................................................................. Fixed obstacle width adjustment factors for walkways .................................................................... Pedestrian level of service on walkways ........................................................................................... Passenger-car equivalent for bicycles ................................................................................................ Reported one-way and two-way high volumes of bicycle facilities.................................................
Updated December 1997
Page 12-17 12-20 12-21 12-21 12-21 12-22 12-24 12-25 12-26 12-27 12-27 12-28 12-29 12-31 12-33 12-35 12-37 12-38 12-39 12-40 12-43 12-43 12-44 12-49 12-50 12-51 12-52 12-54 12-54 12-55 12-55 12-56 12-58 12-59 12-59 12-60 12-60 13-1 13-6 13-8 14-2 14-3
chapter 1
INTRODUCTION, CONCEPTS, AND APPLICATIONS
CONTENTS i.
introduction .......................................................................................................................................................................... Importance of Capacity ......................................................................................................................................................... Purpose of Manual ................................................................................................................................................................ Scope of Manual.................................................................................................................................................................... Organization of Manual ........................................................................................................................................................
1-1 1-1 1-2 1-2 1-3
ii.
concepts .................................................................................................................................................................................. Capacity and Levels of Service ............................................................................................................................................ Capacity ............................................................................................................................................................................ Levels of Service.............................................................................................................................................................. Factors Affecting Capacity and Level of Service ................................................................................................................ Ideal Conditions ............................................................................................................................................................... Roadway Conditions ........................................................................................................................................................ Traffic Conditions ............................................................................................................................................................ Control Conditions ........................................................................................................................................................... Technology ....................................................................................................................................................................... Summary ................................................................................................................................................................................
1-3 1-3 1-3 1-4 1-5 1-5 1-5 1-6 1-6 1-7 1-7
iii.
applications............................................................................................................................................................................ Models of Traffic Flow......................................................................................................................................................... Levels of Analysis................................................................................................................................................................. Operational Analysis ........................................................................................................................................................ Design............................................................................................................................................................................... Planning Analysis............................................................................................................................................................. Precision................................................................................................................................................................................. Field Data .............................................................................................................................................................................. Summary ................................................................................................................................................................................
1-9 1-9 1-9 1-9 1-10 1-10 1-10 1-10 1-11
I. INTRODUCTION This publication is the third update of the third edition of the Highway Capacity Manual (HCM). The first manual was published in 1950 by the then Bureau of Public Roads as a guide to the design and operational analysis of highway facilities. In 1965, the then Highway Research Board, under the guidance of its Highway Capacity Committee, published the second edition. The third edition, published in 1985, reflected more than 2 decades of comprehensive research conducted by a variety of research agencies under the sponsorship of a number of organizations, primarily the National Cooperative Highway Research Program and the Federal Highway Administration. Its development was guided by the Transportation Research Board Committee on Highway Capacity and Quality of Service. As the result of continuing research in capacity, the third edition of HCM has been updated again to incorporate numerous findings of studies conducted since it was published. Previously published
chapters and interim documents have been superseded by the updated chapters identified in Table 1-1.
IMPORTANCE OF CAPACITY
The capacity of a transportation facility reflects its ability to accommodate a moving stream of people or vehicles. It is a measure of the supply side of transportation facilities. Level of service is a measure of the quality of flow. Capacity and level-of-service (LOS) estimates are needed for most traffic engineering and transportation planning decisions and actions. Capacity analysis addresses questions such as the following: 1-1
Updated December 1997
principles of capacity
1-2
Table 1-1. Organization of Manual chapter
description/facility type
update
1
Introduction, Concepts, and Applications Traffic Characteristics
1997
2
1994
Uninterrupted Flow Facilities 3 4 5 6 7 8
Basic Freeway Sections Weaving Areas Ramps and Ramp Junctions Freeway Systems Multilane Rural and Suburban Highways Two-Lane Highways
1997 1997 1997 1997 1997 1985
Interrupted Flow Facilities 9 10 11 12 13 14
Signalized Intersections Unsignalized Intersections Arterial Streets Transit Capacity Pedestrians Bicycles
1997 1997 1997 1985 1985 1985
NOTE: The Metric Analysis Reference Guide (MARG) is available to assist users of the Highway Capacity Manual in the conversion of English units. This guide includes correct metric symbols and provides tables, figures, formulas, and worksheets for metric calculations.
T What is the quality of service provided by an existing facility during peak periods, and how much traffic increase can be tolerated? T What types of roadway or transit facilities are needed to accommodate a given level of person or vehicle flow? T What lane configurations are needed for various levels of average daily traffic on freeways or arterial roads? T What highway or street designs (and hence capacities) are needed to serve a planned development? T How many buses or railcars are needed to serve peak direction flow at the maximum load point, and can these transit vehicles be passed through the busiest station or other point of constriction? T How wide must the sidewalk be on a street with high pedestrian activity, and would the holding space at street corners of a signalized intersection be sufficient? Four primary traffic engineering activities depend on capacity and LOS analyses: 1. When new facilities are planned or existing facilities are to be expanded, their size in terms of width or number of lanes must be determined. 2. When existing facilities are considered for upgrading, either by widening or by traffic operational changes, their operational characteristics and service levels must be assessed. 3. When new developments are planned, capacity and LOS analyses are needed to identify necessary traffic and roadway changes and to help define cost responsibilities. 4. Studies of operating conditions and levels of service provide base values for determining changes in road-user costs, fuel consumption, air pollutant emissions, and noise. PURPOSE OF MANUAL
The parameters and procedures in this manual provide a systematic and consistent basis for assessing the capacity and quality of Updated December 1997
service for individual key elements of transportation systems (i.e., for various types of transportation facilities). They have been developed from a wide range of research studies conducted during the past 45 years. They reflect North American operating experience and may not be representative of traffic, transit, and pedestrian operations in other parts of the world.
SCOPE OF MANUAL
This manual presents operational, design, and planning capacity analysis techniques for a broad range of transportation facilities. It provides procedures for analyzing streets and highways, bus and rail transit, and pedestrian and bicycle facilities. Note that the manual does not address systems of facilities or overall mobility. Nevertheless, the results of these analyses may be used as information for the assessment of broad system issues, such as congestion management. Facilities are classified into two categories of flow: uninterrupted and interrupted. Uninterrupted flow facilities have no fixed elements, such as traffic signals, that are external to the traffic stream and may interrupt the traffic flow. Traffic flow conditions result from the interactions among vehicles in the traffic stream and between vehicles and the geometric and environmental characteristics of the roadway. Interrupted flow facilities have fixed elements that may interrupt the traffic flow. Such elements include traffic signals, stop signs, and other types of controls. These devices cause traffic to stop periodically (or slow significantly), irrespective of how much traffic exists. ‘‘Uninterrupted flow’’ and ‘‘interrupted flow’’ are terms that describe the type of facility, not the quality of traffic flow at any given time. Thus a freeway experiencing extreme congestion is still an uninterrupted flow facility because the causes of congestion are internal to the traffic stream. Freeways and their components operate under the purest form of uninterrupted flow. Not only are there no fixed interruptions to traffic flow, but access is controlled and limited to ramp locations. Multilane highways and two-lane highways may also operate under uninterrupted flow in long segments between points of fixed interruptions. In general, where signal spacing exceeds 2 mi, uninterrupted flow may exist between the signals. Where signal spacing is less than 2 mi, the facility is classified as an arterial, and flow is considered to be interrupted. On multilane and two-lane highways, it is often necessary to examine points of fixed interruption as well as uninterrupted flow segments. The analysis of interrupted flow facilities must account for the impact of fixed interruptions. A traffic signal, for example, limits the time available to various movements in an intersection. Capacity is limited not only by the physical space provided, but also by the time of use that is available to various component movements in the traffic stream. The procedures in this manual do not explicitly address operations of closely spaced signalized intersections. Under such conditions, several unique characteristics must be considered, including spillback potential from the downstream intersection to the upstream intersection, effects of downstream queues on upstream saturation flow rate, and unusual platoon dispersion or compression between intersections. An example of such closely spaced operations is signalized ramp terminals at urban interchanges. Queue
introduction, concepts, and applications interactions between closely spaced intersections may seriously distort the procedures in this manual. Transit, pedestrian, and bicycle flows are generally considered to be interrupted. Uninterrupted flow may exist under certain circumstances, such as in a long busway without stops or a long pedestrian corridor. However, in most situations, capacity is limited by stops elsewhere along the facility.
ORGANIZATION OF MANUAL
The third edition of HCM contains 14 chapters. This third update of the third edition involves nine of these chapters. Table 1-1 shows how the various chapters are organized according to facility type and identifies those that have been updated. In Chapter 1, the role and importance of capacity analysis are described, basic concepts are presented, and general guidelines for application are provided. In Chapter 2, Traffic Characteristics, basic variables related to capacity are identified and their values and relationships as observed throughout North America are discussed. Chapters 3 through 14 are the basic procedural chapters of the manual. They are organized according to the facility types presented in Table 1-1. Chapters 3 through 8 cover uninterrupted flow facilities, with Chapters 3 through 6 treating freeways and their components and Chapters 7 and 8 dealing with multilane and two-lane highways, respectively. Chapters 9 through 14 focus on interrupted flow facilities and their components, including signalized and unsignalized intersections, arterial streets, and transit, pedestrian, and bicycle facilities. Two chapters treat the roadways as operating systems, and the analyses focus on the effect of individual segments or components on the overall performance and operation of the roadway. In Chapter 6, Freeway Systems, the analysis reflects a coordinated evaluation of basic freeway segments, weaving areas, and ramp junctions. The results of the analysis show the effects of operations in one component on other freeway segments or components and
1-3
on the overall operation. In Chapter 11, Arterial Streets, the analysis permits an evaluation of the performance of an arterial roadway through a series of intersections. Each of the procedural chapters is generally organized in four distinct parts: 1. Introduction: The basic characteristics, concepts, and philosophies of capacity analysis as applied to the subject facility are described. 2. Methodology: The basic components of the analysis procedure to be applied to the specific facility are presented. Equations and tabular and graphic information needed to complete the analysis are included. 3. Procedures for application: Step-by-step instructions for applying capacity analysis computations are presented. Procedures are specified for operational analysis, design, and planning, although not all chapters contain these three analysis levels. Worksheets are provided for most computational procedures and are explained in detail. 4. Sample calculations: A variety of example applications, showing all computations required for analysis, and detailed discussions of results and interpretations are presented. Sample calculations are provided for the full range of potential applications in each chapter. Many chapters have separate sections headed by the foregoing titles. In some chapters, sections are combined for clarity of presentation. Where sections are combined, section titles clearly indicate where material is located. The organization of the procedural chapters allows frequent users to focus on step-by-step instructions without having to read or scan an entire chapter. All users of this manual, however, should read the entire chapter being used at least once to become familiar with the concepts, applications, and interpretations of the procedures. As an additional convenience for frequent users, some chapters contain an appendix in which figures and worksheets are reproduced (some to a larger scale than that appearing in the text) for ease of use.
II. CONCEPTS CAPACITY AND LEVELS OF SERVICE
A principal objective of capacity analysis is the estimation of the maximum number of people or vehicles that can be accommodated by a given facility in reasonable safety within a specified time period. However, because facilities generally operate poorly at or near capacity, they are rarely planned to operate in this range. Accordingly, capacity analysis also provides a means of estimating the maximum amount of traffic that can be accommodated by a facility while prescribed operational qualities are maintained. Capacity analysis is, therefore, a set of procedures for estimating the traffic-carrying ability of facilities over a range of defined operational conditions. It provides tools for the analysis of existing facilities and for the planning and design of improved or future facilities. The definition of operational criteria is accomplished by introducing the concept of levels of service. Ranges of operating condi-
tions are defined for each type of facility and are related to amounts of traffic that can be accommodated at each level. The two principal concepts of this manual—capacity and levels of service—are defined in the following sections.
Capacity
The capacity of a facility is defined as the maximum hourly rate at which persons or vehicles can reasonably be expected to traverse a point or uniform section of a lane or roadway during a given time period under prevailing roadway, traffic, and control conditions. Vehicle capacity represents the maximum number of vehicles that can pass a given point during a specified period under prevailing roadway, traffic, and control conditions. This definition asUpdated December 1997
1-4
principles of capacity
sumes no influence of downstream traffic operation, such as backing up of traffic over the analysis point. Person capacity represents the maximum number of people that can pass a given point during a specified period under prevailing conditions. It is commonly used in evaluating public transit services, high-occupancy-vehicle lanes, or pedestrian facilities. Realistic occupancy is a critical factor for transit and other vehicles. Several important points in the definition of capacity warrant clarification. 1. Capacity is defined for prevailing roadway, traffic, and control conditions, which should be reasonably uniform for any section of facility analyzed. Any change in the prevailing conditions will result in a change in the capacity of the facility. The definition assumes that good weather, good pavement conditions, and no incidents exist. 2. Capacity normally refers to a ‘‘point or uniform segment’’ of the facility. Capacity analysis is conducted for segments of a facility having uniform traffic, roadway, and control conditions. Because capacity depends on these factors, segments with different prevailing conditions will have different capacities. Capacity of a route or system can be inferred from the analysis procedures but is not explicitly discussed. The point or segment with the poorest operating conditions often determines the overall levels of service for the facility. 3. Capacity refers to a rate of vehicular or person flow during a specified period, which is most often a peak 15-min period. Capacity does not refer to the maximum volume that can be accommodated during an hour. This definition recognizes the potential for substantial variations in flow during an hour and focuses the analysis on intervals of maximum flow. 4. Capacity is defined on the basis of ‘‘reasonable expectancy.’’ That is, a stated capacity for a given facility is a rate of flow that can be repeatedly achieved during peak periods for which sufficient demand exists and that can be achieved on facilities with similar characteristics throughout North America. It is not the absolute maximum rate of flow ever observed on such a facility type. Driver characteristics vary from region to region and the absolute maximum rate of flow may vary from day to day and from location to location. Occasionally, measured rates of flow at some locations will exceed the defined capacity of the facility type. Such rates, however, are usually not sustainable or cannot be achieved repeatedly. 5. Capacity may be defined in terms of persons per hour or vehicles per hour, depending on the type of facility involved. The concept of person flow is important in making strategic decisions about transportation modes in heavily traveled corridors and in defining the role of transit and high-occupancy-vehicle priority treatments. The concepts of person capacity and person flow weigh each type of vehicle in the traffic stream by the number of occupants they carry. For example, an arterial street carrying 600 vehicles per hour with 1.5 persons per vehicle will have a movement capability of 900 people per hour; 50 buses per hour, each with an average of 40 persons per bus, would carry 2,000 persons per hour for a total person flow of 2,900 persons per hour. As the number of transit vehicles in the traffic stream increases, the number of vehicles that can pass a given point decreases, but the person flow may increase, although possibly at reduced service quality. Levels of Service
The concept of levels of service uses qualitative measures that characterize operational conditions within a traffic stream and their Updated December 1997
perception by motorists and passengers. The descriptions of individual levels of service characterize these conditions in terms of such factors as speed and travel time, freedom to maneuver, traffic interruptions, and comfort and convenience. Six levels of service are defined for each type of facility for which analysis procedures are available. They are given letter designations, from A to F, with LOS A representing the best operating conditions and LOS F the worst. Each level of service represents a range of operating conditions. The volume of traffic that can be served under the stop-and-go conditions of LOS F is generally accepted as being lower than that possible at LOS E; consequently, service flow rate E is the value that corresponds to the maximum flow rate, or capacity, on the facility. For most design or planning purposes, however, service flow rates D or C are usually used because they ensure a more acceptable quality of service to facility users. Levels of service for uninterrupted and interrupted flow facilities vary widely in terms of both the user’s perception of service quality and the operational variables used to describe them. Chapters 3 through 13 of this manual contain detailed descriptions of the levels of service that are defined for each facility type. Service Flow Rates
The procedures attempt to establish or predict the maximum rate of flow that can be accommodated by various facilities at each level of service, except LOS F, for which flows are unstable. Thus each facility has five service flow rates, one for each level of service (A through E). The service flow rate is the maximum hourly rate at which persons or vehicles can reasonably be expected to traverse a point or uniform section of a lane or roadway during a given period under prevailing roadway, traffic, and control conditions while a designated level of service is maintained. The service flow rates are generally based on a 15-min period. Typically, the hourly flow rate is defined as four times the peak 15-min volume. Note that service flow rates are discrete values, whereas levels of service represent a range of conditions. Because the service flow rates are defined as maximums for each level of service, they effectively define flow boundaries between the various levels of service. Measures of Effectiveness
For each type of facility, levels of service are defined on the basis of one or more operational parameters that best describe the operating quality for the facility type. Although the concept of level of service attempts to address a wide range of operating conditions, limitations on data collection and availability make it impractical to treat the full range of operational parameters for every type of facility. The parameters selected to define levels of service for each facility type are called measures of effectiveness and represent available measures that best describe the quality of operation on the subject facility type. Table 1-2 presents the primary measures of effectiveness used to define levels of service for each facility type. Each level of service represents a range of conditions, as defined by a range in the parameter(s) presented in the table. Effectiveness and LOS criteria are not defined for bicycles. The treatment of bicycles herein is limited to their impact on other vehicular flow at critical points in the street and highway system.
introduction, concepts, and applications Table 1-2. Primary Measures of Effectiveness for LOS Definition type of facility Freeways Basic freeway segments Weaving areas Ramp junctions Multilane highways Two-lane highways Signalized intersections Unsignalized intersections Arterials Transit Pedestrians
1-5
way, traffic, or control conditions. Vehicle control and technology represent conditions that change in the long term.
measure of effectiveness Roadway Conditions
Density (pc/mi/ln) Density (pc/mi/ln) Flow rates (pcph) Density (pc/mi/ln) Free-flow speed (mph) Time delay (percent) Average control delay (sec/veh) Average control delay (sec/veh) Average travel speed (mph) Load factor (pers/seat, veh/hr, people/hr) Space (sq ft/ped)
FACTORS AFFECTING CAPACITY AND LEVEL OF SERVICE
Ideal Conditions
Many of the procedures in this manual provide a formula or simple tabular or graphic presentation for a set of specified standard conditions, which must be adjusted to account for any prevailing conditions not matching those specified. The conditions so defined are often ideal conditions. In principle, an ideal condition is one for which further improvement will not achieve any increase in capacity. Ideal conditions assume good weather, good pavement conditions, users familiar with the facility, and no incidents impeding traffic flow. Specific ideal conditions are identified in each chapter. Examples of ideal conditions are given below for uninterrupted flow facilities and for intersection approaches. Ideal conditions for uninterrupted flow facilities include the following: T Lane widths of 12 ft. T Clearance of 6 ft between the edge of the travel lanes and the nearest obstructions or objects at the roadside and in the median. T Design speed of 70 mph for multilane highways, 60 mph for two-lane highways. T Only passenger cars in the traffic stream. T Level terrain. Ideal conditions for intersection approaches include the following: T Lane widths of 12 ft. T Level grade. T No curb parking on the intersection approaches. T Only passenger cars in the traffic stream and no local transit buses stopping in the travel lanes. T All vehicles traveling straight through the intersection. T Intersection located in a non-central business district area. T No pedestrians. T At signalized intersection approaches, green signal available at all times. In most capacity analyses, prevailing conditions are not ideal, and computations of capacity, service flow rate, or level of service must include predictive adjustments to reflect this absence of ideal conditions. Prevailing conditions are generally categorized as road-
Roadway factors include geometric conditions and design elements. In some cases, these factors influence the capacity of a road, whereas in others, the factors may affect a measure of effectiveness, such as speed, while not affecting the capacity or maximum flow rate that can be carried by the facility. Roadway factors include the following: T T T T T T
The type of facility and its development environment. Lane widths. Shoulder widths and lateral clearances. Design speed. Horizontal and vertical alignments. Availability of queueing space at intersections.
The type of facility is critical. The existence of uninterrupted flow, the presence of medians, and other major facility type factors significantly affect flow characteristics and capacity. The development environment has also been found to affect the performance of two-lane roadways, multilane highways, and signalized intersections. Lane and shoulder widths can have a significant impact on traffic flow. Narrow lanes cause vehicles to travel closer to each other laterally than most drivers would prefer. Motorists compensate by slowing down or observing larger longitudinal spacing for a given speed, which effectively reduces capacity, service flow rates, or both. Narrow shoulders and lateral obstructions have two important impacts. Many drivers will steer away from roadside or median objects they perceive to pose a hazard. This action brings them laterally closer to vehicles in adjacent lanes and causes the same reactions as those exhibited in narrow lanes. Restricted design speeds affect operations and level of service; drivers are forced to travel at somewhat reduced speeds and to be more vigilant in reacting to the harsher horizontal and vertical alignments resulting from a reduced design speed. In extreme cases, the capacity of multilane facilities has been found to be affected by low design speeds. The horizontal and vertical alignment of a highway depends greatly on the design speed used and the topography through which the roadway must be constructed. Procedures for uninterrupted flow facilities categorize the general terrain of a highway as follows: T Level terrain: Any combination of grades and horizontal and vertical alignment that allows heavy vehicles to maintain approximately the same speed as passenger cars; this terrain generally includes short grades of no more than 1 to 2 percent. T Rolling terrain: Any combination of grades and horizontal or vertical alignment that causes drivers of heavy vehicles to reduce speeds to substantially below those of passenger cars, but does not require operation at crawl speeds for any significant length of time. T Mountainous terrain: Any combination of grades and horizontal and vertical alignment that causes drivers of heavy vehicles to operate at crawl speeds for significant distances or at frequent intervals. Crawl speed is the maximum sustained speed that heavy vehicles can maintain on an extended upgrade of a given percent. Updated December 1997
1-6
principles of capacity
These definitions are general and depend on the particular mix of heavy vehicles in the traffic stream. In general, as terrain becomes more severe, capacity and service flow rates are reduced. This impact is significant for two-lane rural highways, where the severity of terrain not only affects the operating capabilities of individual vehicles in the traffic stream, but also restricts the opportunities to pass slow-moving vehicles in the traffic stream. In addition to the general impacts of terrain, isolated upgrades of significant length may have a substantial effect on operations. Heavy vehicles slow significantly on such upgrades, creating operational difficulties in the traffic stream and inefficient use of the roadway. Grades also may have a major impact on the operation of intersection approaches; vehicles must overcome both the grade and the inertia of starting from a stopped position at the same time. Traffic Conditions
Traffic conditions that influence capacities and service levels include vehicle type and directional or lane distribution. The procedures assume that drivers are familiar with the facility. Less efficient use of roadway facilities on weekends or in recreation areas is generally attributed mainly to the lack of specific local knowledge. Vehicle Type
Whenever vehicles other than passenger cars (which include small trucks and vans) exist in the traffic stream, the number of vehicles that can be served is affected. Heavy vehicles are defined as vehicles having more than four tires touching the pavement. Heavy vehicles adversely affect traffic in two ways: T They are larger than passenger cars and therefore occupy more roadway space than passenger cars. T They have poorer operating capabilities than passenger cars, particularly with respect to acceleration, deceleration, and the ability to maintain speed on upgrades. The second impact is the more critical. Because heavy vehicles cannot keep pace with passenger cars in many situations, large gaps form in the traffic stream that are difficult to fill by passing maneuvers. These gaps create inefficiencies in the use of roadway space that cannot be completely overcome. This effect is particularly deleterious on sustained, steep upgrades, where the difference in operating capabilities is most pronounced, and on two-lane highways, where passing must be accomplished by using the opposing travel lane. Heavy vehicles also may affect downgrade operations, particularly where downgrades are steep enough to require operation of such vehicles in a low gear. In such cases, heavy vehicles again must operate at speeds slower than those of passenger cars and gaps in the traffic stream will form. Heavy vehicles are generally grouped in three categories: T Trucks: Vehicles involved primarily in the transport of goods or in the delivery of services (other than public transportation). T Recreational vehicles: Vehicles operated by private motorists and involved in the transport of recreational equipment or facilities. T Buses: Vehicles involved in the transportation of groups of people on a for-hire, charter, or franchised transit basis. Buses are further categorized as intercity or local transit buses. Intercity (or ‘‘through’’) buses operate in a traffic stream without making stops Updated December 1997
to pick up or discharge passengers on the road or street. Local transit buses make such stops within the confines of the roadway. There is considerable variation in the characteristics and performance capabilities of vehicles within each class of heavy vehicle, just as there is among passenger cars. Trucks cover a particularly wide range of vehicles, however, from lightly loaded vans and panel trucks to the most heavily loaded coal, timber, and gravel haulers. Individual trucks have widely varying operational characteristics based on how heavily they are loaded. Analysis procedures for each type of facility discuss the mix of trucks on each in some detail. None of the procedures segregate the truck population into subcategories for separate computational consideration, although some analysis procedures allow the user to select various typical trucks on the basis of the prevailing mix. Recreational vehicles also cover a broad range of vehicle types, including campers, both self-propelled and towed; motor homes; and passenger cars or small trucks towing a variety of recreational equipment, such as boat, snowmobile, and motorcycle trailers. Although these vehicles may have considerably better operating capabilities than trucks, drivers of such vehicles are not professionals, which accentuates the impact of such vehicles’ deficiencies. Intercity buses are relatively uniform in their performance capabilities. Urban transit buses are generally not as powerful as intercity buses. Their most severe impact on traffic, however, results from the discharge and pickup of passengers on the roadway. Local transit buses make such stops at the curb, usually at intersections, along multilane suburban highways, arterials, and city streets. Where there is no curb parking on the roadway, the stopped bus blocks a travel lane. Where curb parking does exist, the bus disrupts flow in adjacent travel lanes as it enters and leaves the bus stop. Directional and Lane Distribution
In addition to the distribution of vehicles types, two other traffic characteristics affect capacity, service flow rates, and level of service: directional distribution and lane distribution. Directional distribution has a dramatic impact on two-lane rural highway operation. Optimum conditions occur when the split of traffic is about 50 percent in each direction. Capacity declines as the directional split becomes more unbalanced. Capacity analysis procedures for multilane highways focus on a single direction of flow. Nevertheless, each direction of the facility is usually designed to accommodate the peak rate of flow in the peak direction. Typically, morning peak traffic occurs in one direction and evening peak traffic occurs in the opposite direction. Lane distribution is also a factor on multilane facilities. Typically, the shoulder lane of a multilane facility carries less traffic than other lanes. Analysis procedures assume typical lane distributions for most types of facilities. Control Conditions
For interrupted flow facilities, the control of the time available for movement of specific traffic flows is a critical element affecting capacity, service flow rates, and level of service. The most critical type of control on such facilities is the traffic signal. Operations are affected by the type of control in use, signal phasing, allocation of green time, cycle length, and relationship with adjacent control
introduction, concepts, and applications
1-7
measures. All of these terms are discussed in detail in Chapter 9, Signalized Intersections. For this introduction, it is sufficient to note that the traffic signal determines the amount of time available for movement on various lanes of the intersection. Stop signs also affect capacity, but in a less deterministic way. Whereas the traffic signal positively assigns designated times when each movement is permitted, the stop sign at a two-way stopcontrolled intersection merely assigns the right-of-way permanently to the major street. Motorists traveling on the minor street must find gaps in the major traffic flow through which to execute maneuvers. Thus the capacity of such approaches depends on traffic conditions on the major street. All-way stop control forces drivers to stop and alternately enter the intersection in rotation. Capacity and operational characteristics may vary widely depending on traffic demands on the various approaches. Other types of controls and regulations can significantly affect capacity, service flow rates, and level of service. Restriction of curb parking can increase the number of lanes available on a street or highway. Turn restrictions can eliminate conflicts at intersections and increase capacity. Lane use controls can positively allocate available roadway space to component movements and can be used at intersections and to create reversible lanes on critical arterials. One-way street routings eliminate conflicts between left turns and opposing traffic.
to the analyst to determine the impact of ITS (if any) in individual roadway capacity analysis applications. In light of current ITS studies, the following comments may provide some guidance in analyzing the impact of ITS in specific roadway capacity situations:
Technology
SUMMARY
The factors described in the preceding discussion generally relate to immediate conditions that would reduce roadway capacity below ideal conditions. Emerging transportation technologies under the broad heading of intelligent transportation systems (ITS) are being developed to enhance the safety and efficiency of roadway systems. Depending on the particular application, ITS strategies will tend to increase the safety and performance of roadway facilities beyond the levels experienced under current roadway and vehicle control systems. For the purposes of this discussion, ITS is considered to include any technology that allows real-time information to be gathered and used by drivers and traffic control system operators to provide better vehicle navigation, roadway system control, or both. At the time of publication of this chapter, the implementation of many ITS strategies is only in its beginning stages. Therefore, little research has been conducted to determine their impact on capacity and safety. The procedures in this manual are considered to relate to roadway facilities without ITS enhancements. It is left
The various adjustments necessary to account for less-than-ideal conditions are summarized in Table 1-3 for each type of facility. The importance of roadway, control, and traffic characteristics is twofold. First, the variables discussed are important factors involved in the capacity analysis computations described in this manual. Second, these conditions define the parameters that planners and engineers may consider changing to improve capacity and level of service. The engineer has, to varying degrees, control over the geometric and control parameters discussed. Through construction, reconstruction, or spot improvements, improvements can be made in lane widths, shoulder widths, the number of lanes, horizontal and vertical alignment, and other geometric factors. Through regulation and signalization, all of the control variables are subject to alteration. These are the tools that can be used to address capacity or service deficiencies. One of the most important uses of the procedures in this manual is in the evaluation of alternative improvement plans based on such changes.
T In the case of freeways and other uninterrupted flow facilities, ITS strategies may be able to achieve some decrease in headways, which would tend to increase the capacity of these facilities. In addition, improvements in level of service may be achieved even with no increase in headways if vehicle guidance systems can offer drivers a greater level of comfort than they currently experience in driving conditions with closely spaced headways. T For signalized intersections and arterials, any potential decrease in headways and headway variability would initially be less significant than it would be on uninterrupted flow facilities. The major benefits of ITS for signal and arterial operations would be more efficient allocation of green time. T At unsignalized intersections, capacity improvements related to ITS would tend to occur if assistance were provided to drivers in judging gaps in opposing traffic streams or if gaps were controlled. Many of the roadway improvements related to ITS are systemlevel improvements, such as incident response and driver information systems. Although these improvements will provide benefits to the overall roadway system, they are not expected to have an impact on the methods used to calculate capacity for individual roadway facilities.
Updated December 1997
principles of capacity
1-8
Table 1-3. Adjustment Factors Used for Analyses factors facility
roadway
traffic
control
Uninterrupted Flow Facilities Freeways—basic sections
T T T T T
Lane width Lateral clearance Grade Number of lanes Interchange density
Freeways—weaving
T Same as basic sections, except interchange density, plus T Configuration T Length T Number of lanes
T Same as basic section, plus T Volume ratio T Weaving ratio
Freeways—ramp junctions
T Adjacent ramp configuration T Number of lanes
T Peak-hour factor T Heavy vehicles
Freeways—ramp roadways
T Lane width T Number of ramp lanes
T Heavy vehicles
Two-lane highways
T T T T T
Multilane highways
T Same as freeways, basic sections, except interchange density, plus T Development environment
Signalized intersections
T T T T T T
Unsignalized intersections
T Grade T Number of lanes T Type of lanes
T Peak-hour factor T Heavy vehicles T Turning movements
T Stop control T Upstream signals
Urban arterials
T Same as signalized intersections, plus arterial classification
T Same as signalized intersections, plus free flow speed
T Same as signalized intersections
Transit
T (Level of service within vehicle depends on space per passenger) T Number of lanes T Station and stop design
T Peaking
T Length of bus stop T Fare collection practices
Pedestrians—walkways
T Effective width
T Peaking
Bicycles—bike lanes
T Number of lanes T Turning traffic T Percent heavy vehicles
T Turning traffic T Percent heavy vehicles
Design speed Percent no passing Lane width Shoulder width Grade
T T T T
Peak-hour factor Heavy vehicles Driver type Free flow speed
T Metering rate
T Directional split T Peak-hour factor T Heavy vehicles
T Same as freeways, basic sections
Interrupted Flow Facilities
Updated December 1997
Lane width Area type Grade Number of lanes Type of lanes Turning radius
T T T T T T T T
Lane utilization Peak-hour factor Heavy vehicles Right turns Left turns Pedestrian activity Parking Bus stops
T T T T T
Phasing Green time Cycle length Signal progression Upstream filtering/ metering
introduction, concepts, and applications
1-9
III. APPLICATIONS MODELS OF TRAFFIC FLOW
Models are used to represent the operation of transportation facilities and to facilitate analysis. Field data on traffic characteristics and measures of effectiveness may be considered the simplest type of model; equations solved by a pencil-and-worksheet method are another type. Computer models in the form of software may range from the automation of worksheets to simulations that track the detailed behavior of individual vehicles in space and time. Level of service may be estimated by computer models, provided that T Input parameters, such as free-flow speed or saturation flow rate, are determined in a manner consistent with the procedures described in this manual; and T The measures of effectiveness estimated by the model are consistent with their definitions in this manual. They must either be calculated using the procedures described here or verified and calibrated with field data obtained using methods from this manual. It is the analyst’s responsibility to select the appropriate model for solving a given problem. When the analysis requires consideration of the interaction between elements, over-capacity conditions, or other situations not currently covered in this manual, use of models that produce outputs convertible to the measures of effectiveness used in this manual may be appropriate. The analyst must understand the underlying assumptions of the selected model(s) to be able to perform any calibration required, to recognize that differences may result from use of alternative methodologies, and to present the results in the context of the model used. LEVELS OF ANALYSIS
Most of the procedural chapters address three different computational applications: operational analysis, design, and planning analysis. The operational analysis is used for the detailed determination of the operating conditions. It is appropriate mainly for short-term situations in which the basic factors are well known or can be reasonably estimated. Design procedures, where provided, can be used to determine specific geometric or control parameters to yield the desired level of service. The planning analysis is more general, but is useful for longer-range determination of the type and size of a facility. It should be noted that for any given facility, the operation, design, and planning applications are based on the same principles and basic method. The selection of an appropriate level is the responsibility of the analyst or designer. Availability of the procedures for all three levels of analysis in this manual is shown in Table 1-4. Operational Analysis
In this application, known or projected traffic flow rates and characteristics are compared with known or projected highway
Table 1-4. Analysis Techniques level of analysis type of facility
operational
design
planning
Freeways Basic segments Weaving areas Ramp junctions Multilane highways Two-lane highways Signalized intersections Unsignalized intersections Urban or suburban arterials Transit Pedestrians Bicycles
X X X X X X X X X X X
X X — X — X X — X — —
X — — X X X X X X — —
NOTE: X = addressed in this manual; — = not addressed in this manual.
descriptions to estimate the level of service that exists or is expected to prevail. For existing facilities, this estimation requires detailed information on traffic characteristics, including volumes, peak-hour factors, directional distributions, and vehicle type distributions. All geometric conditions for the facility must be known, including number and width of lanes, shoulder clearances, design speeds, grades, and horizontal and vertical alignments. Where traffic controls exist, such as at signalized intersections, they must be completely specified, including the type of control, cycle length, phasing, green time allocation, and other factors. All other types of control must also be specified. For planned or future facilities, the same type of information is required. It would, however, be based on traffic projections and planned facilities instead of on field-measured data. Operational analysis allows for an evaluation of base year and future levels of service on an existing facility. This evaluation, however, is not its most powerful use. Operational analysis can be used to evaluate the level of service that would result from alternative spot and section improvements to an existing facility. The operational impacts of various improvement measures can be estimated and compared and a rational decision made using the results and other relevant information. Alternative designs for new facilities can be similarly evaluated using the operational analysis approach. Most of the procedures allow not only a determination of level of service, but also an estimation of the value of critical performance parameters. For a freeway segment, density and speed of the traffic stream can be estimated, and for a signalized intersection, average control delay can be estimated. Thus an operational analysis not only yields a determination of the level of service (which covers a range of conditions), but it also provides values of operational parameters. An alternative use of operational analysis is to determine the service flow rates allowable under varying operational (LOS) assumptions. Such analyses are extremely useful in evaluating the Updated December 1997
1-10
principles of capacity
sensitivity of service flow rates to various design or LOS assumptions.
Design
The design application is keyed to a specific objective: to determine the number of lanes required on a particular facility or in a given corridor to provide for a specified level of service. The design application of capacity analysis procedures treats this aspect of the overall ‘‘design process’’ and may also be used to assess the impact of such design variables as lane and shoulder width, lateral clearance, grades, lane use allocations, and other features. Detailed data on expected traffic volumes and characteristics are required, as is the assumption of geometric standards to be used in the design: lane widths, lateral clearances, design speeds, and horizontal and vertical alignment. Design of signal timings may also be accomplished using the procedures presented in Chapter 9, Signalized Intersections, in an iterative process. Design computations are generally limited in scope and may result in the generation of alternatives that are subsequently subjected to detailed operational analyses.
Planning Analysis
Planning analysis represents a broad assessment of the levels of service. Capacity and LOS analysis in transportation planning addresses such questions as the following: T What is the maximum number of people or vehicles that can be accommodated within a specified time period? T What will be the future level of service on an existing or planned facility? T What lane configurations or signalization characteristics are needed for various traffic flow levels on an arterial road considered in a land use plan? The planning applications are frequently intended to produce estimates at the earliest stages of planning when the amount, detail, and accuracy of information are limited. Planning procedures are often based on forecasts of average annual daily traffic and on assumed traffic, roadway, and control conditions. Typical characteristics appear in many chapters and may be used as default values. It should be recognized that extensive use of default values may lead to errors where prevailing conditions differ substantially from those assumed. Therefore, during subsequent project planning and development stages, generalized planning applications should be refined as more information becomes available. The analytical process during these later stages may reach the design or operational level.
PRECISION
The results of capacity computations are no more precise or accurate than the information of data used as inputs to the analysis. Thus where traffic counts are only accurate to within 5 percent, or where projections are subject to even larger errors, computations cannot be expected to be accurate to the nearest vehicle per hour or mile per hour. Updated December 1997
All tabulated service flow rates in this manual have been rounded to the nearest 50 vehicles per hour, and analysts may wish to round all computational results in this manner as well. Traffic volume and capacity values rounded only to the nearest vehicle provide a spurious sense of precision and should be avoided. Because each of the factors used in capacity and LOS analyses is subject to a ‘‘plus or minus’’ accuracy, the results of such calculations should not be presented in a way that portrays them as absolute and precise values. For example, if a delay estimate at a signalized intersection is calculated at 25.4 sec, presentation of the results should be rounded to the nearest second, and in fact, the true delay might be in the range of 25 sec 6 10 percent. In practice, the values calculated for measures of effectiveness might be assumed to have a precision range of 6 5 to 10 percent. Where future traffic volumes are used in the analysis, the source of these volumes should be identified when the results are reported.
FIELD DATA
The procedures in this manual have been calibrated to estimate performance parameters such as speed, density, and delay on the basis of existing or forecast traffic volumes. Basic volume characteristics such as vehicle types, peak-hour factor, directional distribution, and hourly variations are normally required to conduct capacity and LOS analyses. The analysis procedures are mainly keyed to traffic volume characteristics because volume is the most readily and often measured traffic stream parameter and is usually the easiest to predict for future conditions. The various performance procedures are based on average conditions throughout North America. They reflect normalized estimates of capacity and level of service, assuming that a given facility operates like the national average of facilities with the same physical, control, and traffic characteristics. The relationships between volume and performance are subject to variance because of local driving habits and other factors. Thus estimations of operational criteria will rarely duplicate exactly field-measured values at specific locations. Therefore field measurements of existing traffic performance are desirable. It is possible to measure operational variables directly on existing facilities. LOS determinations may then be made by comparing field-measured values against the defined criteria. This procedure is discussed in each chapter. It must be done with some care because criteria are often defined for ideal or other specified conditions. For example, the densities defining level of service for freeways and multilane highways are specified in passenger cars per mile per lane. Field-measured values in vehicles per mile per lane would have to be converted to passenger car units before comparison with the established criteria. Where local data are available in sufficient sample quantities and in an acceptable form, they may be used to fine tune the procedures presented herein. Several chapters contain specific recommendations on when and how such adjustments should be made. Procedures specify certain average relationships and values, determined for average U.S., and in some instances Canadian, conditions. The procedures can often be made more accurate by substituting local calibrations for these average values. Examples of local calibrations that could be used include flow-density-speed relationships for multilane facilities and saturation flow rates for signalized intersections.
introduction, concepts, and applications When such substitutions are made, care must be taken that local data and calibrations are for the same base conditions as those described in this manual. A saturation flow rate for a 10-ft lane should not be substituted for this manual’s value applied to a 12-ft lane without consideration of the impact on lane width, grade, and other adjustment factors, for example. There is no substitute for correctly collected and adequately presented field data. A capacity analysis based on inaccurate roadway, traffic, and control information will produce erroneous results. The results of computations will not be more accurate than the input data on which they were based.
SUMMARY
HCM contains a set of analysis procedures that provide estimates of the performance of a variety of traffic facilities on the
1-11
basis of known or projected roadway, traffic, and control conditions under current vehicle technology. Performance criteria also can be set at desired levels and corresponding traffic, roadway, or control conditions estimated. The results of the procedures provide important comparative information to the engineer or planner. These results should be used with other relevant information to formulate recommendations on highway, transit, and pedestrian improvements. Although some local authorities have made use of the techniques included in this manual mandatory for traffic analyses, no computation based on these procedures should be construed as mandating or requiring the implementation of a particular improvement or design alternative. The professional judgment of the engineer or planner is a necessary input to such decisions. This manual is an important guide to decision making, but the results of capacity analysis do not replace the need to consider local legal, societal, environmental, behavioral, and other specific requirements, constraints, and conditions.
Updated December 1997
chapter 2
TRAFFIC CHARACTERISTICS
CONTENTS
INTRODUCTION ....................................................................................................................................................................................
2-2
PART A. BASIC VARIABLES OF TRAFFIC FLOW .........................................................................................................................
2-2
i.
uninterrupted flow............................................................................................................................................................. Volume and Rate of Flow..................................................................................................................................................... Speed...................................................................................................................................................................................... Density ................................................................................................................................................................................... Spacing and Headways.......................................................................................................................................................... Mathematical Relationships .................................................................................................................................................. Relationships Among Basic Variables..................................................................................................................................
2-2 2-2 2-3 2-4 2-5 2-5 2-5
ii.
interrupted flow.................................................................................................................................................................. Signalized Intersections......................................................................................................................................................... Saturation Flow Rate and Lost Time.................................................................................................................................... Unsignalized Intersections..................................................................................................................................................... Delay ...................................................................................................................................................................................... Speed......................................................................................................................................................................................
2-6 2-6 2-7 2-8 2-9 2-9
PART B. OBSERVED VALUES ...........................................................................................................................................................
2-9
i.
national roadway traffic trends .................................................................................................................................... 2-10
ii.
volumes and flow rates ..................................................................................................................................................... Freeways ................................................................................................................................................................................ Multilane Highways .............................................................................................................................................................. Rural Two-Way, Two-Lane Highways................................................................................................................................. Urban Arterials ......................................................................................................................................................................
2-10 2-10 2-10 2-11 2-11
iii.
volume characteristics ....................................................................................................................................................... Temporal Variations .............................................................................................................................................................. Seasonal and Monthly Variations.................................................................................................................................... Daily Variations ............................................................................................................................................................... Hourly Variations............................................................................................................................................................. Peak Hour and Design Hour............................................................................................................................................ Subhourly Variations in Flow.......................................................................................................................................... Spatial Distributions .............................................................................................................................................................. Directional Distribution.................................................................................................................................................... Lane Distribution.............................................................................................................................................................. Traffic Composition .............................................................................................................................................................. Impact of Weather on Maximum Volumes..........................................................................................................................
2-12 2-12 2-15 2-15 2-16 2-16 2-18 2-19 2-19 2-20 2-21 2-21
iv.
speed characteristics ........................................................................................................................................................... National Speed Trends .......................................................................................................................................................... Speed Variation by Time of Day.......................................................................................................................................... Speed Variation by Lane and Day Versus Night.................................................................................................................
2-24 2-24 2-26 2-27
v.
measured relationships for uninterrupted flow ......................................................................................................... Speed-Flow Relationships ..................................................................................................................................................... Freeways........................................................................................................................................................................... Multilane and Two-Lane Rural Highways......................................................................................................................
2-28 2-28 2-28 2-29
2-1
Updated October 1994
principles of capacity
2-2
Density-Flow Relationships .................................................................................................................................................. 2-29 Headway Distributions and Random Flow........................................................................................................................... 2-30 vi.
interrupted flow facilities................................................................................................................................................ 2-31 Saturation Flow and Lost Time at Signalized Intersections ................................................................................................ 2-31 Gap Acceptance and Saturation Flow at Unsignalized Intersections .................................................................................. 2-33
vii.
summary .................................................................................................................................................................................. 2-33
REFERENCES ......................................................................................................................................................................................... 2-34
INTRODUCTION Chapter 1 identified the objectives and the contents of the manual and explained the basic concepts of capacity and level of service. The focus of this chapter is on basic characteristics of uninterrupted and interrupted traffic flow. Transit, pedestrian, and bicycle characteristics are discussed in Chapters 12, 13, and 14, respectively. In Part A of this chapter, variables such as volume and rate of flow, speed, density, spacing and headways, saturation flow rates, lost times, and delay are introduced. All of these variables, important from the capacity assessment point of view, are discussed separately for uninterrupted and interrupted traffic flow. In Part B a sampling of national observations of key capacity and level-of-service variables, including some measured or fitted relationships among them and their variation in time and space, is presented. It is important to recognize the impact of these charac-
teristics on roadway operations, and therefore on the planning and design requirements of transportation facilities, as well as to note the variation from national averages that occur because of unique local conditions. The procedures of this manual are based on calibrated ‘‘national average’’ traffic characteristics observed over a range of facilities of each type. Observations of these characteristics at specific locations will vary somewhat from national averages because of local driving habits and unique features of the local driving environment. In this chapter the characteristics that have been observed are addressed, and they are related to the values used in capacity analysis procedures of subsequent chapters. Information on traffic parameters not explicitly used in analysis procedures, but whose impact on capacity and level of service is important, is also presented.
PART A. BASIC VARIABLES OF TRAFFIC FLOW Three basic variables—volume or rate of flow, speed, and density—can be used for the description of traffic states on any roadway facility. The procedures of the manual apply volume or traffic flow as a variable common to both uninterrupted and interrupted traffic flow, but speed and density are used mostly for uninterrupted flow. Some variables related to flow rate, such as spacing and headway, are also used for both types of facilities, whereas other variables, such as saturation flow or gap, are specific to interrupted flow.
Section A-I deals with the variables of uninterrupted traffic flow, including the conceptual relationships among them. Section A-II explains the concepts of traffic operations on interrupted flow facilities. Principles of transit and pedestrian flow and measures of effectiveness used to analyze capacity and level of service for transit and pedestrian facilities are defined in Chapters 12 and 13, respectively.
I. UNINTERRUPTED FLOW The operational state of any given traffic stream on an uninterrupted traffic flow facility is defined by three primary measures: T Volume and/or rate of flow, T Speed, and T Density. Spacing and headways are directly related to these primary measures. Updated October 1994
VOLUME AND RATE OF FLOW
Volume and rate of flow are two measures that quantify the amount of traffic passing a point on a lane or roadway during a designated time interval. These terms are defined as follows: T Volume—the total number of vehicles that pass over a given point or section of a lane or roadway during a given time interval;
traffic characteristics volumes may be expressed in terms of annual, daily, hourly, or subhourly periods. T Rate of flow—the equivalent hourly rate at which vehicles pass over a given point or section of a lane or roadway during a given time interval less than 1 hr, usually 15 min. Volume and flow are the variables used to quantify demand, that is, the number of vehicle occupants or drivers (usually expressed as the number of vehicles) who desire to use a given facility during a specific time period. Congestion influences demand patterns, and observed volumes are sometimes more a reflection of capacity constraints than of true demand. The distinction between volume and rate of flow is important. Volume is an actual number of vehicles observed or predicted to be passing a point during a time interval. Rate of flow represents the number of vehicles passing a point during a time interval less than 1 hr, but expressed as an equivalent hourly rate. A rate of flow is found by taking the number of vehicles observed in a subhourly period and dividing it by the time (in hours) over which they were observed. Thus, a volume of 100 vehicles observed in a 15-min period implies a rate of flow of 100 veh/0.25 hr or 400 vph. The following examples further illustrate the difference between hourly volumes and flow rates.
flow, when vehicles arrive at a rate of 4,800 vph—even though volume is less than capacity over the full hour. This is a serious situation, because the dynamics of dissipating a breakdown may extend the effects of congestion up to several hours beyond the time of the breakdown. These dynamics are discussed in greater detail in Chapter 6. Peak rates of flow are related to hourly volumes through the use of the peak-hour factor. This factor is defined as the ratio of total hourly volume to the peak rate of flow within the hour: PHF =
Volume (veh)
Rate of Flow (vph)
5:00–5:15 5:15–5:30 5:30–5:45 5:45–6:00 5:00–6:00
0 200 200 0 400
0 800 800 0
Volumes were observed for four consecutive 15-min periods. The total volume is 400 vehicles, or the sum of the four counts. The rate of flow, however, is zero in two 15-min intervals and 800 vph in the two other 15-min intervals. Thus, a design based on the hourly volume (400 vph) would not prove adequate.
Hourly volume Peak rate of flow (within the hour)
(2-1)
If 15-min periods are used, the PHF may be computed as PHF = V/(4 × V15)
(2-2)
where PHF = peak-hour factor, V = hourly volume (vph), and V15 = volume during the peak 15 min of the peak hour (veh/ 15 min). Where the peak-hour factor is known, it may be used to convert a peak-hour volume to a peak rate of flow, as follows:
Example 1: Employee Parking Lot Exit to Highway Time Period
2-3
v = V/PHF
(2-3)
where v = rate of flow for a peak 15-min period (vph), V = peak-hour volume (vph), and PHF = peak-hour factor. Equation 2-3 need not be used to estimate peak flow rates where traffic counts are available. The chosen count interval must allow the identification of the maximum 15-min flow period. The rate may then be directly computed as 4 times the maximum 15-min count. Many of the procedures use this conversion to allow computations to focus on the peak flow period within the peak hour.
Example 2: Highway The following traffic counts were made during an hour-long study period: Time Period
Volume (veh)
Rate of Flow (vph)
5:00–5:15 5:15–5:30 5:30–5:45 5:45–6:00 5:00–6:00
1,000 1,200 1,100 1,000 4,300
4,000 4,800 4,400 4,000
Volumes were observed for four consecutive 15-min periods. The total volume for the hour is the sum of these counts, or 4,300 veh, or 4,300 vph (since they were observed for 1 hr). The rate of flow, however, varies within each 15-min period. During the 15-min period of maximum flow, the rate of flow is 1,200 veh/0.25 hr, or 4,800 vph. Note that 4,800 vehicles do not pass the point in question during the study hour, but they do pass the point at that rate for 15 min. Consideration of peak flow rates is critically important in capacity analysis. If the capacity of the above segment of highway were 4,500 vph, it would break down during the peak 15-min period of
SPEED
Whereas traffic volumes provide a method of quantifying capacity values, speed (or its reciprocal—travel time) is an important measure of the quality of traffic service provided to the motorist. It is used as an important measure of effectiveness defining levels of service for many types of facilities, such as rural two-lane highways, arterials, freeway weaving sections, and others. Speed is defined as a rate of motion expressed as distance per unit time, generally as miles per hour (mph) or kilometers per hour (km/hr). In characterizing the speed of a traffic stream, some representative value must be used, because there is generally a broad distribution of individual speeds that may be observed in the traffic stream. For the purposes of this manual, the speed measure used is average travel speed. This measure is used because it is easily computed from observation of individual vehicles within the traffic stream and because it is the most statistically relevant measure in relationships with other variables. Average travel speed is computed by taking the length of the highway or street section or segment under consideration and dividing it by the average travel time of vehicles traversing the segment. Thus, Updated October 1994
principles of capacity
2-4
if travel times t1, t2, t3, . . ., tn are measured for n vehicles traversing a segment of length L, the average travel speed would be L
S= n
o
i=1
=
nL
(2-4)
n
ti /n
o
i=1
ti
where S = average travel speed (mph), L = length of the highway segment (mi), ti = travel time of the ith vehicle to traverse the section (hr), and n = number of travel times observed. Consider the following travel times observed for vehicles traversing a 1-mi segment of highway: 1.0 min (0.0167 hr), 1.2 min (0.0200 hr), 1.7 min (0.0283 hr), and 1.1 min (0.0183 hr). The average travel time is found as (0.0167 + 0.0200 + 0.0283 + 0.0183)/4 = 0.0208 hr. The average travel speed is the distance (1 mi) divided by this time, or S = 1.0 mi/0.0208 hr = 48 mph The travel times used in this computation include stopped delays due to fixed interruptions or traffic congestion. They are total travel times to traverse the defined roadway length. Several different speed parameters can be applied to a traffic stream. These include the following: 1. Average running speed—This is also called ‘‘space mean speed’’ in the literature. It is a traffic stream measurement based on the observation of vehicle travel times traversing a section of highway of known length. It is defined as the length of the segment divided by the average running time of vehicles to traverse the segment. ‘‘Running time’’ includes only time that vehicles spend in motion. 2. Average travel speed—This is also a traffic stream measure based on travel time observations over a known length of highway. It is defined as the length of the segment divided by the average travel time of vehicles traversing the segment, including all stopped delay times. It is also a ‘‘space mean speed,’’ because the use of average travel times effectively weights the average according to the length of time a vehicle occupies the defined roadway segment or ‘‘space.’’ 3. Space mean speed—This is a statistical term frequently used in the literature to denote an average speed based on the average travel time of vehicles to traverse a segment of roadway. It is called a ‘‘space’’ mean speed because the use of average travel time essentially weights the average according to the length of time each vehicle spends in the defined roadway segment, or ‘‘space.’’ 4. Time mean speed—This is the arithmetic average of speeds of vehicles observed passing a point on a highway and is also referred to as the ‘‘average spot speed.’’ Individual speeds of vehicles passing a point are recorded and are arithmetically averaged. Most of the procedures using speed as a measure of effectiveness in this manual use average travel speed as the defining parameter. For uninterrupted flow facilities not operating at LOS F, the average travel speed is equal to the average running speed. Updated October 1994
Figure 2-1. Typical relationship between time mean and space mean speed. (Source: Ref. 1)
Figure 2-1 shows a typical relationship between time mean and space mean speeds. Space mean speed is always slower than time mean speed, with the difference decreasing as the absolute value of speed increases. This relationship is based on statistical analysis of observed data and is useful, because time mean speeds are often easier to measure in the field than space mean speeds. For capacity analysis, speeds are best measured by observing travel times over a known length of highway. For uninterrupted flow facilities operating in the range of stable flow, the length taken may be as short as several hundred feet for ease of observation. Radar meters or other devices can be used to measure speeds at a point. Such speeds, when averaged, yield a time mean speed. It is possible to compute a space mean speed for a very short segment of highway using radar or other observations of individual vehicle speeds by calculating the harmonic, rather than the arithmetic, mean of the observations. When used as a measure of effectiveness, speed criteria must recognize driver expectations and roadway function. Thus, a driver expects a higher speed on a freeway than on an urban arterial. Lower speeds will be tolerated on a roadway with more severe horizontal and vertical alignment, since drivers will not be comfortable driving at extremely high speeds. Level of service criteria reflect these and other points. DENSITY
Density is defined as the number of vehicles occupying a given length of a lane or roadway at a particular instant. For the purposes of computations in this manual, density is averaged over time and is usually expressed as vehicles per mile (vpm). Direct measurement of density in the field is difficult, requiring a vantage point from which significant lengths of highway can be photographed, videotaped, or observed. It can be computed, however, from the average travel speed and rate of flow, which are more easily measured. D = v/S where v = rate of flow (vph),
(2-5)
traffic characteristics S = average travel speed (mph), and D = density (vpm). Thus, a highway segment with a rate of flow of 1,000 vph and an average travel speed of 50 mph would have a density of
2-5
between pairs of vehicles. The speed would be that of the second vehicles in an individual pair of vehicles. Flow rate is related to the average headway of the traffic stream: Flow rate (vph) = 3,600 (sec/hr)/headway (sec/veh) (2-8)
D = 1,000 vph/50 mph = 20 vpm RELATIONSHIPS AMONG BASIC VARIABLES
Density is a critical parameter for uninterrupted flow facilities because it characterizes the quality of traffic operations. It describes the proximity of vehicles to one another and reflects the freedom to maneuver within the traffic stream. Roadway occupancy is frequently used as a surrogate for density in control systems because it is easier to measure. Occupancy in space is defined as the proportion of roadway length covered by vehicles, and occupancy in time identifies the proportion of time a roadway cross section is occupied by vehicles. Under the assumption of a homogeneous traffic flow, or for a known traffic flow composition, these two types of occupancy can be taken as equal and used for the derivation of density.
SPACING AND HEADWAYS
Spacing is defined as the distance between successive vehicles in a traffic stream, as measured from front bumper to front bumper. Headway is the time between successive vehicles as they pass a point on a lane or roadway, also measured from front bumper to front bumper. These characteristics are considered to be ‘‘microscopic,’’ since they relate to individual pairs of vehicles within the traffic stream. Within any traffic stream, both spacing and headway of individual vehicles are distributed over a range of values, which are generally related to the speed of the traffic stream and prevailing conditions. In the aggregate, these ‘‘microscopic’’ parameters are related to the ‘‘macroscopic’’ flow parameters density and rate of flow. Headways are used as part of the Chapter 8 methodology to estimate percent time delay in a two-lane rural highway traffic stream. Defined as the percentage of total time vehicles are delayed in an involuntary queue on a two-lane highway, ‘‘percent time delay’’ is estimated as the percentage of vehicle headways less than or equal to 5 sec.
MATHEMATICAL RELATIONSHIPS
Spacing is a distance measure, in feet. It can be measured directly by measuring the distance between common points on successive vehicles at a particular instant. This generally requires complex aerial photographic techniques, so that spacing is usually derived from other direct measurements. Headway, on the other hand, can be more easily measured using stopwatch observations as vehicles pass a point on the roadway. The average vehicle spacing in a traffic stream is directly related to the density of the traffic stream: Density = 5,280/spacing
(2-6)
The relationship between average spacing and average headway in a traffic stream is dependent on speed: Headway (sec/veh) = spacing (ft/veh)/speed (ft/sec) (2-7) This relationship also holds for individual headways and spacings
Equation 2-5 cites the basic relationship among the three variables describing an uninterrupted traffic stream. Although the equation v = S × D algebraically allows for a given rate of flow to occur at an infinite number of combinations of speed and density, there are additional relationships restricting the variety of flow conditions that may exist at any given location. Figure 2-2 shows a generalized representation of these relationships (2), which form the philosophical basis for the capacity analysis of uninterrupted flow facilities. Although more sophisticated theories of traffic flow exist, a linear speed-density relationship simplifies the discussion. The flow-density function is placed directly below the speed-density relationship because of their common horizontal scales, and the speed-flow function is placed next to the speed-density relationship because of their common vertical scales. Speed is represented by space mean speed. The actual form of these functions depends on the prevailing traffic and roadway conditions on the roadway segment under study and on the length of the segment considered in the determination of density. Although the diagrams in Figure 2-2 show continuous curves, it is unlikely that the full range of the functions will be found at any particular measurement location. Surveyed data usually show discontinuities in which a part of these curves is not present. May (2) illustrates and discusses the reasons for these gaps. The curves of Figure 2-2 illustrate a number of significant points. Note that a zero rate of flow occurs under two very different conditions: 1. When there are no cars on the facility, density is zero, and rate of flow is also zero. Speed is purely theoretical for this condition and would be whatever the first driver would select—presumably a high value. This speed is represented by Sf in the graphs. 2. When density becomes so high that all vehicles stop (speed is zero), the rate of flow is also zero, because there is no movement and vehicles cannot ‘‘pass’’ a point on the roadway. The density at which all movement stops is called jam density, denoted by Dj in the diagrams. Between these two extreme points, the dynamics of traffic flow produce a maximizing effect. As density increases from zero, rate of flow also increases, since more vehicles are on the roadway. While this is happening, speed begins to decline (because of the interaction of vehicles). This decline is virtually negligible at low and medium densities and rates of flow. As density continues to increase, these generalized curves suggest that speed decreases significantly before the capacity is achieved. Capacity is reached when the product of density and speed results in the maximum rate of flow. This condition is shown as optimum speed So (often called critical speed), optimum density Do (sometimes referred to as critical density), and maximum flow vm. The slope of any ray line drawn from the origin of the speedflow curve to any point of the curve represents density, based on Equation 2-5. Similarly, a ray line in the density-flow graph Updated October 1994
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principles of capacity
Figure 2-2. Generalized relationships among speed, density, and rate of flow on uninterrupted flow facilities. (Based on May, Ref. 2) represents speed. As examples, Figure 2-2 shows the average free flow speed and speed at capacity, as well as optimum and jam densities. The three diagrams shown in the figure are obviously redundant, since if any one relationship is known, the other two are uniquely defined. Whereas the speed-density function is used mostly for theoretical work, the other two are used in the manual to define the levels of service. As shown in Figure 2-2, any rate of flow other than capacity can occur under two different conditions, one with a high speed and low density and the other with high density and low speed. The high-density, low-speed side of the curves represents forced
or breakdown flow. Sudden changes in the state of traffic (i.e., in speed, density, and rate of flow) may occur. LOS A through E are defined on the low-density, high-speed side of the curves, with the maximum flow boundary of LOS E placed at capacity, whereas LOS F, used to describe congested traffic, is represented by the high-density, low-speed part of the functions. Examples of recent measurements of the speed-flow relationships are shown and discussed in Part B. Although they feature overall trends similar to the functions in Figure 2-2, they differ in details, mostly because they are based on flow rates averaged over longer time intervals.
II. INTERRUPTED FLOW Interrupted flow is more complex than uninterrupted flow because of the time dimension involved in the allocation of space to conflicting traffic streams. Flow on an interrupted flow facility is usually dominated by points of fixed operation, such as traffic signals and stop signs. These control measures have differing impacts on overall flow. A detailed discussion of flow at signalized intersections is contained in Chapter 9, and information for stop signs is presented in Chapter 10. Arterial roadway flow is discussed in Chapter 11. The operational state of traffic at an interrupted traffic flow facility is defined by the following measures: T Volume and/or rate of flow; T Saturation flow and/or departure headways; T Control variables: parameters of stop or signal control; T Gaps available in the conflicting traffic streams; and T Delay. The discussion of volume and rate of flow in the first part of this chapter is also applicable to interrupted flow facilities. An imporUpdated October 1994
tant additional point is the screenline at which the traffic volume or rate of flow is surveyed. Traditional intersection traffic counts yield only the number of vehicles that have departed through the intersection. The maximum flow is therefore limited to the capacity of the facility. Where demand exceeds capacity and a growing queue is forming, it is advisable to survey traffic demand further upstream, before the influence of the congestion. From the capacity computation point of view, speed and density are less important than on uninterrupted flow facilities.
SIGNALIZED INTERSECTIONS
The most significant source of fixed interruptions on interrupted flow facilities is a traffic signal. At traffic signals, flow in each movement or set of movements is periodically halted. Thus, movement on a given set of lanes is only possible for a portion of total time, because the signal prohibits movement during some periods.
traffic characteristics Only the time during which the signal is effectively green is available for movement. For example, if one set of lanes at a signalized intersection receives a 30-sec effective green time out of a 90-sec total cycle, only 30/90 or 1/3 of total time is available for movement on the subject lanes. Thus, out of each hour of real time, only 20 min is available for flow on the lanes. Provided the lanes could accommodate a maximum rate of flow of 1,500 vph if the signal displayed green for a full hour, they could accommodate a total rate of flow of only 500 vph, since only one-third of each hour is available as green. Because signal timings are subject to change, it is convenient to express capacities and service flow rates for signalized intersections in terms of vehicles per hour of green (vphg). In the previous example, the maximum rate of flow would be stated as 1,500 vphg. This can be converted to a real-time value by multiplying by the ratio of effective green time to cycle length for the signal. When the signal turns green, the dynamics of starting a stopped queue of vehicles must be considered. Figure 2-3 shows a queue of vehicles stopped at a signal. When the signal turns green, the queue begins to move. The headway between vehicles can be observed as they cross the stop line of the intersection. The first headway would be the elapsed time, in seconds, between the initiation of the green and the crossing of the rear wheels of the first vehicle over the stop line. The second headway would be the elapsed time between the crossing of rear wheels of the first and second vehicles over the stop line. Subsequent headways would be similarly measured. The driver of the first vehicle in the queue must observe the signal change to green and react to the change by releasing the brake and accelerating through the intersection. The first headway will be comparatively long as a result of this process. The second vehicle in the queue follows a similar process, except that the reaction and acceleration period can occur while the first vehicle is beginning to move. The second vehicle will be moving faster than the first as it crosses the stop line, because it has an additional vehicle length in which to accelerate. Its headway will still be comparatively long, but generally less than that of the first vehicle. The third and fourth vehicles follow a similar procedure, each achieving a slightly lower headway than the preceding vehicle.
2-7
After some number of vehicles, N in Figure 2-3, the effect of the start-up reaction and acceleration has dissipated. Successive vehicles now move through past the stop line at a steady speed until the last vehicle in the original queue has passed. The headway for these vehicles will be relatively constant. In Figure 2-3, this constant average headway is denoted as h and is achieved after N vehicles. The headways for the first N vehicles are, on the average, greater than h and are expressed as h + ti, where ti is the incremental headway for the ith vehicle due to the start-up reaction and acceleration. As i increases from 1 to N, ti decreases. Figure 2-4 shows a conceptual plot of headways measured as described previously. Although, for practical reasons, the passage of the fourth vehicle is used as a starting time for saturation flow measurements in this manual, N may occur as late as with the sixth or seventh vehicle (i.e., the start-up and acceleration increment disappears after the sixth or seventh vehicle). The value h is defined as the saturation headway and is estimated as the constant average headway between vehicles occurring after the Nth vehicle in the queue and continuing until the last vehicle in the initial queue clears the intersection. The saturation headway is the amount of time consumed by a vehicle that was in the stopped queue as it passes through a signalized intersection on the green signal, assuming that a continuous queue of vehicles is available to move through the intersection. The definition of the saturation headway on interrupted flow facilities in the manual is different from that of uninterrupted flow headways. For intersections, headway represents the time period between the passage of the rear axle of one vehicle and the passage of the rear axle of the next vehicle over a given cross section on the roadway, whereas the vehicle reference points for uninterrupted flow facilities are usually the front bumpers.
SATURATION FLOW RATE AND LOST TIME
Saturation flow rate is defined as the flow rate per lane at which vehicles can pass through a signalized intersection in such a stable moving queue. By definition, it is computed as s = 3,600/h
(2-9)
where s = saturation flow rate (vphgpl), h = saturation headway (sec), and 3,600 = number of seconds per hour.
Figure 2-3. Conditions at traffic interruption in an approach lane of a signalized intersection.
The saturation flow rate represents the number of vehicles per hour per lane that can pass through a signalized intersection if the green signal were available for the full hour and the flow of vehicles were never halted. This assumes that, in addition to a full hour of green being available, the average headway of all vehicles entering the intersection is h sec. Each time a flow is stopped, it must be started again, and it will experience start-up reaction and acceleration headways shown in Figure 2-4 for the first N vehicles. In this figure, the first six vehicles in the queue experience headways longer than h. The increments, ti, are called start-up lost times. The total start-up lost time for these vehicles is the sum of these increments, or Updated October 1994
principles of capacity
2-8
Figure 2-4. Concept of saturation flow rate and lost time. N
l1 =
o i=1
ti
(2-10)
where l1 = total start-up lost time (sec), and ti = lost time for the ith vehicle in queue (sec). When a queue of vehicles receives a green signal, it will consume h sec per vehicle plus the start-up lost time, l1, assuming that there are at least N vehicles in the queue. Each time a stream of vehicles is stopped, another source of lost time is experienced. As one stream of vehicles stops, safety requires that there be some clearance time before a conflicting stream of traffic is allowed to enter the intersection. During this period, no vehicles use the intersection. This interval is called clearance lost time, l2. In practice, signal cycles provide for this clearance through the use of ‘‘change intervals,’’ which may include yellow or all red indications, or both. Drivers generally cannot observe this entire interval and do use the intersection during some portion of it. The clearance lost time, l2, is the portion of this change interval that is not used by motorists. The relationship between saturation flow rate and lost times is a critical one. For any given lane or movement, vehicles use the intersection at the saturation flow rate for a period of time equaling the available green time plus the change interval minus the startup and clearance lost times. Because the lost times are experienced each time a movement is started and stopped, the total amount of time lost over an hour is related to the signal timing. For instance, if a signal has a 60-sec cycle length, it will start and stop each movement 60 times per hour, and the total lost time per movement will be 60(l1 + l2). If the signal has a 120-sec cycle, each movement will be stopped and started 30 times per hour, and the total lost time per movement will be 30(l1 + l2), half as much as the for the 60-sec cycle. Whereas the preceding discussion suggests that the evaluation of lost time may be rather simple, its determination becomes much Updated October 1994
more complex with an increasing number of phases in a signal cycle. The amount of lost time affects capacity and delay. The preceding logic suggests that the capacity of the intersection increases with increasing cycle length. This is somewhat offset by observations that the saturation headway, h, may increase if the length of continuous green indication becomes very long. Other intersection features may offset the reduction in capacity due to short cycles, such as turning lanes. Longer cycle lengths increase the number of vehicles in the queues and may cause the left-turn lane to overflow, thus reducing capacity by blocking through lanes. As cycle length is increased, the average stopped-time delay per vehicle also tends to increase, assuming that adequate capacity is provided. Delay, however, is a complex variable that is affected by many variables, of which cycle length is only one. Part B of this chapter contains a discussion of the measured values of saturation flow, and Chapter 9 presents analytic relationships among saturation headway, saturation flow rate, lost times, signal timing parameters, and delay. UNSIGNALIZED INTERSECTIONS
The driver on a minor street or a driver turning left from the major street of a two-way stop-controlled intersection faces a judgmental task. A gap must be selected in the priority flow through which to execute the desired movement. The term gap is commonly used to identify headways in the traffic flow on the roadway with the right-of-way at unsignalized intersections. Gap acceptance describes the resulting behavior. The capacity of a minor street approach depends on two factors: 1. The distribution of available gaps in the major street traffic stream, and 2. The gap sizes required by minor street drivers to execute their desired movements. The distribution of available gaps in the major street traffic stream depends on the total volume on the street, its directional distribu-
traffic characteristics tion, the number of lanes on the major street, and the degree and type of platooning in the traffic stream. The gap sizes required by the minor street drivers depend on the type of maneuver (left, through, right) that must be executed, the number of lanes on the major street, the speed of major street traffic, sight distances, the length of time the minor street vehicle has been waiting, and driver characteristics (eyesight, reaction time, age, etc.). The critical gap is the minimum interval between two successive vehicles in the major traffic stream that allows intersection entry to one minor street vehicle. Note that critical gap has been redefined in this update of the manual. When more than one minor street vehicle uses one major street gap, the time between two subsequent vehicles is called follow-up time. In general, the follow-up time is shorter than the critical gap. At an all-way stop-controlled intersection, all drivers must come to a complete stop. The decision to proceed is based in part on the ‘‘rules of the road,’’ which suggests that the driver on the right has the right-of-way, and is also a function of the traffic condition on the other approaches. The capacity procedures are based on analyzing each intersection approach independently. The departure headway for the subject approach is defined as the difference between the successive times of departure of that vehicle and the previous departing vehicle on the subject approach. A departure headway is considered to be a saturation headway if there was already a vehicle ahead of the given vehicle at the stop line. If traffic is present on one approach only, vehicles depart as rapidly as individual drivers can safely accelerate into and clear the intersection. If traffic is present on other approaches, the saturation headway on the subject approach will increase somewhat, depending on the degree of conflict between the subject approach vehicles and the vehicles on the other approaches. As at signalized intersections, the vehicle reference points for the determination of saturation headways of the vehicles departing from the stop line of two- and all-way stop-controlled intersection approaches are the rear axles of two consecutive vehicles. For the unobstructed flow of vehicles on the main roadway with the rightof-way at two-way stop-controlled intersections, however, the front bumpers are normally used as reference points, as in other instances of uninterrupted flow. Flow at two- and all-way stop-controlled intersection approaches and analytic relationships relating critical variables to capacity are described in Chapter 10. DELAY
A critical performance measure on interrupted flow facilities is delay. There are several types of delay, but the manual uses only
2-9
average stopped-time delay as the principal measure of effectiveness in evaluating level of service at signalized intersections and average total delay at unsignalized intersections. In the text, it is frequently called only delay. Stopped-time delay is the time an individual vehicle spends stopped in a queue while waiting to enter a signalized intersection. Average stopped-time delay is the total stopped delay experienced by all vehicles in an approach or lane group of a signalized intersection during a designated time period divided by the total volume entering the intersection in the approach or lane group during the same time period, expressed in seconds per vehicle. At two-way stop-controlled and all-way stop-controlled intersections, total delay is defined as the total elapsed time from when a vehicle joins the queue until the vehicle departs from the stopped position at the head of the queue. The use of a similar measure of effectiveness for both signalized and unsignalized intersections provides a means to compare the operation of an intersection under a variety of control conditions. Analysis procedures for arterials (Chapter 11) consider both the travel time between signalized intersections and the delay encountered at intersections. Stopped-time delay is used for signalized intersections because it is a reasonably easy parameter to measure and is conceptually simple. Total delay (sometimes called overall delay) involves movements at slower speeds on intersection approaches, as vehicles move up in queue position or slow down upstream of an intersection. Drivers frequently reduce speed when a downstream signal is red or a queue is present at the downstream intersection approach. Total delay requires the determination of a realistic average speed for each roadway segment and is implied in the estimates of the average travel speed on urban arterial roads.
SPEED
The discussion of speed in the first section of the chapter also applies to roadway segments with signalized or unsignalized intersections. For such interrupted flow facilities, segments on which average travel speed or average running speed is to be determined should be long enough to include those points of fixed interruption of interest. Since travel time lost to flow interruptions is the major component of the evaluation, speed is generally not relevant. Spot speed measurements at these facilities are usually used only for research or enforcement purposes.
PART B. OBSERVED VALUES The procedures in this manual are based on calibrated ‘‘national average’’ traffic characteristics observed over a range of facilities of each type. Observations of these characteristics at specific locations will vary somewhat from national averages because of the local habits and unique features of the local driving environment. The range of traffic characteristics that have been observed are
addressed in this chapter, and they are related to the values used in the capacity analysis procedures of the subsequent chapters. Information on traffic parameters not explicitly used in analysis procedures but whose impact on capacity and level of service is important is also presented in this chapter. Updated October 1994
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principles of capacity
I. NATIONAL ROADWAY TRAFFIC TRENDS The number of motor vehicles in the United States has been steadily increasing, reaching almost 200 million registered vehicles in 1990. The increase during the 10-year period from 1980 represented more than 21 percent (Figure 2-5). The number of passenger cars increased during that period by more than 22 million, and the number of trucks grew by almost 11 million, with most of them in the light truck category. The number of motorcycles decreased from 5.7 million to 4.3 million. Automobiles and light trucks and buses on the rural Interstate system account for about 80 percent of average daily traffic volumes, with heavy trucks and buses representing the remainder (Figure 2-6). Annual travel on the roadways of the United States reached an estimated 2.2 trillion vehicle-miles, or about three times
the level reported in 1960 as shown in Figure 2-7. Travel grew about 54 percent during the 1960s, another 38 percent in the 1970s, and another 41 percent in the 1980s. Travel in urban areas accounted for 1.3 trillion vehicle-miles in 1991, or 60 percent of the total, compared with 44 percent in 1960. The amount of travel in urban areas has increased by almost 50 percent in the 1980s, faster than in rural regions, where the growth was still very significant at 30 percent. Traffic congestion, especially in urban and suburban areas, has become more severe. As a result, traffic and transportation management has gained even more importance. Capacity and level of service analyses are a critical element in the design and evaluation of traffic operations and management.
II. VOLUMES AND FLOW RATES Capacity is defined in terms of the maximum rate of flow that can be accommodated by a given traffic facility under prevailing conditions. The determination of capacity involves the observation of highways of various types operating under high-volume conditions. The direct observation of absolute capacity is difficult to achieve for several reasons. The recording of a high, or even a maximum, volume or rate of flow for a given facility does not ensure that a higher flow could not be accommodated at another time. Further, capacity is sometimes not a stable operating condition. It has sometimes been estimated by fitting parabolic speed-flow or density-flow curves that included both uncongested and congested conditions. The peak of these curves would define capacity. Highest reported volume and flow rate observations on various types of facilities throughout the United States and Canada are discussed in the following sections. It is noted that these reported observations may or may not represent the absolute capacities of the subject highways and that they reflect prevailing conditions at the locations in question. These observations are a sample of high volumes recorded by state and local highway agencies and do not suggest that there are no other facilities experiencing similar, or even higher, volumes. In some cases, auxiliary lanes may be present, resulting in lower actual flows per lane than shown in the tables. The data were collected from the literature and from surveys conducted by the Committee on Highway Capacity and Quality of Service of the Transportation Research Board and by the Federal Highway Administration over a number of years.
daily volumes exceeding 20,000 vehicles per lane operate at or close to capacity during many hours of an average day. Table 22 contains a sample of the maximum reported hourly one-way volumes and the average volumes per lane on rural and urban freeways in the United States. Most volumes in this table exceed 2,000 vehicles per hour per lane, with several freeways featuring average lane volumes of more than 2,400 vphpl. The highest reported lane volumes on selected freeways are given in Table 2-3. Freeway capacity analysis procedures of this manual use a rate of flow of 2,200 pcphpl for freeways with two lanes in one direction and 2,300 for freeways with three or more lanes in one direction as the basic capacity of such facilities under ideal conditions. These are the average per lane capacities across all lanes in a given direction and represent a 200 or 300 pcphpl increase over the values used in earlier manuals. Table 2-2 contains observations of values higher than this standard, but it should be remembered that these are the maximums reported on a given freeway. It should also be noted that an individual lane of a freeway can carry volumes in excess of 2,200 or 2,300 pcphpl. The highest reported volumes per lane are given in Table 2-3 for several freeways with the highest observation close to 2,700 vphpl on a sixlane urban freeway. Note that the peak lane volumes may be substantially higher than the average volumes per lane. The recommended values of 2,200 and 2,300 pcphpl should be considered national averages, around which some variation from region to region and from facility to facility are to be expected. MULTILANE HIGHWAYS
FREEWAYS
The reported average annual daily traffic volumes on selected Interstate highways are given in Table 2-1. Most of these highvolume freeways are found in the largest metropolitan areas. Daily traffic volumes on these heavily used roadways exceed 200,000 vehicles per day. A large number of short Interstate sections in other areas also carry similar volumes. As a rule, all freeways with Updated October 1994
The observation of multilane rural highways operating under capacity conditions is difficult, because such operations rarely occur. Table 2-4, however, does contain some data for four-, six-, and eight-lane highways in suburban settings operating under uninterrupted flow conditions, as well as data for two three-lane bridges. The procedures of this manual assume that the capacity of a surface multilane facility is the same as for four-lane freeways for uninterrupted flow segments—2,200 pcphpl.
traffic characteristics
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Figure 2-5. Motor vehicle registrations.
RURAL TWO-WAY, TWO-LANE HIGHWAYS
URBAN ARTERIALS
High-volume data on two-lane, two-way rural highways in the United States and Canada are difficult to obtain. Such highways rarely operate at volumes approaching capacity, and thus the observation of capacity operations in the field is extremely complex. A sampling of high-volume observations is given in Table 2-5, but it is emphasized that none of these may be taken to represent absolute capacity for the facilities shown. In several cases, the volumes noted were accompanied by good operating conditions. European observations on two-lane, two-way rural highways have been reported at far higher volumes. Volumes of more than 2,700 vph have been observed in Denmark, more than 2,800 in France, more than 3,000 in Japan, and more than 2,450 in Norway. Some of these volumes have contained significant numbers of trucks, some as high as 30 percent of the traffic stream (3). The difficulty in observing capacity operations on two-lane highways in North America presents problems in suggesting a standard value for use in computational procedures. The procedures for such highways, presented in Chapter 8, are based on a combination of field observations and simulation, which suggested that a maximum capacity of 2,800 pcph be adopted, total in both directions under ideal conditions (4). These ideal conditions include a 50/50 directional distribution of traffic. Capacity on twolane rural highways varies with directional distribution and reduces as the split moves away from 50/50 to a minimum value of 2,000 pcph when the split is 100/0.
Since flow on urban arterials is uninterrupted only in the roadway segments between intersections, the interpretation of highvolume observations on urban arterials is not as straightforward as for uninterrupted flow facilities. Signal timing plays a major role in the capacity of such facilities, limiting the portion of time that is available for movement along the arterial at critical intersection locations. The volumes reported in Table 2-6 are shown with the green to cycle time ratios in effect for the subject segments. Flow rates in vehicles per hour of green time are estimated by taking the reported volumes and dividing by the reported green over cycle time ratio. These estimates therefore produce a set of flow observations on a basis comparable with uninterrrupted flow facilities. The prevailing conditions on urban arterials may vary greatly, and such factors as curb parking, transit buses, lane widths, upstream intersections, and similar factors may substantially affect operations and observed volumes. Note that the comparison of maximum flow rates in vehicles per hour of green per lane varies widely for the various size arterials. These observations did not include such factors as left- and right-turn lanes at intersections, which may enhance the capacity of the intersection approach, nor were other prevailing conditions cited. The procedures of Chapter 11 for arterials focus on the issue of level of service. Capacity of the arterial is generally limited by the capacity of signalized intersections, with segment characteristics rarely playing a major role in the determination of capacity. Updated October 1994
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Table 2-1. Maximum Annual Average Daily Traffic Reported on Selected Interstate Routes (1990)
location
section length (mi)
annual average daily traffic (vpd)
average daily traffic per lane (vpdpl)
328,500 270,491 270,400
23,464 19,321 19,314
304,000 288,200 275,883 254,172 253,600 219,300 208,900 208,768
25,333 24,017 22,990 21,181 21,133 18,275 17,408 17,379
330,600 314,000 263,600 242,000 231,200 222,229 220,455 216,390 209,158
33,060 31,400 26,360 24,200 23,120 22,223 22,046 21,639 20,916
280,700 258,800 250,000 241,000 224,600 212,060 210,497 208,590
35,088 32,350 31,250 30,125 28,075 26,508 26,312 26,074
223,200 216,390 210,000
37,200 36,065 35,000
14-Lane Routes I-405, Los Angeles–Long Beach, California I-95, New Jersey Turnpike, NE New Jersey I-95, George Washington Bridge, New York
2.530 0.610 0.470 12-Lane Routes
I-5, Los Angeles–Long Beach, California I-405, Los Angeles–Long Beach, California I-90, Chicago, Illinois I-5, Seattle-Everett, Washington I-8, San Diego, California I-15, San Diego, California I-280, San Francisco–Oakland, California I-95, Northeastern New Jersey
0.500 1.960 1.030 1.260 1.260 2.880 1.880 1.890 10-Lane Routes
I-10, Los Angeles–Long Beach, California I-405, Los Angeles–Long Beach, California I-5, Los Angeles–Long Beach, California I-80, San Francisco–Oakland, California I-210, Los Angeles–Long Beach, California I-95, Northeastern New Jersey I-395, Washington, District of Columbia I-610, Houston, Texas H-1, Honolulu, Hawaii
3.450 3.500 2.100 4.700 5.140 1.620 0.480 1.355 1.690 8-Lane Routes
I-5, Los Angeles–Long Beach, California I-94, Chicago, Illinois I-580, San Francisco–Oakland, California I-10, Los Angeles–Long Beach, California I-90, Chicago, Illinois I-285, Atlanta, Georgia I-635, Dallas–Fort Worth, Texas I-395, Northern Virginia
2.690 3.000 1.750 5.830 1.800 0.210 4.730 1.770 6-Lane Routes
I-880, San Francisco–Oakland, California I-610, Houston, Texas I-680, San Francisco–Oakland, California
2.900 0.304 0.400
SOURCE: Federal Highway Administration
III. VOLUME CHARACTERISTICS Traffic volumes vary in both space and time. These variations are critical determinants of the way highway facilities are used and control many of the planning and design requirements for adequately serving traffic demand. Because traffic volume is not evenly distributed throughout the day, facilities are often designed to meet peak demands occurring for periods as short as 15 min or 1 hr. During other time periods, highways are often underused. Similarly, traffic does not distribute equally over available lanes or directions on a given facility. Whereas the nonuniformity of traffic demand in time and space produces an inefficient use of available transportation resources, the spatial and temporal variations are an integral part of the society and life-style served by those resources. Updated October 1994
TEMPORAL VARIATIONS
Traffic demand varies by month of the year, by day of the week, by hour of the day, and by subhourly intervals within the hour. These variations are important if highways are to effectively serve peak demands without breakdown. As discussed in Chapter 6, breakdowns into LOS F operation may occur because of the inability to process demand for periods as short as 15 min. The effects of a breakdown may extend far beyond the time during which demand exceeds capacity and may take up to several hours to dissipate. Thus, highways minimally adequate to handle a peak-hour demand may be subject to breakdown if flow rates within the peak hour exceed the capacity.
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Table 2-2. Reported Maximum One-Way Hourly Volumes on Selected Freeways location
total volume (vph)
avg. vol. per lane (vphpl)
5301 5256 4802 4690 4672 4624 4480 4458 4446 4436 4398 4342 4240 4152 4083 3962 3840 3804
2650 2628 2401 2345 2336 2312 2240 2229 2223 2218 2199 2171 2120 2077 2041 1982 1920 1902
7495 7378 7188 6909 6786 6673 6611 6608 6533 6357 6280 6251 6151 6149 6120 6113 6104 5610
2498 2459 2396 2303 2262 2224 2203 2203 2177 2119 2093 2083 2050 2047 2040 2038 2035 1870
9090 8911 8793 8702 8610 8360 8295 8284 8268 8168 6851 6682
2272 2228 2198 2175 2152 2090 2073 2071 2067 2042 1712 1670
4278 3922 3166 3059 5840
2139 1961 1584 1530 1460
4-Lane Freeways I-66, Fairfax, Virginia U.S. 71, Kansas City, Missouri I-59, Birmingham, Alabama I-35W, Minneapolis, Minnesota I-225, Denver, Colorado I-287, Morris Co., New Jersey I-295, Washington, D.C. I-235, Des Moines, Iowa I-71, Louisville, Kentucky I-55, Jackson, Mississippi I-35, Kansas City, Kansas CA 4, Contra Costa County, California I-45, Houston, Texas I-64, Charleston, West Virginia U.S. 4/NH 16, Newington, New Hampshire I-564, Norfolk, Virginia Northern State Parkway, New York I-93, Windham, New Hampshire 6-Lane Freeways I-495, Montgomery Co., Maryland U.S. 6, Denver, Colorado I-5, Portland, Oregon I-35W, Minneapolis, Minnesota CA 17, San Jose, California Texas 121, Bedford, Texas I-35E, Dallas, Texas Garden State Parkway, New Jersey I-5, Seattle-Everett, Washington I-15, Salt Lake City, Utah I-24, Nashville, Tennessee NJ 3, Secaucus, New Jersey I-287, Somerset Co., New Jersey I-290, Hillside, Illinois I-90, Northwest Tollway, Illinois I-80, Omaha, Nebraska I-40, Nashville, Tennessee Southern State Parkway, New York 8-Lane Freeways I-635, Dallas, Texas Garden State Parkway, New Jersey I-495, Montgomery Co., Maryland I-25, Denver, Colorado I-495, Fairfax, Virginia I-405, Los Angeles, California I-5, Seattle, Washington U.S. 50, Sacramento, California U.S. 59, Houston, Texas I-35W, Minneapolis, Minnesota I-80, W. Paterson, New Jersey I-71, Columbus, Ohio Tunnels I-279, Fort Pitt Tunnel, Pittsburgh, Pennsylvania (4-lane) I-376, Squirrel Hill Tunnel, Pittsburgh, Pennsylvania (4-lane) I-895, Harbor Tunnel, Baltimore, Maryland (4-lane) SR 1A, Callahan Tunnel, Boston, Massachusetts (2-lane, half of one-way pair) I-95, Fort McHenry Tunnel, Baltimore, Maryland (8-lane)
SOURCE: HCQS Survey, Federal Highway Administration, Maryland Transportation Authority, and Callahan Tunnel TSM One Way Toll Project, SG Associates and Herbert S. Levinson, 1983
Updated October 1994
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Table 2-3. Reported Maximum Lane Volumes on Selected Freeways location
avg. vol. per lane (vphpl)
vol. in peak lane (vphpl)
— 2218 2229
2552 2542 2466
2035 2177 2093
2664 2630 2500
2073 — 1670
2596 2298 2088
4-Lane Freeways I-70, Wheeling, West Virginia I-55, Jackson, Mississippi I-235, Des Moines, Iowa 6-Lane Freeways I-40, Nashville, Tennessee I-5, Seattle, Washington I-24, Nashville, Tennessee 8-Lane Freeways I-5, Seattle, Washington I-70, Columbus, Ohio I-71, Columbus, Ohio SOURCE: HCQS Survey and Federal Highway Administration
Figure 2-6. Rural Interstate travel by vehicle type. (Source: Our Nation’s Highways, Selected Facts and Figures, Federal Highway Administration, 1992)
Figure 2-7. Annual vehicle miles of travel. (Source: Our Nation’s Highways, Selected Facts and Figures, Federal Highway Administration, 1992)
Updated October 1994
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Table 2-4. Reported Maximum One-Way Volumes for Selected Multilane Highways location
total volume (vph)
avg. vol. per lane (vphpl)
4124 3989 3776 3304
2062 1995 1888 1652
5596 5348 4776
1865 1783 1592
5428
1357
4-Lane Highways U.S. 101, Sonoma County, California Utah 201, Salt Lake City, Utah SR 17, Bergen County, New Jersey U.S. 301, Prince Georges County, Maryland 6-Lane Highways U.S. 46, Passaic County, New Jersey SR 3, Passaic County, New Jersey U.S. 1, Essex County, Massachusetts 8-Lane Highways Almaden Expressway, San Jose, California SOURCE: HCQS Survey, Federal Highway Administration, and Ref. 33
Table 2-5. Reported Maximum Volumes on Selected Two-Lane Rural Highways
location
total volume (vph)
peak dir. volume (vph)
off-peak dir. volume (vph)
3107 3027 2450 2250 2198 2050 1796 1714 1517
1651 1839 — — 1504 — 1386 1445 —
1456 1188 — — 694 — 410 269 —
3195 2920 2701 2242 1960 1919
— 1827 — 1146 1041 971
— 1093 — 1096 919 948
Highways Madera-Olsen Rd., Simi Valley, California Madera-Olsen Rd., Simi Valley, California Hwy. 1, Banff, Alberta, Canada Hwy. 35/115, Kirby, Ontario, Canada Wasatch Blvd., Salt Lake City, Utah Hwy. 35, Kirby, Ontario, Canada U.S. 50, Lake Tahoe, California NJ 50, Cape May Co., New Jersey Hwy. 1, Banff-Yoho, Alberta–British Columbia, Canada Bridges/Tunnels U.S. 158, Nags Head, North Carolina Midtown Tunnel, Norfolk/Portsmouth, Virginia Sagamore Bridge, Hudson, New Hampshire TH 15, St. Cloud, Minnesota Underwood Bridge, Hampton, New Hampshire Staley Viaduct, Decatur, Illinois SOURCE: HCQS Survey and Federal Highway Administration
Seasonal peaks in traffic demand are also of great importance, particularly for primarily recreational facilities. Highways serving beach resort areas may be virtually unused during much of the year, only to be subject to regular congestion during peak summer periods. The sections that follow present observed patterns of time variation in traffic demand for various types of facilities in North America. Seasonal and Monthly Variations
Seasonal fluctuations in traffic demand reflect the social and economic activity of the area being served by the highway. Figure 2-8 shows monthly variation patterns observed in Illinois and Minnesota. Several significant characteristics are apparent: 1. Monthly variations are more severe on rural routes than on urban routes. 2. Monthly variations are more severe on rural routes serving primarily recreational traffic than on rural routes serving primarily business routes.
3. Daily traffic patterns vary by month of year most severely for recreational routes. These observations lead to the conclusion that commuter and business-oriented travel occurs in more uniform patterns and that recreational traffic is subject to the greatest variation among trippurpose components of the traffic stream. The data for Figure 2-8b were collected on the same Interstate route. One segment is within 1 mi of the central business district of a large metropolitan area. The other segment is within 50 mi of the first but serves a combination of recreational and intercity business travel. The wide difference in seasonal variation patterns for the two segments underscores the effect of trip purpose and may also reflect capacity restrictions on the urban section. Daily Variations
Volume variations by day of the week are also related to the type of highway on which observations are made. Figure 2-9 shows that weekend volumes are lower than weekday volumes for highways serving predominantly business travel, such as urban freeUpdated October 1994
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Table 2-6. Reported Maximum One-Way Volumes on Selected Urban Arterials
location Ill. 83, DuPage Co., Illinois So. Virginia St. (US 395), Reno, Nevada Tara Blvd., Clayton, Georgia Dougall Ave. SB, Windsor, Ontario, Canada Antoine, Houston, Texas Woodway WB, Houston Texas North Shepard NB, PM, Houston, Texas Col. 2, Denver, Colorado US 74/NC 27, Charlotte, North Carolina Almaden Expressway, San Jose, California Ygnacio Valley Road, Walnut Creek, California Southwest Trafficway, Kansas City, Missouri U.S. 19, Clearwater, Florida Ward Parkway, Kansas City, Missouri Seward Highway, Anchorage, Alaska Telegraph Rd., Detroit, Michigan FM 1093, Houston, Texas FM 1093, Houston, Texas
total volume (vph) 4-Lane 3819 2831 2137 2240 2310 2156 5-Lane 2100 6-Lane 3435 4882 3960 3790 3492 4305 3477 3177 8-Lane 4400 4500a 4268a
avg. volume per lane (vphpl)
g/C ratio
total flow rate (vphg)
avg. flow rate per lane (vphgpl)
1910 1415 1068 1120 1155 1078
0.80 0.62 0.47 0.60 0.65 0.76
4774 4566 4547 3733 3553 2836
2387 2282 2272 1867 1777 1418
1050
0.60
3500
1750
1145 1627 1320 1263 1164 1435 1159 1059
0.50 0.80 0.66 0.65 0.60 0.75 0.61 0.70
6870 6102 6000 5831 5820 5740 5700 4538
2290 2034 2000 1943 1940 1913 1900 1513
1100 1125 1067
0.60 0.70 0.70
7333 6429 6097
1833 1607 1524
Arterials
Arterials Arterials
Arterials
a
9-ft lanes. SOURCE: HCQS Survey, Federal Highway Administration, Case Studies in Access Management, Draft Final Report, F. J. Koepke, Jr., and Herbert Levinson, 1992
ways. In comparison, peak traffic occurs on weekends on main rural and recreational access facilities. Furthermore, the magnitude of daily variation is highest for recreational access routes and least for urban commuter routes. Figure 2-10 shows the variation in traffic by vehicle type for the shoulder lane of an urban freeway. Truck traffic is the most severely reduced on weekends. The extent of daily volume variation decreases as volume increases, often reflecting the effect of capacity restrictions on demand. Although the values shown in Figures 2-9 and 2-10 are illustrative of typical patterns that may be observed, they are not meant to substitute for local studies and analyses. The average daily traffic averaged over a full year is referred to as the annual average daily traffic, or AADT, and is often used in forecasting and planning.
The repeatability of hourly variations is of great importance. The stability of peak-hour demands affects the feasibility of using such values in design and operational analysis of highways and other transportation facilities. Figure 2-12 shows data obtained over a 77-day period in metropolitan Toronto. The shaded area indicates the range within which one can expect 95 percent of the observations to fall. Whereas the variations by hour of the day are typical for urban areas, the relatively narrow and parallel fluctuations among the 77 days indicate the repeatability of the basic pattern. The observations shown were obtained from detectors measuring one-way traffic only, as evidenced by the single peak hour shown for either morning or afternoon. It is again noted that the data of Figures 2-11 and 2-12 are typical of observations that can be made. The patterns illustrated, however, vary in response to local travel habits and environments, and these examples should not be used as a substitute for locally obtained data.
Hourly Variations Peak Hour and Design Hour
Typical hourly variation patterns are shown in Figure 2-11, where the patterns are related to highway type and day of the week. The typical morning and evening peak hours are evident for urban commuter routes on weekdays. The evening peak is generally somewhat more intense than the morning peak, as shown in Figure 2-11. On weekends, urban routes show a peak that is less intense and more ‘‘spread out,’’ occurring early to midafternoon. Recreational routes also have single daily peaks. Saturday peaks on such routes tend to occur in the late morning or early afternoon (as travelers go to their recreational destination) and in late afternoon or early evening on Sundays (as they return home). Updated October 1994
Capacity and other traffic analyses focus on the peak hour of traffic volume, because it represents the most critical period for operations and has the highest capacity requirements. The peakhour volume, however, is not a constant value from day to day or from season to season. If the highest hourly volumes for a given location were listed in descending order, a large variation in the data would be observed, depending on the type of route and facility under study. Rural and recreational routes often show a wide variation in peak-hour volumes. Several extremely high volumes occur on a
traffic characteristics
Figure 2-8(a). Examples of monthly traffic volume variations showing monthly variations in traffic for a freeway in Minnesota.
few selected weekends or other peak periods, and traffic during the rest of year is at much lower volumes, even during the peak hour. This occurs because the traffic stream consists of few daily or frequent users; the major component of traffic is generated by seasonal recreational activities and special events. Urban routes, on the other hand, show very little variation in peak-hour traffic. Most users are daily commuters or frequent users, and occasional and special event traffic are at a minimum. Furthermore, many urban routes are filled to capacity during each peak hour, and variation is therefore severely constrained. In many urban areas, both the a.m. and p.m. peak periods extend for more than 1 hr. Figure 2-13 shows hourly volume relationships measured on a variety of highway types in Minnesota. Recreational facilities show the widest variation in peak-hour traffic, with values ranging from 30 percent of the AADT occurring in the highest hour of the year to about 15.3 percent of AADT occurring in the 200th-highest hour of the year and 8.3 percent in the 1,000th-highest hour of the year. Main rural facilities also display a wide variation. The highest hour is subjected to 17.9 percent of the AADT, decreasing to 10 percent in the 100th hour and 6.9 percent in the 1,000th hour. Urban radial and circumferential facilities show far less variation. The range in percent of AADT covers a narrow band, from approximately 11.5 percent for the highest hour to 7 to 8 percent for the
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1,000th-highest hour. Figure 2-13 includes all hours, not just peak hours of each day. It is apparent from these characteristics that traffic engineers are faced with the need for substantial judgments. Provision of a recreational facility adequate to handle the highest peak-hour volume of the year for a given level of service results in gross underutilization of capacity during all but a few hours of the year. On the other hand, providing sufficient capacity for the 30th, 100th, 500th, or other hour would guarantee the occurrence of substantial congestion and delay during those special event or recreational peak hours occurring less frequently. The selection of an appropriate hour for planning, design, and operational purposes is a compromise between providing an adequate level of service for every (or almost every) hour of the year and economic efficiency. Customary practice in the United States is to base rural highway design on an hour between the 30th- and 100th-highest hour of the year. This range generally encompasses the ‘‘knee’’ of the curve—the area in which the slope of the curve changes from sharp to flat. For rural highways, the knee has often been assumed to occur at the 30th-highest hour, which is often used as the basis for estimates of design hour volume. For urban roadways, a design hour for the repetitive weekday peak periods is common. Signal timing analyses frequently use traffic conditions typical of certain periods of the day or week. Past studies (7,8) have emphasized the difficulty in locating a distinct knee on hourly volume curves. Figure 2-14 shows hourly volumes for all hours of the year at a Kentucky counting station. The first and third curves illustrate the continuous nature of the relationship, with no distinct breaks or knee in the decreasing hourly volume pattern. The second curve shows a rather spreadout knee, which could easily be located anywhere within the first 100 hr. These curves illustrate the point that arbitrary selection of a design hour between the 30th- and 100th-highest hour is not a rigid criterion and indicate the need for local data on which to make informed judgments. Since the first knee may be followed by another occurring on different days of the week or month or with different prevailing trip purposes, it is advisable to identify the nature of traffic in the highest hours. The selection of a design hour must consider the impact of the selection on the higher-volume hours that are not accommodated. The recreational access route curve of Figure 2-14 shows that the highest hours of the year have more than twice the volume of the 100th hour, whereas the highest hours of an urban radial route are only about 15 percent higher than the volume in the 100th hour. Use of a design criterion set at the 100th hour would create substantial congestion on a recreational access route during the highestvolume hours but would have less effect on an urban facility, where the variation in peak-hour volumes is less. Another consideration is the level of service objective. A route designed to operate at LOS B can absorb larger amounts of additional traffic than a route designed to operate at LOS D during those extreme hours of the year with higher volumes than the design hour. As a general guide, the most repetitive peak volumes may be used for the design, and the level of service during higher-volume periods should be tested as to the acceptability of the resulting traffic conditions. The proportion of AADT occurring in the design hour is often referred to as the K-factor. It is expressed as a decimal and varies on the basis of the hour selected for design or planning application and the characteristics of the subject route and its development Updated October 1994
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principles of capacity
Figure 2-8(b). Examples of monthly traffic volume variations showing relative traffic volume trends by route type on rural roads in Lake County, Illinois. (Source: Ref. 51) environment. Where the K-factor is based on the 30th-highest hour of the year, several general characteristics can be noted: 1. The K-factor generally decreases as the AADT on a highway increases. 2. The reduction rate for high K-factors is faster than that for lower values. 3. The K-factor decreases as development density increases. 4. The highest K-factors generally occur on recreational facilities, followed by rural, suburban, and urban facilities, in descending order. Subhourly Variations in Flow
Whereas volume forecasts for long-range planning studies are frequently expressed in units of AADT (vehicles per day), subsequently reduced to hourly volumes, the analysis of level of service is based on peak rates of flow occurring within the peak hour. Most of the procedures in this manual are based on peak 15min rates of flow. Figure 2-15 shows the substantial short-term fluctuation in flow rate that can occur during an hour. The data shown are for I-35W in Minneapolis, Minnesota, in 1983. Updated October 1994
In Figure 2-15 the maximum 5-min rate of flow is 2,232 vph, whereas the maximum rate of flow for a 15-min period is 1,980 vph. The full hour volume is only 1,622 vph. A design for a peak 5-min flow rate would result in substantial excess capacity during the rest of the peak hour, whereas a design for the peak-hour volume would result in congestion for a substantial portion of the hour. Note that Figure 2-15 treats discrete 15-min periods for clarity. In practice, the peak 15 min may occur during any 15-min interval within the hour. Consideration of these peaks is important. Congestion due to inadequate capacity occurring for only a few minutes could take substantial time to dissipate because of the dynamics of breakdown flow, which are explained in greater detail in Chapter 6. Fifteenmin flow rates have been selected as the basis for most procedures of this manual to incorporate these peak flows. Five-min flow rates have been avoided, since research has shown them to be statistically unstable. The operational effects of a 5-min flow surge are virtually impossible to predict with any certainty. The relationship between the peak 15-min flow rate and the full hourly volume is given by the peak-hour factor, defined in Part A of this chapter.
traffic characteristics
Figure 2-9. Examples of daily traffic variation by type of route. Legend: MR curve represents main rural route I-35, Southern Minnesota, AADT 10,823, 4-lanes, 1980; RA curve represents recreational access route MN 169, North-Central Lake Region, AADT 3,863, 2-lanes, 1981; UF curve represents urban freeway, four freeways in Minneapolis–St. Paul, AADTs 75,000–130,000, 6–8 lanes, 1982. (Source: Minnesota Department of Transportation)
Whether the design hour was measured, established from the analysis of peaking patterns, or based on modeled demand, the peak-hour factor (PHF) is applied to determine design hour flow rates. Peak-hour factors in urban areas generally range between 0.80 and 0.98. Lower values signify greater variability of flow within the subject hour, and higher values signify little flow variation. Peak-hour factors over 0.95 are often indicative of high traffic volumes, sometimes with capacity constraints on flow during the peak hour. SPATIAL DISTRIBUTIONS
Whereas traffic volume varies in time, it also varies in space. The two critical spatial characteristics of interest in capacity analysis are directional distribution and lane distribution. Volume may also vary longitudinally along various segments of a facility, but this does not explicitly affect capacity analysis computations. Each facility segment serving different traffic demands must be analyzed separately. Directional Distribution
During any particular hour, traffic volume may be greater in one direction than in the other. An urban radial route, serving strong directional demands into the city in the morning and out of
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Figure 2-10. Daily variation in traffic by vehicle type. Data for this figure were collected on I-494, 4-lanes, in Minneapolis–St. Paul. (Source: Minnesota Department of Transportation)
it at night, may display as much as a 2:1 imbalance in directional flows. Recreational and rural routes may also be subject to significant directional imbalances, which must be considered in the design process. Table 2-7 gives the directional distribution on various highway types in Minnesota between 1980 and 1982. Directional distribution is an important factor in highway capacity analysis. This is particularly true for two-lane rural highways. Capacity and level of service vary substantially on the basis of directional distribution because of the interactive nature of directional flows on such facilities. Procedures for two-lane highways include explicit consideration of directional distribution. Whereas there is no explicit consideration of directional distribution in the analysis of multilane facilities, the distribution has a dramatic impact on both design and level of service. As indicated in Table 2-7, urban radial routes have been observed to have up to two-thirds of their peak-hour traffic in a single direction. Unfortunately, this peak occurs in one direction during the morning and in the other in the evening. Thus, both directions of the facility must be adequate for the peak directional flow. This characteristic has led to the use of reversible lanes on some urban freeways and arterials. Directional distribution is not a static characteristic. It changes by hours of the day, day of the week, season, and from year to year. Development in the vicinity of highway facilities often inUpdated October 1994
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Figure 2-12. Repeatability of hourly traffic variations for four 2-lane arterials in Toronto, Ontario, Canada. (Source: Ref. 6)
Lane Distribution
Figure 2-11. Examples of hourly traffic variations for rural routes in New York State. (Source: Ref. 5)
duces traffic growth that changes the existing directional distribution. The proportion of traffic occurring in the peak direction of travel during peak hours is often denoted as D. The K-factor, the proportion of AADT occurring in the design hour, was discussed previously. These factors are used to estimate the peak-hour traffic volume in the peak direction using the following equation: DDHV = AADT × K × D
(2-11)
where DDHV = directional design hour volume (vph), AADT = average annual daily traffic (vpd), K = proportion of AADT occurring in the peak direction, and D = proportion of peak hour traffic in peak direction. The product of the factors K and D is given for a number of facilities in Table 2-8. The product gives the proportion of AADT occurring in the maximum direction of the peak hour. Updated October 1994
When two or more lanes are available for traffic in a single direction, the distribution in lane use varies widely. The lane distribution depends on traffic regulations, traffic composition, speed and volume, the number of and location of access points, the origin-destination patterns of drivers, development environment, and local driver habits. Because of these factors, there are no ‘‘typical’’ lane distributions. The procedures of this manual assume an average capacity of multilane uninterrupted flow facilities of 2,200 pcphpl. It is recognized that flow in some lanes will be higher and in others lower. Recent data collected as part of the Highway Capacity and Quality of Service Committee survey of highvolume facilities indicate no consistency in lane distribution. Data indicate that the peak lane on a six-lane freeway, for example, may be the shoulder, middle, or median lane, depending on local conditions. Table 2-9 gives lane distribution data for various vehicle types on selected freeways. These are illustrative and are not intended to represent ‘‘typical’’ values. The trend indicated in Table 2-9 is reasonably consistent throughout North America. Heavier vehicles tend toward the righthand lanes, partially because they may operate at lower speeds than other vehicles and partially because of regulations prohibiting them from using leftmost lanes. Lane distribution is a critical factor in the analysis of freeway ramp junctions, because the traffic in the shoulder lane forms the merge or diverge volume in conjunction with ramp vehicles.
traffic characteristics
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Figure 2-13. Ranked hourly volumes on Minnesota highways. (Source: Minnesota Department of Transportation) Procedures for their analysis in Chapter 5 focus on estimating traffic in the shoulder lane as well as truck presence in the lane.
TRAFFIC COMPOSITION
The fraction of trucks, recreational vehicles, and buses in the traffic stream is also required to apply the procedures of this manual. Adjustments for these three categories of vehicles, especially as they relate to grade-climbing capabilities, are given for each of the procedures in following chapters. Lighter-weight vehicles dominate the new-car market. Figures 2-16 and 2-17 show trends in passenger car power characteristics since 1967, with projections to 1995. Whereas the trend is clearly toward less powerful vehicles (as indicated by the ratio of horsepower to weight in Figure 2-16), the average 1995 vehicle will have about 85 percent of the hp/lb of an average 1978 vehicle. The impact of these changes on capacity and operations is expected to be minimal.
IMPACT OF WEATHER ON MAXIMUM VOLUMES
Figure 2-14. Ranked hourly volume distribution showing indistinct knee for Kentucky location in 1977. (Source: Ref. 7)
There have been relatively few efforts to quantify the effects of adverse weather on capacity. Some measure of the impact can be gained from studies conducted on two freeways with automated data collection systems—the Gulf Freeway (I-45) in Houston (11) and I-35W in Minneapolis (12). For both freeways, observations were made on three-lane segments influenced by bottlenecks such that a history of ‘‘capacity volumes’’ was available. For the Gulf Freeway, it was reported that rain significantly reduces capacity by 14 to 19 percent compared with clear-weather values. Updated October 1994
principles of capacity
2-22
Figure 2-15. Relationship between short-term and hourly flows. (Source: Minnesota Department of Transportation)
Table 2-7. Directional Distribution Characteristics percent traffic in peak directions type of facility
highest hour of the year
urban circ
urban radial
rural
1st 10th 50th 100th
53 53 53 50
66 66 65 65
57 53 55 52
SOURCE: Minnesota Department of Transportation, 1980–1982
Updated October 1994
Results from the I-35W study suggested that even a trace of precipitation reduced capacity by 8 percent. Each 0.01 in./hr increase in rainfall resulted in a further decrease of 0.6 percent in capacity. When precipitation falls as snow, the impact is even greater: an additional 2.8 percent decrease in capacity for each 0.01 in./hr of snow (water equivalent) beyond the initial trace decrease of 8 percent. The procedures of this manual do not specifically account for inclement weather conditions. However, in areas where such conditions are prevalent, analysts may wish to modify results to account for these impacts.
traffic characteristics
2-23
Table 2-8. Observed Values of K and D on Selected Freeways and Expressways
city and 1990 urbanized area population
facility
year count taken
number of lanes
annual average daily traffic (2-way)
volumes in peak direction vehicles (1-way)
% 2-way aadt (K × D)
average volume per lane (vphpl)
Atlanta, Ga. 2,157,806
I-20 I-20 I-75 I-75 I-85
E. of CBD at Moreland Ave. at Martin Luther King Jr. Drive S. of CBD at University Ave. N. of CBD (N. of I-85) N. of I-75 at Monroe Dr.
1984 1984 1984 1984 1984
8 8 8 8 8
99,900 91,200 146,050 82,830 95,300
7,794 (5,198) (8,179) (5,135) 6,765
7.8 5.7 (1975) 5.6 (1975) 6.2 (1975) 7.1
1,948 (1,299) (2,045) (1,284) 1,641
Boston, Mass. 2,775,370
I-93 N. of I-495 S.E. Expressway at Southampton St. I-95 E. of Rt. 128 N. of Middlesex
1984 1982 1984
6 6 8
76,500 143,300 125,050
5,200 6,860 7,282
6.8 4.8 5.8
1,733 2,286 1,823
Denver, Colo. 1,517,977
I-25 S. of I-70 I-70, Colorado Blvd. to Dahlia U.S. 6 W. of Federal Blvd.
1984 1984 1985
8 6 6
175,000 114,000 112,000
7,500 4,650 5,835
4.3 4.1 5.2
1,875 1,550 1,945
Detroit, Mich. 3,697,529
I-96 Jeffers Freeway at Warren Lodge at E. Grand Blvd.
1980 1981
8 6
67,600 111,450
6,270 4,660
9.3 4.2
1,568 1,558
Houston, Tex. 2,901,851
I-10 E. of Taylor St. I-10 E. of McCarty I-610 at Ship Channel
1985 1985 1985
10 8 10
151,000 110,200 103,200
7,600 7,530 5,540
5.0 6.8 5.4
1,520 1,882 1,108
Milwaukee, Wis. 1,226,293
N.-S. Freeway at Wisconsin N.-S. Freeway at Greenfield E.-W. Freeway at 26th St. Zoo Freeway at Wisconsin Airport Freeway at 68th
1984 1984 1984 1984 1984
8 8 6 6 6
118,080 110,050 121,150 110,730 81,020
5,730 6,380 5,700 4,760 3,940
4.5 5.8 4.7 4.3 4.9
1,342 1,595 1,900 1,581 1,313
New York, N.Y. 16,044,012
Holland Tunnel
1982
4
73,200
2,700
3.7
1,350
San Francisco, Calif. 3,629,516
I-80 Oakland Bay Bridge
1984
10
223,000
8,898
4.0
1,780
Washington, D.C. 3,363,061
I-66 Theodore Roosevelt Bridge Anacostia Freeway at Howard Road
1984 1984
6 6
86,200 121,700
(7,413) (6,085)
8.6 (1975) 5.0 (1975)
(2,471) (2,028)
NOTE: Values in parentheses based on K × D value for the year indicated if different from the year the count was taken. SOURCE: Characteristics of Urban Transportation Demand—An Update, July 1988, Charles River Associates in association with H. S. Levinson, and Ref. 52
Table 2-9. Lane Distribution by Vehicle Type percent distribution by lane highway
b
vehicle type
lane 1
lane 2
lane 3
Lodge Freeway, Detroit
Lighta SU Trucks Combinations All Vehicles
29.2 30.8 88.5 30.9
38.4 61.5 2.9 37.8
32.4 7.7 8.6 31.3
I-95, Connecticut Turnpike
Lighta All Vehicles
34.6 37.1
40.9 40.4
24.5 22.5
I-4, Orlando, Florida
All Vehicles
29.9
31.7
38.4
a
Passenger cars, panel trucks, and pickup trucks. b Lane 1 = shoulder lane; lanes numbered from shoulder to median. SOURCE: Ref. 14 and Florida Department of Transportation, 1993
Updated October 1994
principles of capacity
2-24
Figure 2-16. Distribution of power-to-mass ratios of passenger cars. (Source: Ref. 9)
Figure 2-17. On-highway passenger car characteristics. (Source: Ref. 10, Figure 2-13)
IV. SPEED CHARACTERISTICS NATIONAL SPEED TRENDS
Nationwide speed trends through 1975 are shown in Figure 218a for various vehicle types and in Figure 2-18b for all vehicles on Interstate rural highways through 1991. Figure 2-18a, for main rural highways, shows a clear increasing speed trend from 1942 through the middle of 1972. This reflects the better design of both highways and vehicles occurring throughout this period. In 1973, in response to a severe fuel shortage, the 55-mph national speed limit was introduced, and a sharp decline in speeds was observed. The figure also shows that buses and passenger cars travel at similar speeds on rural highways, whereas trucks travel at somewhat lower speeds. To 1973, the difference Updated October 1994
between average truck and passenger car speed was about 7 to 8 mph. After 1973, this difference was reduced considerably, to about 2 mph, because of the lower overall speeds being observed. Figure 2-18b indicates that speeds have been gradually increasing despite the 55-mph speed limit. With the restoration of the 65mph speed limit on some of the major roadways, further increases in average speeds can be expected. Table 2-10 confirms the increasing speed trends on U.S. highways. All of the highways referenced in Table 2-10 had a 55-mph speed limit in effect. Aside from the general interest in the speed limit issue, these speed trends have an impact on the procedures presented in this manual. Uninterrupted flow procedures incorporate national aver-
traffic characteristics
2-25
Figure 2-18. Nationwide speed trends through 1975 and 1993. (Source: Ref. 13 and Highway Statistics)
Table 2-10. National Spot Speed Trends for 55-mph Facilities fiscal year
average speed (mph)
1985 1987 1989 1991
57.2 58.0 58.9 58.8
1985 1987 1989 1991
59.5 59.7 60.1 59.9
1985 1987 1989 1991
54.9 55.9 56.2 56.4
1985 1987 1989 1991
53.5 54.0 54.6 54.0
median speed (mph) Urban Interstate Highways 57.4 58.0 59.0 58.8 Rural Interstate Highways 59.4 59.7 60.3 59.4 Rural Arterials 55.2 56.1 56.4 56.3 Urban Principal Arterials 53.6 54.1 55.1 53.9
85th percentile speed (mph)
percent > 55 mph
64.0 64.8 66.1 66.1
64.1 67.4 71.3 69.8
66.1 66.5 67.2 67.2
75.4 73.7 76.8 75.5
61.7 62.8 63.1 63.1
50.5 54.3 56.0 56.5
60.5 60.7 61.3 60.8
42.1 44.7 47.7 42.2
NOTE: All highways have 55-mph speed limit. SOURCE: Highway Statistics, Federal Highway Administration, 1992
Updated October 1994
2-26
principles of capacity
age speed-flow and speed-density trends. The exact shape of these curves and the calibration of speeds (especially at the free-flow end of the relationships) reflect current trends. Curves used in this manual allow for average speeds up to 70 mph, 5 or 15 mph over the usual speed limit, in response to the observed increase in driverselected speeds under free-flow conditions.
SPEED VARIATION BY TIME OF DAY
Figures 2-19 and 2-20 show variations of speed with time of day, along with hourly volume variations, over a 24-hr period for
I-35W in Minneapolis. Figure 2-19 shows a weekday variation pattern, whereas Figure 2-20 shows a similar distribution for a Saturday. In these exhibits note that speed remains relatively constant despite significant changes in volume. In Figure 2-19, speed shows a marked response to volume increases only when the volume exceeds approximately 1,600 vphpl. This trend is illustrated later and is an important characteristic in all of the procedures of this manual. If speed does not vary with rate of flow over a broad range of flows, it becomes difficult to use speed as the sole measure of effectiveness defining level of service. This important characteristic is the major reason that such measures as density and percent
Figure 2-19. Speed variation by hour of day for I-35W in Minneapolis, weekdays, in relation to volume variations. (Source: Minnesota Department of Transportation) Updated October 1994
traffic characteristics
2-27
Figure 2-20. Speed variation by hour of day for I-35W, Minneapolis, Saturdays, in relation to volume variations. (Source: Minnesota Department of Transportation)
time delay have been introduced as primary measures of effectiveness for uninterrupted flow facilities, with speed playing a secondary role. The speeds in Figures 2-19 and 2-20 are also virtually the same, despite significantly lower volumes on weekends. This is a reflection of driver populations and trip purpose effects. Saturday drivers may be less familiar with the facility, or, if familiar, they do not drive with the same sense of urgency devoted to the daily commute to work. Procedures of this manual also take this into account by introducing adjustments for driver population types in several chapters.
SPEED VARIATION BY LANE AND DAY VERSUS NIGHT
Table 2-11 gives a comparison of speeds by day versus night conditions on the Connecticut Turnpike near Bridgeport. The table shows that day/night variations are slight, on the order of 1 mph. Variations by lane are considerably greater, a factor indicated in Table 2-12 for a number of other facilities. Level of service speed criteria in the manual refer to average values across all lanes of the facility or all lanes in one direction of the facility. The data indicate that drivers in general are using the lanes of multilane facilities as intended—slower drivers to the right and faster drivers in the middle and median lanes.
Updated October 1994
principles of capacity
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Table 2-11. Average Speed by Day vs. Night and Lane in mph lane 1a
lane 2
lane 3
vehicle type
day
night
day
night
day
night
Passenger cars Trucks Percent trucks in lane
49.5 47.5 (15.0)
48.8 46.4 (17.3)
57.7 54.3 (7.5)
57.4 54.6 (13.0)
65.1 59.4 (0.7)
61.6 58.1 (5.4)
a
Lane 1 = shoulder lane; lanes numbered from shoulder to median. SOURCE: Ref. 14
Table 2-12. Average Speeds by Lane in mph
location N.J. Turnpike Conn. Turnpike L.I. Expwy., N.Y. I-8, San Diego SR 94, San Diego I-4, Orlando, Florida
lane 1a
lane 2
lane 3
lane 4
avg. volume per lane (vph)
46 49 52 49 44 50 47 56
55 57 56 51 48 53 49 61
60 64 57 58 53 57 52 61
— — — 62 55 56 49 —
1120 692 1460 1503 2386 1282 2168 —
a
Lane 1 = shoulder lane; lanes numbered from shoulder to median. SOURCE: Refs. 14 and 15, California Department of Transportation, 1984, and Florida Department of Transportation, 1993
V. MEASURED RELATIONSHIPS FOR UNINTERRUPTED FLOW Part A of this chapter introduced the generalized basic form of the relationships among speed, flow rate, and density for uninterrupted flow facilities. Rarely is it possible to observe these characteristics, especially at flow rates approaching capacity, under ideal conditions. Practically all data collected for the calibration of such relationships are subject to the influences of changing environmental conditions, nonhomogeneity of vehicles in the traffic stream, and (particularly for urban facilities) lack of complete isolation from ramps and interchanges. The shape and calibration of such relationships are important, because they provide the basis for the selection of measures of effectiveness and the definition of level of service ranges for uninterrupted flow facilities. Such relationships also serve to estimate the capacity of uninterrupted flow facilities and the operating conditions under which it occurs. Estimation of capacity requires clear identification of the maximum flow point on a speed-flow or speeddensity curve, a process fraught with difficulty because of the stochastic nature of the observations near capacity. Even under ideal conditions, observations of capacity flows will not be constant but will form a distribution of values. It is not possible to take a single measurement and know with certainty where it fits within that distribution. In recognition of such difficulties, many researchers have developed analytical models describing these relationships. These models have sometimes been used to identify the capacity of a highway by extrapolation of data for both uncongested and congested conditions. The results of many research projects show the difficulties of extrapolation from these models in the vicinity of capacity flows (16–20). Work within the last decade has therefore focused more Updated October 1994
on an empirical rather than on an analytical approach to defining the shape of the curves and the values of capacity.
SPEED-FLOW RELATIONSHIPS
Freeways
Research attention has largely focused on the speed-flow relationship. These two variables are the traffic stream characteristics most often measured and have been traditionally used in the assessment of traffic operations. The general shape of the speed-flow data tend to be similar regardless of the location within North America. Figure 2-21 shows data from San Diego, California (21). Figure 2-22 shows data from near Toronto, Ontario, Canada (22). The lack of data points in the low-flow, high-speed region of the curve reflects the fact that these surveys took place during busy morning peak periods. In both cases the data were collected in 30-sec intervals, but the data were averaged over 6-min intervals in San Diego and 5-min intervals in Toronto. Both figures show high speeds up to what may be capacity flows and a cluster of points at a speed half of that at capacity. Figure 2-21 (San Diego) also includes more points on what may be considered the lower branch of the theoretical curve. Other studies support that general pattern with some variations: Figure 2-23 from a Northern California study (23) shows only the uncongested top portion of the curve with a gradual but minor decrease of speed from 60 to 50 mph with increasing flow. The
traffic characteristics
2-29
Figure 2-23. Observed speed-flow relationship at Caldecott Tunnel in 15-min sampling intervals (California State Highway 24, 1990). (Source: Ref. 23) Figure 2-21. Observed speed-flow relationship on a San Diego freeway in 6-min sampling intervals (Interstate Highway 8, 1987). (Source: Ref. 21)
Figure 2-22. Observed speed-flow relationship on an Ontario freeway in 5-min sampling intervals (Queen Elizabeth Way near Toronto, 1987). Different data symbols represent different survey days. (Source: Ref. 22)
maximum flow has been reached at slightly over 2,200 vph. Other recent studies also lend support to the general form of the relationship shown in these figures (24–28). Some studies suggested that there is in fact a drop in the maximum observed flows with the onset of congestion (29–31), whereas others failed to identify this effect (32). Note that these curves differ from the functions used in the 1985 Highway Capacity Manual. In measuring the speed-flow relationship, it is important to use appropriate time intervals, since they strongly influence the form of the curve, especially around the capacity flow and in the congested region. Five-min intervals are recommended as the shortest time base for practical purposes. Multilane and Two-Lane Rural Highways
Whereas the bulk of the data for uninterrupted flow come from freeways, these conditions also occur on rural multilane and twolane roads. In many respects, traffic flow on multilane roadways is similar to that on freeways (33,34). Two-lane roads, however,
have different characteristics. The relationship between speed and flow found on a two-lane rural highway in Alberta, Canada (35), is shown in Figure 2-24. The curve shows a virtually constant speed for two-way flows up to 2,400 pcph, and the entire speed range is only 59 to 50 mph for the full range of flows. Speeds of 50 mph are not unusual at capacity of two-lane highways. Most of the new speed-flow data for multilane flow also suggest that capacity occurs at a critical speed in the vicinity of 50 mph (33). It should be remembered, however, that capacity of a two-lane highway occurs at a total flow of between 2,000 and 2,800 pcph depending on directional distribution, whereas for multilane highways the flow at capacity is 2,200 pcphpl. Speeds on multilane highways for similar per lane flows (1,000 to 1,400 pcphpl) are well over 50 mph. The capacity of two-lane highways is more influenced by interactions between directional flows than by roadway space availability. As a result, other measures have been proposed as primary level of service criteria for multilane and twolane roadways. They are discussed in Chapters 7 and 8. DENSITY-FLOW RELATIONSHIPS
A number of early analytical efforts paid considerable attention to density-flow relationships. The main problem with this approach to the capacity problem is in the direct measurement of density. In most instances, its values were calculated from observed speeds and flows using Equation 2-4. Some researchers have fit continuous curves through density-flow data, yielding a single maximum flow rate. Others have projected discontinuous curves through data, with one curve treating stable flow points and another unstable or forced flow points. In these cases two maxima are achieved, one for each curve. All such models indicate that the maximum flow rate for the stable flow curve is considerably higher than that for the unstable flow curve, perhaps as much as 200 vph higher. This is an interesting feature that projects a discontinuity in flow near capacity, the point at which flow breaks down. It also explains the difficulty in recovering from a breakdown, since the maximum flow that can be achieved from an unstable flow condition is less than that for stable flow. A paper by Easa and May (20) contains several sample calibrations and illustrations of density-flow data. It has been shown, however, that determination of density from speed and flow leads to a biased estimate of the relationships (36,37). The emphasis on the density-flow relationship has therefore decreased recently. Occupancy in time, which is readily availUpdated October 1994
principles of capacity
2-30
Figure 2-24. Speed-flow relationship for two-lane rural highways. (Source: Ref. 4)
able from many freeway control systems, is sometimes used. The general shape of the occupancy-flow relationship is similar to the density-flow curve.
HEADWAY DISTRIBUTIONS AND RANDOM FLOW
At any given lane flow rate, the mean or average headway is the reciprocal of flow rate. Thus, at a flow of 1,200 vphpl, the average headway is 3,600/1,200 or 3 sec. Vehicles do not, however, travel at constant headways. Vehicles tend to travel in groups, or platoons, with varying headways between successive vehicles. An example of the distribution of headways observed on the Long Island Expressway is shown in Figure 2-25. Lane 3 has the most uniform headway distribution, as evidenced by the range of values and the high frequency of the modal value—the peak of the distribution curve. The distribution of Lane 2 is similar to that of Lane 3, with slightly greater scatter (range from 1⁄2 to 9.0 sec). Lane 1 shows a much different pattern: it is far more dispersed, with headways ranging from 1⁄2 to 12.0 sec, and the frequency of the modal value is only about one-third of that for the other lanes. This reflects the lower flow usually occurring in Lane 1 (shoulder lane) and the driver desires of Lane 1 users. Updated October 1994
Figure 2-25 shows relatively few headways less than 1.0 sec. A vehicle traveling at 60 mph (88 ft/sec) would have a spacing of 88 ft with a 1.0-sec headway, and only 44 ft with a 1⁄2-sec headway. This effectively reduces the space between vehicles (rear bumper to front bumper) to only 25 to 30 ft and would be extremely difficult to maintain and would allow little margin for driver error. Drivers react to this intervehicle spacing, which they perceive directly, rather than to the traditional front bumper–to–front bumper measures used by traffic engineers. The latter include the length of the vehicle, which became smaller for passenger cars in the vehicle mix of the 1980s. If drivers maintain essentially the same intervehicle spacing and car lengths continue to get shorter, some increases in capacity could conceivably result. If traffic flow were truly random, small headways (less than 1.0 sec) would occur frequently. Several mathematical models have been developed that recognize the absence of small headways in most traffic streams as described by Gerlough and Huber (15). These models have been useful in developing simulation models of traffic flow, thereby extending research on flow characteristics beyond conditions that can be observed and monitored in the field. Traffic flow in urban areas is rarely purely random. Traffic signals and other controls regulate flows, and the trip generation characteristics of adjacent land generally produce trips in a nonrandom fashion.
traffic characteristics
2-31
Figure 2-25. Time headway distribution for Long Island Expressway. (Source: Ref. 40)
VI. INTERRUPTED FLOW FACILITIES SATURATION FLOW AND LOST TIME AT SIGNALIZED INTERSECTIONS
The basic concepts of saturation headway and saturation flow rate and of start-up and change interval lost times were introduced in Part A. The empirical studies referenced in this section span more than 40 years, from Greenshields in 1946 to the latest research before the printing of this update. Table 2-13 summarizes the results of representative past and recent studies. The table indicates that saturation headways have been becoming shorter in the last decade and, consequently, saturation flow rates have been increasing. This trend has been observed by both practicing professionals and researchers (38). In the table, saturation headway ranges from a low of 1.8 sec to a high of 2.4 sec—corresponding to a range of saturation flow rate of 2,000 to 1,500 vphgpl. Figure 2-26 shows vehicle headway by position in the queue resulting from several past studies. It shows that, in most studies, the saturation headway does not become established until the sixth or seventh vehicle in the queue, indicating that the first five or six vehicles experience some start-up lost time. In discussing the results of Figure 2-26, Berry and Gandhi (40) noted that the variation in discharge headways of the first several vehicles depended on the choice of a screenline for measuring headways rather than any real difference in the observed headways. Stop lines or curb lines have been used in combination with the front bumper, front or rear axles, or rear bumper. Caution is therefore advisable in comparing values of discharge headways from different studies. The update of Chapter 9 uses only the stop line as the screenline and rear
wheels as measurement benchmark. Some other national practices apply different definitions or measurement techniques of saturation flow (41–44). For that reason, the values quoted in international literature are not quite comparable (38). The Canadian survey technique (42,43), however, allows the estimation of saturation flow rates for situations with queues as short as four to five vehicles. Saturation flow rates cited in various sources may also be influenced by the choice of vehicle positions included and by the definition of lost time (45). Although most studies of intersection discharge headways have focused on the observation of the first 10 to 12 vehicles, there is
Figure 2-26. Comparison of various research results on queue discharge headways. (Source: Ref. 39) Updated October 1994
principles of capacity
2-32
Table 2-13. Observed Saturation Flow Rates at Signalized Intersections
source
date of study
city or state
sample size
saturation flow measurement starting with queue position number
Los Angeles, Santa Monica, California Ames, Iowa Nationwide Lexington, Kentucky Lawrence, Kansas Austin, Dallas, Houston
6 Int.
5
2.05
1470
2.45
4 Int.
4 5 4 5 6
0.75 — 1.40 3.04 —
1572 1682 1651 1827 2000
2.29 2.14 2.18 1.97 1.8
5
1.31
1875
1.92
5
—
1896
1.9
5
—
1832
1.97
5
—
1936
1.86
5
—
1785
2.02
Gerlougha
1967
Carstensb Kingc Agentd Leee Molinaf
1971 1976 1983 1986 1986
Zegeerg
1986
Fambroh
1987
Chicago, Houston, Los Angeles Houston (peak)
Fambroh
1987
Houston (off peak)
Fambroh
1987
Los Angeles (peak)
Fambroh
1987
Los Angeles (off peak)
Prevedourosi
1988
Chicago
Roessj
1988
Roessj
1988
Shortk
1989
California, New York, Texas (single lane) California, Illinois, New York, Texas (multilane) College Station
Gastonl
1991
Dallas
Zegeerm
1992
Florida
a
8 hr 3 Int. 7 Int.
start-up lost time (sec)
saturation flow rate (pcphgpl)
saturation headway (sec)
30 hr 2 Int. 30 hr 2 Int. 34 hr 2 Int. 34 hr 2 Int. 6.25 hr 10 Int. 5 Int.
4
—
2000
1.8
5
—
1791
2.01
7 Int.
5
—
1937
1.86
30 hr 2 Int. 25 hr 4 Int. 16 Int.
4
1.31
1905
1.89
5
—
1910
1.88
—
—
1840
1.96
Gerlough, D.L., and Wagner, F.A., ‘‘Improved Criteria for Traffic Signals at Individual Intersections.’’ NCHRP Report 32 (1967). Carstens, R.L., ‘‘Some Parameters at Signalized Intersections.’’ Traffic Engineering (Aug. 1971). King, G., and Wilkinson, M., ‘‘Relationship of Signal Design to Discharge Headway, Approach Capacity, and Delay.’’ Transportation Research Record 615, Transportation Research Board, Washington, D.C. (1973). d Agent, K., and Crabtree, J., Analysis of Lost Times at Signalized Intersections. Report, Kentucky Transportation Research Program, University of Kentucky, Lexington, Ky. (1983). e Lee, J., and Chen, L.R., ‘‘Engineering Headway at Signalized Intersections in Small Metropolitan Area.’’ Transportation Research Record 1091, Transportation Research Board, Washington, D.C. (1986). f Molina, C.J., Messer, C.J., and Fambro, D.B., Passenger Car Equivalencies for Large Trucks at Signalized Intersections. TTI Research Report 397-2, Texas Transportation Institute, Texas A&M University, College Station, Tex. (1987). g Zegeer, J.D., ‘‘Field Validation of Intersection Capacity Factors.’’ Transportation Research Record 1091, Transportation Research Board, Washington, D.C. (1986). h Fambro, D.B., Chang, E.P.C., and Messer, C.J., ‘‘Effects of the Quality of Traffic Signal Progression on Delay.’’ NCHRP Report 339 (1991). i Prevedouros, P.D., and Jovanis, P.P., ‘‘Validation of Saturation Flows and Progression Factors for Traffic Actuated Signals.’’ Transportation Research Record 1194, Transportation Research Board, Washington, D.C. (1988). j Roess, R.P., Papayannoupoulis, J.M., Ulerio, J.M., and Levinson, H.S., Levels of Service in Shared-Permissive Left-Turn Lane Groups at Signalized Intersections. Report DTFH 61-87-C-00012, Transportation Training and Research Center, Polytechnic University, Brooklyn, N.Y. (1989). k Short, J.T., ‘‘Effects of Dips and Bumps on Saturation Flow Rates at Signalized Intersections.’’ Thesis, Texas A&M University, College Station, Tex. (1989). l Gaston, G.D., ‘‘An Operational Analysis of Protected Lead-Lag Left Turn Phasing.’’ Thesis, Texas A&M University, College Station, Tex. (1991). m Zegeer, J., Data Collected for Florida Department of Transportation (1992). b c
Updated October 1994
traffic characteristics some indication that the saturation headway may increase somewhat when green time becomes quite long. This effect implies that green phases longer than 40 or 50 sec may not be proportionally as efficient as those in the normal range (43). Zegeer (46) has shown the significance of prevailing conditions of lane width, parking, transit interference, pedestrian interference, turning movements, flow composition, signal progression, and other factors, all of which influence saturation flow values. For ideal conditions, including 12-ft lanes, all through vehicles, all passenger cars, no parking, no transit interference, and low pedestrian volumes, the procedures of Chapter 9 recommend a saturation flow rate of 1,900 pcphgpl, corresponding to a saturation flow headway of 1.9 sec. This represents an increase of 100 pcphpl compared with the 1985 manual. Start-up lost times were also measured during the studies mentioned in Table 2-13 and other research projects (47,48) for a variety of conditions, including city size (population), location within the city, signal timing, speed limit, and other factors. Typical values observed range from 1.0 to about 2.0 sec. Corresponding values of change-interval lost time range from 1.2 to 2.8 sec. The length of the change interval (yellow + all red) has a significant effect on the value observed. The latest research suggests that the lost time associated with a phase may be up to 3.0 sec shorter than its change interval (49). The variation in the data in Table 2-13 and the importance of prevailing conditions suggest that local data collection to determine saturation flow rate and lost time can lead to more accurate compu-
2-33
tations. A data collection technique to measure saturation flow is described in an appendix of Chapter 9. Signalized intersection procedures of this manual rely heavily on saturation headway and lost time calibrations as a means of describing the use of available green time. GAP ACCEPTANCE AND SATURATION FLOW AT UNSIGNALIZED INTERSECTIONS
Two variables are used to estimate capacity flow rate at twoway stop-controlled intersections: the critical gap and the followup time (50). Typical values of the critical gap for an urban two-way stopcontrolled intersection on a four-lane road with a 30-mph speed limit range from 5.0 sec for the left-turning traffic from the major street to 6.5 sec for the left-turning traffic from the minor street. Follow-up gaps range from 2.1 to 3.4 sec for the same maneuvers. In effect, the follow-up gap is a saturation flow headway, since it is the gap between consecutive minor street vehicles using a long major street gap. Saturation flow at a stop line of an all-way stop-controlled intersection depends mostly on the presence of vehicles at other intersection approaches. When no traffic was present on other intersection approaches, the saturation flow rate on a single lane approach was measured at 1,100 vph (50), whereas for an intersection with four evenly loaded approaches and ideal conditions, 2,000 vph was achieved. These saturation flows correspond to the departure headways of 3.3 and 7.2 sec, respectively.
VII. SUMMARY The range and use of important highway traffic characteristics in capacity analysis have been addressed in this chapter. It is emphasized that these characteristics are not uniform or constant throughout North America and that variations due to local driving habits and environments are to be expected. Direct measurement of such characteristics may be used to fine-tune or improve the results of the analysis procedures of this manual, which are based on observed national averages. The values and relationships presented in this chapter provide a backdrop to capacity and service levels discussed in the following chapters. The expression ‘‘capacity’’ depends on the units being observed (vehicles, passenger car units, pedestrians), the time period, and the area of the facility being considered (lane, width in feet, area). Each facility type has specific units for expressing capacity. Table
2-14 presents a summary. In terms of passenger car units, capacity under ideal conditions is characterized by 2,200 pcphpl for uninterrupted flow along four-lane freeways and multilane highways and 2,300 pcphpl on freeways with six or more lanes. On two-lane rural highways, capacity ranges from 2,000 to 2,800 pcph total for both directions of flow, depending on the directional split of volume. At signalized intersections, 1,900 passenger car units (pcu) can depart from the stop line for each hour of green time, on a per lane basis. The capacity of minor approaches of unsignalized intersections is influenced by the type of control and by the competing traffic flows. It varies from 500 to 1,100 vph. Because specific local situations are seldom ideal, downward adjustments are normally made to account for actual operating conditions. The following chapters detail these procedures.
Updated October 1994
principles of capacity
2-34
Table 2-14. Capacity by Facility Type facility
units
time perioda
area
units of flow
capacity (ideal conditions)
Uninterrupted Flow Facilities Freeway Basic section, four lanes Basic section, six or more lanes Weaving area Ramp junction
Passenger cars
Hour
Lane
pcphplb
2,200
Passenger cars
Hour
Lane
pcphpl
2,300
Passenger cars Passenger cars
Hour Hour
pcphpl pcph
1,900 2,000
One-lane ramp Multilane highway Two-lane highway
Passenger cars Passenger cars Passenger cars
pcph pcphpl pcph
1,700 2,200 2,800c
Signalized intersection
Passenger cars
pcphgpl
1,900d
pcph
1,060e
vph
500–1,100f
90–120
Unsignalized intersection Two-way stop controlled All-way stop controlled Urban arterialg Exclusive transit bus lane on urban arterial with stops Pedestrian walkway Bikeway
Lane Merge or diverge area Hour Ramp roadway Hour Lane Hour Both lanes Interrupted Flow Facilities Hour of Lane green
Passenger cars
Hour
Vehicles
Hour
Lane or movement Entering lane
Buses
Hour
Lane
bphpl
Foot of effective width Lane
p/min/ft
Pedestrians Bicycles
Minute Hour
bike/hr
25 2,150h
a
Time periods of 1 hr are usually based on a peak 15-min volume expanded to an ‘‘hourly rate of flow.’’ Passenger cars per hour per lane. c For 50-50 volume split by direction. d Saturation flow rate, in passenger cars per hour of green per lane. e Potential capacity with no conflicting volume. f Depending on volume distribution from conflicting approaches. g Capacity usually measured and controlled by most restrictive signalized intersection. h Middle of reported range. b
REFERENCES 1. Drake, J., Schofer, J., and May, A., ‘‘A Statistical Analysis of Speed-Density Hypotheses.’’ Highway Research Record 154, Transportation Research Board, Washington, D.C. (1967). 2. May, A.D., Traffic Flow Fundamentals. Prentice-Hall, Englewood Cliffs, N.J. (1990) pp. 284–315. 3. Two-Lane Rural Roads: Design and Traffic Flow. Organization for Economic Cooperation and Development, Paris, France (1972). 4. Messer, C., Two-Lane, Two-Way Rural Highway Capacity. Final Report, NCHRP Project 3-28A, Texas Transportation Institute, College Station, Tex. (1983). 5. Transportation and Traffic Engineering Handbook. 2nd Edition, Prentice-Hall, Englewood Cliffs, N.J. (1982). 6. McShane, W., and Crowley, K., ‘‘Regularity of Some Detector-Observed Arterial Traffic Volume Characteristics.’’ Updated October 1994
7.
8.
9.
10. 11.
Transportation Research Record 596, Transportation Research Board, Washington, D.C. (1976). Crabtree, J., and Deacon, J., ‘‘Highway Sizing.’’ Transportation Research Record 869, Transportation Research Board, Washington, D.C. (1982). Werner, A., and Willis, T., ‘‘Cost-Effective Level of Service and Design Criteria.’’ Transportation Research Record 699, Transportation Research Board, Washington, D.C. (1979). Glauz, W., Harwood, D., and St. John, A., ‘‘Projected Vehicle Characteristics Through 1995.’’ Transportation Research Record 772, Transportation Research Board, Washington, D.C. (1980). Highway Statistics—Summary to 1975. Federal Highway Administration, Washington, D.C. (1975). Jones, E., Goolsby, M., and Brewer, K., ‘‘The Environmen-
traffic characteristics
12. 13.
14. 15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
tal Influence of Rain on Freeway Capacity.’’ Highway Research Record 321, Transportation Research Board, Washington, D.C. (1970). Ries, G., Impact of Weather on Freeway Capacity. Minnesota Department of Transportation, Minneapolis, Minn. (1981). Hurdle, V., and Datta, P., ‘‘Speeds and Flows on an Urban Freeway: Some Measurements and a Hypothesis.’’ Transportation Research Record 905, Transportation Research Board, Washington, D.C. (1983). Huber, M., and Tracy, J., ‘‘Operating Characteristics of Freeways.’’ NCHRP Report 60 (1968). Gerlough, D., and Huber, M., Traffic Flow Theory. Special Report 165, Transportation Research Board, Washington, D.C. (1975). Drake, J., Schofer, J., and May, A., ‘‘A Statistical Analysis of Speed-Density Hypotheses.’’ Vehicular Traffic Science, American Elsevier, New York, N.Y. (1967). Drake, J., Schofer, J., and May, A., ‘‘A Statistical Analysis of Speed-Density Hypotheses.’’ Highway Research Record 154, Transportation Research Board, Washington, D.C. (1967). Ceder, A., ‘‘Investigation of Two-Regime Traffic Flow Models at the Micro- and Macroscopic Levels.’’ Thesis, University of California at Berkeley, Berkeley, Calif. (1975). Ceder, A., and May, A.D., ‘‘Further Evaluation of Singleand Two-Regime Traffic Models.’’ Transportation Research Record 567, Transportation Research Board, Washington, D.C. (1976). Easa, S.M., and May, A.D., ‘‘Generalized Procedures for Estimating Single- and Two-Regime Traffic Flow Models.’’ Transportation Research Record 772, Transportation Research Board, Washington, D.C. (1980). Banks, J.H., ‘‘Freeway Speed-Flow-Concentration Relationship: More Evidence and Interpretations.’’ Transportation Research Record 1225, Transportation Research Board, Washington, D.C. (1989). Hall, F.L., and Hall, L.M., ‘‘Capacity and Speed-Flow Analysis of the QEW in Ontario.’’ Transportation Research Record 1287, Transportation Research Board, Washington, D.C. (1990). Chin, H.C., and May, A.D., ‘‘Examination of the SpeedFlow Relationship at the Caldecott Tunnel.’’ Transportation Research Record 1320, Transportation Research Board, Washington, D.C. (1991). Wemple, E.A., Morris, A.M., and May, A.D., ‘‘Freeway Capacity and Level of Service Concepts.’’ In Highway Capacity and Level of Service, Branolte, U. (ed.), Balkema, Rotterdam, Netherlands (1991). Allen, B.L., Hall, F.L., and Gunther, M.A., ‘‘Another Look at Identifying Speed-Flow Relationships on Freeways.’’ Transportation Research Record 1005, Transportation Research Board, Washington, D.C. (1985). Gunther, M.A., and Hall, F.L., ‘‘Transitions in the Speed Flow Relationship.’’ Transportation Research Record 1091, Transportation Research Board, Washington, D.C. (1986). Hurdle, V.F., and Datta, P.K., ‘‘Speeds and Flows on an Urban Freeway: Some Measurements and a Hypothesis.’’ Transportation Research Record 905, Transportation Research Board, Washington, D.C. (1983). Persaud, B.N., and Hurdle, V.F., ‘‘Some New Data that Challenge Some Old Ideas About Speed-Flow Relationships.’’
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44. 45.
2-35
Transportation Research Record 1194, Transportation Research Board, Washington, D.C. (1988). Agyemang-Duah, K., and Hall, F.L., ‘‘Freeway Capacity Drop and the Definition of Capacity.’’ Transportation Research Record 1320, Washington, D.C. (1991). Hall, F.L., and Agyemangh-Duah, K., ‘‘Some Isues Regarding the Numerical Value of Capacity.’’ In Highway Capacity and Level of Service, Branolte, U. (ed.), Balkema, Rotterdam, Netherlands (1991). Banks, J.H., ‘‘The Two-Capacity Phenomenon: Some Theoretical Issues.’’ Transportation Research Record 1320, Transportation Research Board, Washington, D.C. (1991). Urbanik, T., Hinshaw, W., and Barnes, K., ‘‘Evaluation of High-Volume Urban Texas Freeway.’’ Transportation Research Record 1320, Transportation Research Board, Washington, D.C. (1991). Reilly, W.R., Harwood, D.W., Schoen, J.M., Kuehl, R.O., Bauer, K., and St. John, A.D., Capacity and Level of Service Procedures for Multilane Rural and Suburban Highways. Final Report, NCHRP Project 3-33, JHK & Associates and Midwest Research Institute (May 1989). Roess, R., McShane, W., and Pignataro, L., ‘‘Freeway Level of Service: A Revised Approach.’’ Transportation Research Record 699, Transportation Research Board, Washington, D.C. (1980). Morrall, J., Two-Lane, Two-Way Highway Capacity—Canadian Data and Input to NCHRP 3-28A. Report, Texas Transportation Institute, College Station, Tex. (1983). Duncan, N.C., ‘‘A Note on Speed/Flow/Concentration Relations.’’ Traffic Engineering and Control, London, England (1976) p. 34. Duncan, N.C., ‘‘A Further Look at Speed/Flow/Concentration.’’ Traffic Engineering and Control, London, England (1979) p. 482. Teply, S., and Jones, A.M., ‘‘Saturation Flow: Do We Speak the Same Language?’’ Transportation Research Record 1320, Transportation Research Board, Washington, D.C. (1991). King, G., and Wilkinson, M., ‘‘Relationship of Signal Design to Discharge Headway, Approach Capacity, and Delay.’’ Transportation Research Record 615, Transportation Research Board, Washington, D.C. (1976). Berry, D., and Gandhi, P., ‘‘Headway Approach to Intersection Capacity.’’ Highway Research Record 453, Transportation Research Board, Washington, D.C. (1973). Akcelik, R., Traffic Signals: Capacity and Timing Analysis. Research Report ARR 123, Australian Road Research Board, Victoria, Australia (1981). Teply, S. (ed.), Canadian Capacity Guide for Signalized Intersections (1st edition). Institute of Transportation Engineers, District 7, Canada, and University of Alberta, Edmonton, Alberta, Canada (1984). Teply, S., Allingham, D., Richardson, D., and Stephenson, B., Factual Draft, Second Edition of the Canadian Capacity Guide for Signalized Intersections. Institute of Transportation Engineers, District 7, Canada (1993). Richtlinien fuer Lichtsignalanlagen, Forschungsgesellschaft fuer Strassen- und Verkehrswesen, Ko¨ln, Germany (1992). Bonneson, J.A., ‘‘Study of Headway and Lost Time at Single-Point Urban Interchanges.’’ Transportation Research Record 1365, Transportation Research Board, Washington, D.C. (1992). Updated October 1994
2-36
principles of capacity
46. Zegeer, J.D., ‘‘Field Validation of Intersection Capacity Factors.’’ Transportation Research Record 1091, Transportation Research Board, Washington, D.C. (1986). 47. Agent, K., and Crabtree, J., Analysis of Saturation Flow at Signalized Intersections. Report, Kentucky Transportation Research Program, University of Kentucky, Lexington, Ky. (May 1982). 48. Agent, K., and Crabtree, J., Analysis of Lost Times at Signalized Intersections. Report, Kentucky Transportation Research Program, University of Kentucky, Lexington, Ky. (Feb. 1983). 49. Bonneson, J., ‘‘Change Interval Timing and Lost Time for Single Point Urban Interchanges.’’ Journal of Transportation Engineering, Vol. 118, No. 5 (1992).
Updated October 1994
50. Transportation Research Circular 373: Interim Materials on Unsignalized Intersection Capacity. Transportation Research Board, Washington, D.C. (1991). 51. Mutanyi, T., ‘‘A Method of Estimating Traffic Behavior on All Routes in a Metropolitan County.’’ Highway Research Record 41, Transportation Research Board, Washington, D.C. (1963). 52. Levinson, H., Characteristics of Urban Transportation Demand—A Handbook for Transportation Planners. Urban Mass Transportation Administration, Washington, D.C. (1978).
Highway Capacity Manual 1997 Chapter 3
BASIC FREEWAY SECTIONS
CONTENTS I.
INTRODUCTION .................................................................................................. Definitions ............................................................................................... Freeway Facilities ............................................................................ Freeway Capacity Terms................................................................. Base Conditions for Freeway Capacity ........................................... Flow Characteristics................................................................................ Ideal Conditions for Freeway Flow .................................................. Speed-Flow Relationship ................................................................. Free Flow.................................................................................. Queue Discharge and Congested Flow ................................... Factors Affecting Free-Flow Speed ................................................. Lane Width and Lateral Clearance .......................................... Number of Lanes ...................................................................... Interchange Density.................................................................. Other Factors............................................................................ Vehicle Equivalents ......................................................................... Driver Population .............................................................................
3-1 3-1 3-1 3-1 3-2 3-2 3-3 3-3 3-3 3-4 3-4 3-4 3-5 3-6 3-7 3-7 3-8
II.
METHODOLOGY ................................................................................................. Performance Measures........................................................................... Levels of Service .................................................................................... Basic Relationships................................................................................. Determination of Flow Rate ............................................................. Peak-Hour Factor ..................................................................... Heavy-Vehicle Adjustment Factor ............................................ Extended General Freeway Segments ............................. Specific Grades ................................................................. Equivalents for Extended General Freeway Segments ........... Level Terrain ..................................................................... Rolling Terrain ................................................................... Mountainous Terrain ......................................................... Equivalents for Specific Upgrades ........................................... Equivalents for Specific Downgrades....................................... Equivalents for Composite Grades .......................................... Computation of Heavy-Vehicle Factor ..................................... Driver Population Adjustment ................................................... Determination of Free-Flow Speed ................................................. Field Measurement ................................................................... Estimation Guidelines ............................................................... Ideal Free-Flow Speed ...................................................... Lane Width ........................................................................ Lateral Clearance .............................................................. Number of Lanes............................................................... Interchange Density .......................................................... Determination of Level of Service ...................................................
3-8 3-8 3-8 3-14 3-14 3-15 3-15 3-15 3-16 3-16 3-16 3-16 3-16 3-16 3-18 3-19 3-19 3-19 3-19 3-20 3-20 3-20 3-21 3-21 3-21 3-22 3-22
III.
APPLICATIONS ................................................................................................... Segmenting the Freeway ........................................................................ Computational Steps............................................................................... Planning Analysis....................................................................................
3-23 3-23 3-24 3-25
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Basic Freeway Sections
Highway Capacity Manual 1997 HOV Facilities ......................................................................................... 3-25 Tools for Analysis ................................................................................... 3-25 IV.
EXAMPLE PROBLEMS ......................................................................................... Example Problem 1 ................................................................................ Example Problem 2 ................................................................................ Example Problem 3 ................................................................................ Example Problem 4 ................................................................................ Example Problem 5 ................................................................................
3-26 3-26 3-28 3-30 3-32 3-34
V.
REFERENCES .................................................................................................... 3-36 APPENDIX I. Precise Procedure for Determining Passenger-Car Equivalents of Trucks on Composite Upgrades ................................................................ 3-37 APPENDIX II. Worksheet for Analysis of Basic Freeway Sections................... 3-40
FIGURES AND TABLES Figure 3-1. Example of Basic Freeway Section...........................................................
3-2
Figure 3-2. Speed-Flow Relationships .........................................................................
3-4
Figure 3-3. Queue Discharge and Congested Flow ....................................................
3-5
Figure 3-4. LOS Criteria ............................................................................................... 3-10 Figure 3-5. Worksheet for Analysis of Basic Freeway Sections.................................. 3-14 Figure I.3-1. Sample Solution for Composite Grade.................................................... 3-37 Figure I.3-2. Performance Curves for Standard Trucks (200 lb/hp) ............................ 3-38 Table 3-1. LOS Criteria for Basic Freeway Sections ................................................... 3-11 Table 3-2. Passenger-Car Equivalents on Extended General Freeway Segments....................................................................................................... 3-16 Table 3-3. Passenger-Car Equivalents for Trucks and Buses on Specific Upgrades ................................................................................................... 3-17 Table 3-4. Passenger-Car Equivalents for Recreational Vehicles on Specific Upgrades ...................................................................................................................... 3-18 Table 3-5. Passenger-Car Equivalents for Trucks and Buses on Specific Downgrades.................................................................................................................. 3-18 Table 3-6. Adjustment Factors for Lane Width ............................................................ 3-21 Table 3-7. Adjustment Factors for Right-Shoulder Lateral Clearance......................... 3-21 Table 3-8. Adjustment Factors for Number of Lanes .................................................. 3-22 Table 3-9. Adjustment Factors for Interchange Density .............................................. 3-22
Basic Freeway Sections
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Highway Capacity Manual 1997 I. INTRODUCTION The procedures in this chapter are intended to analyze the capacity, level of service, lane requirements, and effects of traffic and design features of basic freeway sections. DEFINITIONS Freeway Facilities A freeway may be defined as a divided highway with full control of access and two or more lanes for the exclusive use of traffic in each direction. Freeways provide uninterrupted flow. There are no signalized or stop-controlled at-grade intersections, and direct access to and from adjacent property is not permitted. Access to and from the freeway is limited to ramp locations. Opposing directions of flow are continuously separated by a raised barrier, an at-grade median, or a raised traffic island. Operating conditions on a freeway primarily result from interactions among vehicles and drivers in the traffic stream and between vehicles and their drivers and the geometric characteristics of the freeway. Operations can also be affected by environmental conditions, such as weather or lighting conditions, by pavement conditions, and by the occurrence of traffic incidents. A tollway or toll road is similar to a freeway, except that tolls are collected at designated points along the facility. Although the collection of tolls does involve interruptions to traffic, these facilities may generally be treated as freeways. However, special attention should be given to the unique characteristics, constraints, and delays caused by toll collection facilities. A freeway consists of three component parts: T Basic freeway sections: Segments of the freeway that are outside of the influence area of ramps or weaving areas. T Weaving areas: Segments of the freeway where two or more vehicle flows must cross each other’s path along a length of the freeway. They are usually formed when merge areas are followed by diverge areas. They are also formed when an onramp is followed by an off-ramp and the two are connected by an auxiliary lane (for analysis of weaving areas, see Chapter 4). T Ramp junctions: Points at which on- and off-ramps join the freeway. The junction formed at this point is an area of turbulence because of concentrations of merging or diverging vehicles (for analysis of ramps and ramp junctions, see Chapter 5). Figure 3-1 illustrates a basic freeway section. The integration of these three component parts into a freeway facility is covered in Chapter 6.
Freeways provide uninterrupted flow.
Toll road is similar to a freeway.
Basic sections are outside the influence of ramps or weaving.
Freeway Capacity Terms T Freeway capacity: the maximum sustained 15-min rate of flow, expressed in passenger cars per hour per lane (pcphpl), that can be accommodated by a uniform freeway segment under prevailing traffic and roadway conditions in a specified direction. T Traffic characteristics: any characteristic of the traffic stream that may affect capacity, free-flow speed, or operations, including the percentage composition of the traffic stream by vehicle type and the familiarity of drivers with the roadway. T Roadway characteristics: the geometric characteristics of the freeway segment under study, including the number and width of lanes, right-shoulder lateral clearance, interchange spacing, vertical alignment, and lane configurations. T Free-flow speed: the mean speed of passenger cars under low to moderate flow rates that can be accommodated on a uniform freeway section under prevailing roadway and traffic conditions. It should be noted that capacity analysis is based on freeway segments with uniform traffic and roadway conditions. If any of these prevailing conditions change
Updated December 1997
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Basic Freeway Sections
Highway Capacity Manual 1997 See Chapter 4, Weaving Areas. See Chapter 5, Ramps and Ramp Junctions. See Chapter 6, Freeway Systems.
FIGURE 3-1. EXAMPLE
OF
BASIC FREEWAY SECTION
significantly, the capacity of the segment and its operating conditions change as well. Therefore, each uniform segment should be analyzed separately. Base Conditions for Freeway Capacity Conditions under which the full capacity of a basic freeway section is achieved are good weather, good visibility, and no incidents or accidents. When one or more of these conditions fail to exist, the speed, level of service, and capacity of the freeway section all tend to be reduced. FLOW CHARACTERISTICS Traffic flow within basic freeway sections can be highly varied depending on the conditions at upstream and downstream bottleneck locations that constrict the flow into and out of the freeway section. Bottlenecks can be created by ramp merge and weaving areas, lane drops, maintenance and construction activities, accidents, and objects in the road. An incident does not have to block a travel lane to create a bottleneck. Disabled vehicles in the median or shoulder can influence traffic flow within freeway lanes. Recent freeway research has resulted in a better understanding of the characteristics of freeway flow relative to the influence of upstream and downstream bottlenecks. Traffic flow within a basic freeway segment can generally be categorized into three flow types: free flow, queue discharge flow, and congested flow. Each flow type can be defined within general speed-flow-density ranges and represents different conditions on the freeway. T Free flow represents traffic flow that is unaffected by upstream or downstream conditions. This flow regime is generally defined within a speed range of 55 to 75 mph at low to moderate flow rates and a range of 45 to 65 mph at high flow rates. T Queue discharge flow represents traffic flow that has just passed through a bottleneck and is accelerating back to the free-flow speed of the freeway. Queue discharge flow is characterized by relatively stable flow as long as the effects of another bottleneck downstream are not present. This flow type is generally defined within a narrow range of flows, 2,000 to 2,300 pcphpl, with speeds typically ranging from 35 mph up to the free-flow speed of the freeway section. Lower speeds are typically observed just downstream of the bottleneck. Depending on horizontal and vertical alignment, queue discharge flow usually accelerates back to the free-flow Basic Freeway Sections
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Highway Capacity Manual 1997 speed of the facility within 1⁄2 to 1 mi downstream from the bottleneck. Recent studies suggest that the queue discharge flow rate from the bottleneck is lower than the maximum flows observed before a breakdown. A general rule of thumb for this drop in flow rate is approximately 5 percent. T Congested flow represents traffic flow that is influenced by the effects of a downstream bottleneck. Traffic flow in the congested regime can vary over a broad range of flows and speeds depending on the severity of the bottleneck. Queues may extend many thousands of feet upstream from the bottleneck. Freeway queues differ from queues at intersections in that they are not static or ‘‘standing.’’ On freeways vehicles move slowly through a queue, with periods of stopping and movement. Ideal Conditions for Freeway Flow The specific speed-flow-density relationship depends on prevailing traffic and roadway conditions for the basic freeway section in question. The basic characteristics described here were established for the following ideal conditions: T Minimum lane widths of 12 ft; T Minimum right-shoulder lateral clearance between the edge of the travel lane and the nearest obstacle or object influencing traffic behavior of 6 ft (minimum median lateral clearance is 2 ft); T Traffic stream consisting of passenger cars only; T Ten or more lanes (in urban areas only); T Interchanges spaced every 2 mi or more; T Level terrain, with grades no greater than 2 percent; and T Driver population dominated by regular and familiar users of the facility. These ideal conditions represent the highest type of basic freeway section, one with a free-flow speed of 70 mph or greater. It should be noted that these conditions are considered ideal only from the point of view of free-flow speed, capacity, and level of service, and that the term ‘‘ideal’’ has no connotation with respect to safety or other factors. Speed-Flow Relationship
Free Flow Figure 3-2 describes the speed-flow relationships for free flow on basic freeway sections. All recent freeway studies indicate that speed on freeways is insensitive to flow if the flow is low to moderate. This is reflected in Figure 3-2, which shows speed to be constant for flows up to 1,300 pcphpl for a 70-mph free-flow speed. For freeways with a lower free-flow speed, the region over which speed is insensitive to flow extends to even higher flow rates. Thus, free-flow speed is easily measured in the field as the average speed of passenger cars when flow rates are less than 1,300 pcphpl. Field determination of free-flow speed is easily accomplished by performing travel time or spot speed studies during periods of low flows. Note that although Figure 3-2 shows only curves for free-flow speeds of 75, 70, 65, 60, and 55 mph, curves representing any free-flow speed between 75 and 55 mph can be obtained by interpolation. Also, the speed-flow curve representing a 75-mph free-flow speed, which corresponds with the recent increase in the posted speed limit on many rural freeway sections throughout the United States, shown by a dashed line, is not based on empirical field research but was created by extrapolation from the 70-mph free-flow speed curve. Capacity at free-flow speeds greater than or equal to 70 mph is considered to be 2,400 pcphpl. Research leading to these speed-flow curves found that a number of factors affect free-flow speed, including number of lanes, lane width, lateral clearance, and interchange density or spacing. Other factors believed to influence free-flow speed, but for which little is known quantitatively, include horizontal and vertical alignment, speed limit, level of enforcement, lighting conditions, and weather. Under ideal traffic and geometric conditions, freeways will operate with capacities as high as 2,400 pcphpl. This capacity is typically achieved on freeways with free-flow Updated December 1997
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Basic Freeway Sections
Highway Capacity Manual 1997 speeds of 70 mph or greater. As the free-flow speed decreases, there is a slight decrease in capacity. For example, the capacity of a basic freeway section with a freeflow speed of 55 mph is expected to be approximately 2,250 pcphpl. The average speed of passenger cars at flow rates that represent capacity is expected to range from 53 mph (free-flow speeds of 70 mph or greater) to 50 mph for a section with a 55-mph free-flow speed. Note that the higher the free-flow speed, the greater the drop in speed as flow rates move toward capacity. Thus, for a 70-mph freeflow speed, there is a 17-mph drop from low-volume conditions to capacity conditions. The drop is only 5 mph for a freeway with a 55-mph free-flow speed. As indicated in Figure 3-2, the point at which an increase in flow rate begins to affect the average passenger car speed varies from 1,300 to 1,750 pcphpl. Speed will begin to be reduced at 1,300 pcphpl for free-flow speeds of 70 mph or greater. For lower-speed facilities, the free-flow speed begins to diminish at higher flow rates. Curves are based on research conducted in 1992– 1995 under NCHRP Project 3-45 (1).
FIGURE 3-2. SPEED-FLOW RELATIONSHIPS
Queue Discharge and Congested Flow Unlike free flow, queue discharge and congested flow have not been extensively studied, and these traffic flow types can be highly variable. However, freeway research performed since 1990 has provided valuable insight into possible speed-flow relationships that describe these two flow regimes. Figure 3-3 presents one suggested relationship and is intended for informational purposes only. This relationship is not included in the level of service (LOS) procedures in this chapter, which address free-flow conditions only. Users of this manual are cautioned that although the alternative relationship in Figure 3-3 may provide a general predictive model for speed under queue discharge and congested flows, it should be considered conceptual at best. Further research is needed to better define flow in these two regimes.
Factors affecting free-flow speed.
Lateral clearance is measured from edge of travel lane to curb, guardrail, or other physical obstruction. Basic Freeway Sections
Factors Affecting Free-Flow Speed Recent research has found that the free-flow speed on a freeway depends on the traffic and roadway conditions present on a given facility. These conditions are described in the following sections.
Lane Width and Lateral Clearance When lane widths are less than 12 ft, drivers are forced to travel closer to one another laterally than they would normally desire. The effect of restricted lateral clearance is similar. When objects are located too close to the edge of the median and roadside lanes, drivers in these lanes will shy away from them, positioning themselves Page 3-4
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Highway Capacity Manual 1997 FIGURE 3-3. QUEUE DISCHARGE
AND
CONGESTED FLOW
further from the lane edge. This restricted lateral clearance has the same effect as narrow lanes: it forces drivers closer together laterally. Drivers have been found to compensate by reducing their speed. The closeness of objects has been found to have a greater effect on drivers in the right shoulder lane than on those in the median lane. Drivers in the median lane appear to be unaffected by lateral clearance when minimum clearance is 2 ft, whereas drivers in the right shoulder lane are affected when lateral clearance is less than 6 ft. Illustration 3-1 shows the effects of lane width and lateral clearance on lateral placement of vehicles. Illustration 3-2 shows a freeway section considered ideal with respect to lane width and lateral clearance.
Number of Lanes The number of lanes on a freeway section influences free-flow speed. As the number of lanes increases, so does the opportunity for drivers to position themselves to avoid slower-moving traffic. In typical freeway driving, traffic tends to be distributed across lanes according to speed. Traffic in the median lane or lanes typically moves faster than in the lane adjacent to the right shoulder. Thus, a four-lane freeway (two lanes in each direction) provides less opportunity for drivers to move around slower traffic than does a freeway with 6, 8, or 10 lanes. The effect of decreased maneuverability is to reduce the average speed of vehicles in the traffic stream.
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Basic Freeway Sections
Highway Capacity Manual 1997 Illustration 3-1.
Vehicles shy away from both roadside and median barriers, driving as close to the lane marking as possible. The existence of narrow lanes compounds the problem, making it difficult for two vehicles to travel alongside each other.
Illustration 3-2. Ideal conditions of lane width and lateral clearance: the concrete median barrier does not cause vehicles to shift their lane position and therefore would not be considered an obstruction.
Interchange Density Research findings from NCHRP Project 3-45 (1).
Basic Freeway Sections
Merging and weaving associated with interchanges affect the speed of traffic. Freeway sections with closely spaced interchanges, such as those in heavily developed urban areas, operate at lower free-flow speeds than sections on suburban or rural freeways where interchanges are less frequent. Recent research that formed the basis for the analysis procedures presented in this chapter found that speeds generally decrease with increasing frequency of interchanges. The ideal average interchange spacing over a reasonably long freeway section (5 to 6 mi) is 2 mi or more. The Page 3-6
Updated December 1997
Highway Capacity Manual 1997 minimum average interchange spacing over a sustained length of freeway that is considered possible, though highly unlikely, is 1⁄2 mi.
Other Factors Design speed, a factor found in previous LOS guidelines, is not included in this chapter. The design speed of the primary physical elements of a freeway can affect travel speed. In particular, horizontal and vertical alignments of a highway may contribute to the free-flow speed of a given freeway section. Although factors describing the effects of these physical features on free-flow speed are not included in this chapter, if a freeway has somewhat extreme horizontal or vertical conditions, the user is encouraged to determine free-flow speed from field observation and field study rather than to rely on the estimation of free-flow speed given in this chapter.
Horizontal and vertical geometry may influence freeflow speed.
Vehicle Equivalents The concept of vehicle equivalents is based on observations of freeway conditions in which the presence of heavy vehicles, including trucks, buses, and recreational vehicles (RVs), creates less-than-ideal conditions. These nonideal conditions include longer and more frequent gaps of excessive lengths both in front of and behind heavy vehicles. Also, the speed of vehicles in adjacent lanes and their spacing may be affected by these generally slower-moving large vehicles. Finally, physical space taken up by a large vehicle is typically two to three times greater in terms of length than that of a typical passenger car. To allow the method for estimating freeway capacity to be based on a consistent measure of flow, each heavy vehicle is converted into the equivalent number of passenger cars. The conversion results in a single value for flow rate in terms of passenger cars per hour per lane. The conversion factor used depends on the proportion of heavy vehicles present in the traffic stream as well as the length and severity of the upgrade or downgrade. Illustrations 3-3 and 3-4 show the effects of trucks and other heavy vehicles on freeway traffic. Illustration 3-3.
Large gaps form in front of slow-moving trucks climbing the grade.
Updated December 1997
Page 3-7
Basic Freeway Sections
Highway Capacity Manual 1997 Illustration 3-4.
Even on relatively level terrain, large gaps in front of trucks or other heavy vehicles are unavoidable.
Driver Population Among the ideal conditions defined for freeway flow is a driver population consisting primarily of commuters. It has been noted in several studies across the nation that non-commuter-oriented driver populations do not display the same characteristics as commuter driver populations. For recreational traffic streams, capacities have been observed to be as much as 20 percent lower than for commuter traffic traveling on the same section. An effect on free-flow speed has not been reported. This effect on capacity, however, is highly variable and should be locally calibrated.
II. METHODOLOGY PERFORMANCE MEASURES A basic freeway section can be characterized by three performance measures: density in terms of passenger cars per mile per lane, speed in terms of mean passenger car speed, and volume-to-capacity ratio. Each of these measures is an indication of how well or how poorly traffic flow is being accommodated by the freeway. The assigned primary performance measure used to provide an estimate of level of service is density. The three measures of speed, density, and flow or volume are interrelated. When two of these measures are known, the third can be solved for.
Density is used to define level of service.
Basic Freeway Sections
LEVELS OF SERVICE Although speed is a major indicator of service quality to drivers, freedom to maneuver within the traffic stream and proximity to other vehicles are equally noticeable concerns. These other concerns are related to the density of the traffic stream. Furthermore, unlike speed, density increases as flow increases up to capacity, resulting in a measure of effectiveness that is sensitive to a broad range of flows. For these reasons, density is the parameter used to define levels of service for basic freeway sections. The ranges of density used to define levels of service are as follows:
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Highway Capacity Manual 1997 Level of Service A B C D E F
Density Range (pc/mi/ln) 0–10.0 10.1–16.0 16.1–24.0 24.1–32.0 32.1–45.0 > 45.0
For any given level of service, the maximum allowable density is somewhat lower than that for the corresponding level of service on multilane highways. This reflects the higher service quality drivers expect when using freeways as compared with surface multilane facilities. This does not imply that under similar conditions an atgrade multilane highway will perform better than a freeway with the same number of lanes. For any given density, a freeway will carry higher flow rates at higher speeds than will a comparable multilane highway. Although the specification of maximum densities for LOS A through D is based on the collective professional judgment of the members of the Committee on Highway Capacity and Quality of Service, the upper value shown for LOS E (45 pc/mi/ln) is not. That value is the density at which capacity occurs for different free-flow speeds; it is the maximum density at which sustained flows at capacity are expected to occur. LOS criteria for basic freeway sections are provided in Table 3-1 for free-flow speeds of 75, 70, 65, 60, and 55 mph. To be within a given level of service, the density criterion must be met. In effect, under ideal conditions, these are the speeds and flow rates expected to occur at the designated densities. Local variations in driving behavior, however, may cause some variance from these expectations. It should be noted that the LOS F operations observed within a queue are the result of a breakdown or bottleneck at a downstream point. LOS F is also used to describe conditions at the upstream point of the breakdown or bottleneck as well as the operations within the queue that forms behind it. Failure, breakdown, congestion, and LOS F occur when queues begin to form on the freeway. Density tends to increase sharply within the queue and may be expected to be considerably higher than the maximum value of 45 pc/mi/ln for LOS E. Figure 3-4 shows the relationship among speed, flow, and density for basic freeway sections. It also shows the definition of the various levels of service using density boundary values. Operational characteristics for the six levels of service are shown in Illustrations 3-5 through 3-10. The levels of service were defined to represent reasonable ranges in the three critical flow variables: speed, density, and flow rate. LOS A describes free-flow operations. Free-flow speeds prevail. Vehicles are almost completely unimpeded in their ability to maneuver within the traffic stream. Even at the maximum density for LOS A, the average spacing between vehicles is about 530 ft, or 26 car lengths, which affords the motorist a high level of physical and psychological comfort. The effects of incidents or point breakdowns are easily absorbed at this level. LOS B represents reasonably free flow, and free-flow speeds are maintained. The lowest average spacing between vehicles is about 330 ft, or 17 car lengths. The ability to maneuver within the traffic stream is only slightly restricted, and the general level of physical and psychological comfort provided to drivers is still high. The effects of minor incidents and point breakdowns are still easily absorbed. LOS C provides for flow with speeds at or near the free-flow speed of the freeway. Freedom to maneuver within the traffic stream is noticeably restricted at LOS C, and lane changes require more care and vigilance on the part of the driver. Minimum average spacings are in the range of 220 ft, or 11 car lengths. Minor incidents may still be absorbed, but the local deterioration in service will be substantial. Queues may be expected to form behind any significant blockage. LOS D is the level at which speeds begin to decline slightly with increasing flows. In this range, density begins to increase somewhat more quickly with increasing flow. Freedom to maneuver within the traffic stream is more noticeably limited, and the Updated December 1997
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Highway Capacity Manual 1997 FIGURE 3-4. LOS CRITERIA
Conditions that create LOS F.
Basic Freeway Sections
driver experiences reduced physical and psychological comfort levels. Even minor incidents can be expected to create queueing, because the traffic stream has little space to absorb disruptions. Minimum average vehicle spacings are about 165 ft, or eight car lengths. At its highest density value, LOS E describes operation at capacity. Operations at this level are volatile, there being virtually no usable gaps in the traffic stream. Vehicles are spaced at approximately six car lengths, leaving little room to maneuver within the traffic stream at speeds that are still over 49 mph. Any disruption to the traffic stream, such as vehicles entering from a ramp or a vehicle changing lanes, can establish a disruption wave that propagates throughout the upstream traffic flow. At capacity, the traffic stream has no ability to dissipate even the most minor disruptions, and any incident can be expected to produce a serious breakdown with extensive queueing. Maneuverability within the traffic stream is extremely limited, and the level of physical and psychological comfort afforded the driver is poor. LOS F describes breakdowns in vehicular flow. Such conditions generally exist within queues forming behind breakdown points. Such breakdowns occur for a number of reasons: T Traffic incidents cause a temporary reduction in the capacity of a short segment, so that the number of vehicles arriving at the point is greater than the number of vehicles that can move through it. T Points of recurring congestion exist, such as merge or weaving areas and lane drops where the number of vehicles arriving is greater than the number of vehicles discharged. T In forecasting situations, any location where the projected peak-hour (or other) flow rate exceeds the estimated capacity of the location presents a problem. Note that in all cases, breakdown occurs when the ratio of demand to actual capacity or the ratio of forecast demand to estimated capacity exceeds 1.00. Operations immediately downstream of such a point, however, are generally at or near Page 3-10
Updated December 1997
Highway Capacity Manual 1997 TABLE 3-1. LOS CRITERIA FOR BASIC FREEWAY SECTIONS Level of Service
Maximum Density (pc/mi/ln)
Minimum Speed (mph)
Maximum Service Flow Rate (pcphpl)
Maximum v/c Ratio
Free-Flow Speed = 75 mph A B C D E F
10.0 16.0 24.0 32.0 45.0 >45.0
75.0 75.0 71.0 65.0 53.0 1
2.0 6.0 9.0 12.5 13.0 13.0
2.0 4.5 7.0 9.0 9.5 9.5
1.5 4.0 6.0 8.5 9.0 9.0
1.5 4.0 6.0 8.0 8.0 8.0
1.5 3.5 5.5 7.0 7.5 7.5
1.5 3.0 5.0 7.0 7.0 7.0
1.5 3.0 4.5 6.0 6.5 6.5
1.5 2.5 4.0 6.0 6.0 6.0
1.5 2.0 3.5 5.0 5.5 5.5
0–1⁄4 ⁄4–1⁄3 1 1 ⁄3– ⁄2 1 3 ⁄2– ⁄4 3 ⁄4–1 >1
4.5 9.0 12.5 15.0 15.0 15.0
3.5 6.5 9.5 11.0 11.0 11.0
3.0 6.0 8.5 10.0 10.0 10.0
3.0 6.0 8.0 9.5 9.5 9.5
3.0 5.0 7.0 9.0 9.0 9.0
2.5 5.0 6.5 8.0 8.5 8.5
2.5 4.0 6.0 8.0 8.0 8.0
2.0 3.5 6.0 7.5 7.5 7.5
2.0 3.0 5.5 6.5 6.5 6.5
2
1
1
3
1
4
1
5
1
6
1
NOTE: If the length of grade falls on a boundary, apply the longer category; interpolation may be used to find equivalents for intermediate percent grades.
Updated December 1997
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Basic Freeway Sections
Highway Capacity Manual 1997 Critical point for analysis.
In the analysis of upgrades, the critical point is usually at the end of the grade, where heavy vehicles presumably have the maximum effect on operations. However, if a ramp junction is located mid-grade, the point of the merge or diverge would also be a critical point for analysis. In the case of composite grades, the point at which heavy vehicles are traveling slowest is the critical point for analysis. If a 5 percent upgrade is followed by a 2 percent upgrade, it is reasonable to assume that the end of the 5 percent portion would be critical, since heavy vehicles would be expected to accelerate on the 2 percent portion of the grade.
Equivalents for Specific Downgrades There is little specific information on the effect of heavy vehicles on traffic flow on downgrades. In general, if the downgrade is not severe enough to cause trucks to shift into low gear, it may be treated as a level terrain segment, and passenger-car equivalents are selected accordingly. When more severe downgrades occur, trucks must often use low gear to avoid gaining too much speed and running out of control. In such cases, their effect on traffic flow is greater than it would be on level terrain. Table 3-5 gives values of ET. For RVs, downgrades may be treated as level terrain. TABLE 3-4. PASSENGER-CAR EQUIVALENTS FOR RECREATIONAL VEHICLES ON SPECIFIC UPGRADES Passenger-Car Equivalent, ER Percent RVs
Grade (%)
Length (mi)
2
4
5
6
8
10
15
20
25
1⁄2
1.2 2.0
1.2 1.5
1.2 1.5
1.2 1.5
1.2 1.5
1.2 1.5
1.2 1.2
1.2 1.2
1.2 1.2
1
0–1⁄4 ⁄4–1⁄2 >1⁄2
1.2 2.5 3.0
1.2 2.5 2.5
1.2 2.0 2.5
1.2 2.0 2.0
1.2 2.0 2.0
1.2 2.0 2.0
1.2 1.5 2.0
1.2 1.5 1.5
1.2 1.5 1.5
1
0–1⁄4 ⁄4–1⁄2 >1⁄2
2.5 4.0 4.5
2.0 3.0 3.5
2.0 3.0 3.0
2.0 3.0 3.0
1.5 2.5 3.0
1.5 2.5 2.5
1.5 2.0 2.5
1.5 2.0 2.0
1.5 2.0 2.0
0–1⁄4 ⁄4–1⁄2 >1⁄2
4.0 6.0 6.0
3.0 4.0 4.5
2.5 4.0 4.0
2.5 3.5 4.0
2.5 3.0 3.5
2.0 3.0 3.0
2.0 2.5 3.0
2.0 2.5 2.5
1.5 2.0 2.0
3 4
5
6
1
NOTE: If the length of grade falls on a boundary, apply the longer category; interpolation may be used to find equivalents for intermediate percent grades.
TABLE 3-5. PASSENGER-CAR EQUIVALENTS FOR TRUCKS AND BUSES ON SPECIFIC DOWNGRADES Passenger-Car Equivalent, ET
Basic Freeway Sections
Percent Trucks/Buses
Grade (%)
Length (mi)
5
10
15
20
6
All ≤4 >4 ≤4 >4 ≤4 >4
1.5 1.5 2.0 1.5 5.5 1.5 7.5
1.5 1.5 2.0 1.5 4.0 1.5 6.0
1.5 1.5 2.0 1.5 4.0 1.5 5.5
1.5 1.5 1.5 1.5 3.0 1.5 4.5
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Highway Capacity Manual 1997 Equivalents for Composite Grades The vertical alignment of most freeways results in a continuous series of grades. It is often necessary to determine the effect of a series of significant grades in succession. Consider the following example: a 2 percent grade of 1⁄2 mi is followed immediately by a 4 percent grade of 1⁄2 mi. The analysis problem of interest is the maximum effect of heavy vehicles, which would occur at the end (top) of the 4 percent segment. The most straightforward technique is to compute the average grade to the point in question. The average grade is defined as the total rise in feet from the beginning of the composite grade divided by the length of the grade in feet. Passenger-car equivalents for this composite grade would be found for a 3 percent grade, 1 mi long. The average-grade technique is an acceptable approach for grades in which all subsections are less than 4 percent or the total length of the composite grade is less than 4,000 ft. For more severe composite grades, a detailed technique that uses vehicle performance curves and equivalent speeds to determine the effective simple grade for analysis is presented in Appendix I. For the example cited above, the total rise is (2,640 × 0.02) + (2,640 × 0.04) = 165.4 ft. The average grade is 165.4/5,280 = 0.03 or 3 percent. Computation of Heavy-Vehicle Factor Once the values of ET and ER have been found, the determination of the adjustment factor, fHV, is straightforward: fHV =
1 1 + PT (ET − 1) + PR (ER − 1)
(3-2)
Average grade technique.
Appendix I gives detailed example of composite grade.
Calculate heavy-vehicle factor to reflect proportion of trucks, buses, and RVs, and grade or terrain.
where ET, ER = passenger-car equivalents for trucks or buses and RVs in the traffic stream, PT, PR = proportion of trucks or buses and RVs in the traffic stream, and fHV = heavy-vehicle adjustment factor.
In many cases, trucks will be the only heavy vehicle type present in the traffic stream to a significant degree. Where the percentage of RVs is small compared with the percentage of trucks, it is sometimes convenient to consider all heavy vehicles to be trucks. Thus, a traffic stream consisting of 10 percent trucks and 2 percent RVs might be analyzed as having 12 percent trucks. It is generally acceptable to do this where the percentage of trucks and buses in the traffic stream is at least 5 times the percentage of RVs present.
Driver Population Adjustment The traffic stream characteristics that are the basis for the procedure described here are representative of regular drivers who are substantially commuters or are familiar with the facility. It is generally accepted that traffic streams with different characteristics (i.e., recreational drivers) use freeways less efficiently. Whereas data are sparse and reported results vary substantially, significantly lower capacities have been reported on weekends, particularly in recreational areas. It may generally be assumed that the reduction in capacity extends to service volumes for other levels of service as well. The adjustment factor fp is used to reflect this effect. The values for fp range from 1.0 to 0.85. In general, the analyst should select 1.0, which reflects commuter traffic (i.e., familiar users), unless there is sufficient evidence or it is the analyst’s judgment that a lesser value reflecting more recreational traffic characteristics should be applied. When greater accuracy is needed, comparative field studies of commuter and recreational traffic flow and speeds are recommended. Determination of Free-Flow Speed Free-flow speed is the mean speed of passenger cars measured under low to moderate flows (up to 1,300 pcphpl). For a specific section of freeway, speeds are virtually constant in this range of flow rates. Two methods can be used to determine Updated December 1997
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Measure or estimate free-flow speed.
Basic Freeway Sections
Highway Capacity Manual 1997 the free-flow speed of the basic freeway section being studied: field measurement and estimation with guidelines provided in this chapter. The field measurement procedure is provided for users who prefer to gather these data directly. However, field measurement is not necessary for application of this procedure.
Field Measurement The free-flow speed of a basic freeway section can be determined directly from a speed study conducted in the field. If field-measured data are used, no subsequent adjustments are made to the free-flow speed. The speed study should be conducted at a representative location within the freeway section being evaluated; for example, a segment on an upgrade or downgrade should not be selected within a section that is generally considered level. Any speed measurement technique that has been found acceptable for other types of traffic engineering speed studies may be used. The speed study should be conducted when flows are low (up to 1,300 pcphpl). Weekday off-peak hours are generally good times to observe low to moderate flow rates. The speed study should measure the speeds of all passenger cars or use a systematic sample (e.g., every 10th passenger car). The speed study should also measure at least 100 passenger-car speeds across all lanes. Further guidance on the conduct of speed studies is found in standard traffic engineering publications, such as the Manual of Traffic Engineering Studies published by the Institute of Transportation Engineers. The average of all passenger-car speeds measured in the field under low-volume conditions can be used directly as the free-flow speed of the freeway section. This speed reflects the net effects of all conditions at the study site that influence speed, including those considered in this procedure (lane width, lateral clearance, number of lanes, and interchange density) as well as others such as speed limit and vertical and horizontal alignment. Highway agencies with ongoing speed-monitoring programs or with existing speed data on file may prefer to use those data rather than conduct a new speed study or use an indirect method to estimate speed. Such data can be used directly if collected in accordance with the procedures presented above. Data that include both passenger cars and heavy vehicles can probably be used for level terrain or moderate downgrades but should not be used for rolling or mountainous terrain.
Estimate free-flow speed if field measurement is not possible.
Estimation Guidelines If field measurement of free-flow speed is not possible, the free-flow speed can be estimated indirectly on the basis of the physical characteristics of the freeway section being studied. These physical characteristics include lane width, right-shoulder lateral clearance, number of lanes, and interchange density. Equation 3-3 is used to estimate the free-flow speed of a basic freeway section: FFS = FFSi − fLW − fLC − fN − fID
(3-3)
where FFS FFSi fLW fLC fN fID
= = = = = =
estimated free-flow speed (mph); estimated ideal free-flow speed, 70 or 75 mph; adjustment for lane width from Table 3-6 (mph); adjustment for right-shoulder lateral clearance from Table 3-7 (mph); adjustment for number of lanes from Table 3-8 (mph); and adjustment for interchange density from Table 3-9 (mph).
Ideal Free-Flow Speed. Estimation of a free-flow speed for an existing or future freeway section being studied is accomplished by adjusting ideal free-flow speed downward to reflect the influence of four factors: lane width, lateral clearance, number of lanes, and interchange density. Thus, the analyst is required to select an appropriate ideal free-flow speed (FFSi) as a starting point. FFSi represents the mean speed for passenger cars under low to moderate flow rates and the ideal conditions defined previously. The research on which these procedures are based found that FFSi ranged between 70 and 75 mph. In using this Basic Freeway Sections
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Highway Capacity Manual 1997 procedure to estimate FFS, it is recommended that an FFSi of 70 or 75 mph be selected. As a rule of thumb, 75 mph can generally be considered to represent FFSi on a rural freeway, whereas on urban and suburban freeways, FFSi is best represented by 70 mph. The analyst should use careful judgment if it is believed that a higher or lower FFSi is more representative of freeway traffic flow in a given area. Again, measurement of actual free-flow speeds on the freeway section being studied or an area freeway with similar features is highly encouraged. Lane Width. The ideal condition for lane width is 12 ft or greater. When the average lane width across all lanes within a freeway section is less than 12 ft, the ideal free-flow speed (e.g., 70 mph) is reduced. Adjustment factors to reflect the effect of narrower average lane width are provided in Table 3-6. These factors were developed on the basis of studies conducted on multilane highways. Adjustment factors are provided only for average lane widths of 11 and 10 ft. It should be noted that freeway sections with average lane widths below 11 ft are generally considered rare. Lateral Clearance. Ideal lateral clearance is 6 ft or greater on the right side and 2 ft or greater on the median or left side. When the right-shoulder lateral clearance is less than 6 ft, the ideal free-flow speed is reduced. Adjustment factors to reflect the effect of narrower right-shoulder lateral clearance are provided in Table 3-7. No adjustment factors are available to reflect the effect of median lateral clearance less than 2 ft; however, lateral clearance on either the right or left sides less than 2 ft is considered rare. Considerable judgment must be used in determining whether objects or barriers along the right side of a freeway section present a true obstruction. Such obstructions may be continuous, such as a retaining walls, concrete barriers, or guardrails, or may be periodically occurring objects, such as light supports or bridge abutments. In some cases, drivers may become accustomed to certain types of obstructions, in which case their effect on traffic flow may become negligible. Number of Lanes. Freeway sections with five or more lanes (in one direction) are considered ideal with respect to number of lanes. When fewer lanes are present, the ideal free-flow speed is reduced. Table 3-8 provides adjustment factors to reflect the effect of number of lanes on ideal free-flow speed. When number of lanes is determined, only mainline lanes, both basic and auxiliary, should be considered. Highoccupancy-vehicle (HOV) lanes should not be included. The adjustment factors in Table 3-8 are based exclusively on data collected on urban and suburban freeway sections and do not reflect conditions on rural freeways,
Adjustment for lateral clearance reflects right shoulder width only.
Adjustment for number of lanes is not applicable to rural freeway segments.
TABLE 3-6. ADJUSTMENT FACTORS FOR LANE WIDTH Lane Width (ft)
Reduction in Free-Flow Speed fLW (mph)
≥12 11 10
0.0 2.0 6.5
TABLE 3-7. ADJUSTMENT FACTORS FOR RIGHT-SHOULDER LATERAL CLEARANCE Reduction in Free-Flow Speed, fLC (mph) Lanes in One Direction
Right Shoulder Lateral Clearance (ft)
2
3
4
≥6 5 4 3 2 1 0
0.0 0.6 1.2 1.8 2.4 3.0 3.6
0.0 0.4 0.8 1.2 1.6 2.0 2.4
0.0 0.2 0.4 0.6 0.8 1.0 1.2
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Highway Capacity Manual 1997 TABLE 3-8. ADJUSTMENT FACTORS FOR NUMBER OF LANES Number of Lanes (One Direction)
Reduction in Free-Flow Speed fN (mph)
≥5 4 3 2
0.0a 1.5 3.0 4.5
a
For rural freeway sections, fN = 0.0.
TABLE 3-9. ADJUSTMENT FACTORS FOR INTERCHANGE DENSITY
A 6-mi section is used to determine interchange density.
Interchanges per Mile
Reduction in Free-Flow Speed fID (mph)
≤0.50 0.75 1.00 1.25 1.50 1.75 2.00
0.0 1.3 2.5 3.7 5.0 6.3 7.5
which typically carry two lanes in each direction. Therefore, in using Equation 3-3 to estimate the free-flow speed of a rural freeway section, the value of the adjustment for number of lanes, fN, should be 0. Interchange Density. The ideal interchange density is 0.5 interchange per mile, or 2-mi interchange spacing. Ideal free-flow speed is reduced when interchange density is greater. Adjustment factors to reflect the effect of interchange density are provided in Table 3-9. Interchange density is determined over a 6-mi section of freeway (3 mi upstream and 3 mi downstream) in which the freeway section being studied is located. An interchange is defined as having at least one on-ramp. Therefore, interchanges that have only off-ramps would not be considered in determining interchange density. Interchanges considered should include typical interchanges with arterials or highways and major freeway-to-freeway interchanges. Determination of Level of Service The level of service on a basic freeway section can be determined directly from Figure 3-4 on the basis of the free-flow speed and the flow rate. The procedure is as follows: Step 1. Define and segment the freeway section as appropriate. Step 2. On the basis of the measured or estimated free-flow speed on the freeway segment, construct an appropriate speed-flow curve of the same shape as the typical curves shown in Figure 3-2. The curve should intercept the y-axis at the free-flow speed. Step 3. On the basis of the flow rate, vp, read up to the free-flow speed curve identified in Step 2 and determine the average passenger-car speed and level of service corresponding to that point. Step 4. Determine the density of flow as D = vp /S
(3-4)
where D = density (pc/mi/ln), vp = flow rate (pcphpl), and S = average passenger-car speed (mph).
The level of service can also be determined using the density ranges provided in Table 3-1. Basic Freeway Sections
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Highway Capacity Manual 1997 III. APPLICATIONS The methodology presented in this chapter may be used for operational analysis, design, or planning of basic freeway sections. The analyst should refer to Chapter 4, Weaving Areas, and Chapter 5, Ramps and Ramp Junctions, for additional information regarding definition of the freeway section being analyzed to confirm that the procedures provided in this chapter are indeed appropriate. Operational analysis involves the consideration of a known present or projected freeway for which all geometric variables and traffic variables can be specified. The analysis results in the determination of a level of service, as well as a probable operating speed and density. In design, a forecast demand volume is used to determine the number of lanes needed to provide the desired level of service. The objectives of a planning analysis are to determine the number of lanes needed to deliver a desired level of service. The difference between planning and design analysis is the level of detail available as input. In planning, annual average daily traffic (AADT) is generally known with very little detail concerning composition and/or hourly distribution. A planning analysis consists of making an estimate of directional design-hour volume (DDHV) and then applying typical (i.e., default) values for inputs to a design-type analysis. These procedures do not present a separate computational application for planning, since computations for both operational analysis and design are relatively simple and straightforward. Applications can be set into four general analysis types, each having a target output with the remaining parameters being known and being used as inputs.
Analysis types.
Type I analysis resolves the primary question, ‘‘Within what level of service does the freeway operate?’’ Thus, hourly flow rate (vp) and free-flow speed (FFS) are needed as inputs. This analysis type is used for operational studies. Type II analysis produces an estimate of speed (S) as the output. For the input, vp, level of service, and FFS must be used. Typically, this type of analysis is applied when travel time is the parameter of interest, for example, in feasibility or economic studies. Environmental studies (air and noise) would also depend on estimates of mean speed. For Type III analysis, an estimate of vp (pcphpl) is computed. As known inputs, both level of service and FFS are required. Typical applications include comparing the estimate of vp with the year-by-year forecast volumes for the freeway section. The timing of future improvements to maintain a specified level of service can be identified in this application. Type IV analysis results in an estimate of the number of lanes, N, required for a given set of conditions. As known inputs, vp, FFS, and level of service are required. This application has traditionally been called ‘‘design.’’ Also, when the analyst is using AADT data as a starting point, this same analysis can be termed ‘‘planning analysis.’’ SEGMENTING THE FREEWAY Any capacity or LOS analysis requires that the freeway section to be analyzed have uniform traffic and roadway conditions. A number of locations on any freeway form natural boundaries for identifying uniform segments. Any on-ramp or off-ramp is such a boundary, since the volume of freeway traffic changes at each. The beginning and end of specific simple or composite grades also act as boundaries between uniform freeway segments. Any point at which the traffic or roadway conditions change should be used as a boundary between uniform segments, each of which should be analyzed separately. In addition to the natural boundaries created by on-ramps and off-ramps, changes in the following characteristics generally dictate that the freeway section under analysis be segmented: Updated December 1997
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Basic Freeway Sections
Highway Capacity Manual 1997 T Number of lanes, T Right-shoulder lateral clearance that would result in a lower estimated freeflow speed, T Grade of 2 percent or more or a constant upgrade over 4,000 ft long, and T Speed limit.
Type I Analysis. Find LOS. Enter speed-flow graph with vp to find LOS.
Type II Analysis. Find speed (S). Enter speed-flow graph with vp to find S.
Type III Analysis. Find vp. Enter graph at intersection points of LOS lines and facility-specific speed-flow curve. Read vp on horizontal axis.
Type IV Analysis. Find number of lanes (N). Enter graph at intersecting points of specific speed-flow curve and LOS threshold. Read vp on horizontal axis. Use equation for vp and solve for N.
Basic Freeway Sections
COMPUTATIONAL STEPS The worksheet for computations is shown in Figure 3-5. For all analysis types, the analyst enters data in the General Information and Site Information portions of the worksheet. For Type I analysis, all information in the Traffic and Roadway Conditions section of the worksheet is entered except speed, S (which typically will be a secondary output). Flow is then computed with the aid of the tables of passenger-car equivalents. Free-flow speed (FFS) is estimated by applying adjustments for four factors to an ideal FFS determined by the analyst. Finally, level of service is derived (using vp) from the speed-flow graph at the top of the worksheet by intersecting the specific curve that has been selected or constructed for the freeway section being analyzed. This point of intersection identifies the level of service and also (on the vertical axis of the graph) the estimated speed, S. If the analyst requires a value for density (D), it is calculated as vp /S. For Type II analysis, all information in the Traffic and Roadway Conditions section is filled in by the analyst with the exception of speed, S. The flow rate calculations are performed by using the heavy-vehicle equivalents and the free-flow speed is estimated by using the adjustment factors in Tables 3-6 through 3-9. Alternatively, free-flow speed may have been directly measured in the field; then the direct measurement can be entered on the worksheet. With the free-flow speed established, the specific speed-flow curve for the section being analyzed is constructed or selected. The point of intersection between the flow rate, vp, and the appropriate speed-flow curve gives the speed, S. As secondary outputs, level of service can be read directly from the graph and density can be computed using flow rate and speed. The objective of Type III analysis is to estimate the flow rate in passenger cars per hour per lane given a set of traffic, roadway, and free-flow speed conditions. Typically a desired level of service is stated and entered on the worksheet. Then the free-flow speed of the section is established by using either the ideal speed (70 or 75 mph) and the four adjustment factors or a free-flow speed directly measured in the field. Once this facility-specific speed-flow curve has been established, the analyst can determine what flow rate is achievable with the given level of service. This flow rate would be the maximum flow rate achievable or allowable for the given level of service. Also directly available from the graph is the estimated average passenger-car speed. Finally, if a value for density is required, it can be directly calculated by using the estimated flow rate and the average speed. Type IV analysis is used to establish the required number of lanes in a design application. A planning estimate of the required number of lanes can also be made. The key to Type IV analysis is the establishment of an hourly volume on which the design is to be based. All information except number of lanes can be entered in the Traffic and Roadway Conditions portion of the worksheet. A free-flow speed, either computed or measured directly, is entered on the worksheet, and the appropriate curve representative of the free-flow speed is established on the graph. The required or desired level of service is also entered. Then the analyst takes the intersection of the LOS threshold and the appropriate speed-flow curve and projects downward to the horizontal axis of the graph to establish the maximum flow rate per lane. Using this maximum allowable flow rate in the equation for flow rate on the worksheet, the analyst can solve for number of lanes, N. Since, in this case, N will be a fractional or decimal number, the analyst has the ability to use judgment on whether to round upward or round slightly downward to estimate the number of lanes required in one direction. Note that again density is easily calculated using vp and S. The number of lanes on a specific freeway section depends not only on the desired level of operation, but also on the continuity of lanes with adjacent sections and along Page 3-24
Updated December 1997
Highway Capacity Manual 1997 the freeway system. Frequent adding or dropping of lanes along a freeway is not practical, yet can be considered within critical freeway sections. On specific grades, the need for a larger number of lanes on an upgrade than on a downgrade carrying the same traffic volume is a clear indication that a climbing lane is required. PLANNING ANALYSIS Planning-level analysis can be done using the analysis worksheet. Planning information on future AADT is required and can be converted to an estimated DDHV using the known or forecast values of proportion of AADT occurring during the peak hour, K, and directional distribution factor, D: DDHV = AADT × K × D
(3-5)
Most highway traffic agencies have data on K and D, which tend to be regional for a particular class of highway. Normal values for K range from about 0.08 in dense urban areas to as high as 0.15 to 0.20 in rural areas. D varies from about 52 percent to as high as 80 percent in some rural situations. Traffic during a peak hour is rarely distributed evenly in both directions, even on urban circumferential routes. Planning applications typically are used to estimate either the level of service or the number of lanes required to carry a specified amount of traffic. The analyst typically has few, if any, of the input values required for Types I, II, III, and IV analyses. The following default values are suggested for planning analysis: Volume, V (from DDHV) ET = 1.5 ER = 1.2 % Trucks and buses = 5 percent % RVs = 2 percent fp = 1.0 fHV = 0.939 fLW = 0.0 fLC = 0.0 fN = 3.0 mph fID = 0.0 FFSi = 70 mph FFS = 67 mph HOV FACILITIES These procedures apply only to the analysis of traffic conditions on the freeway mainline and are not generally intended for use in analyzing capacity and level of service of HOV lanes. However, when the HOV facility has two or more lanes in each direction during all or part of the day and access to the HOV facility from adjacent general use freeway lanes is limited (e.g., 1.0-mi or greater access point spacing), these procedures may be used to analyze the sections of the HOV facility between access points. These procedures should not be used to analyze the operation of HOV facilities composed of one lane in each direction. Further guidelines for the analysis of HOV facilities are provided in Chapter 6, Freeway Systems. TOOLS FOR ANALYSIS The worksheet shown in Figure 3-5 and provided in Appendix II can be used to perform analysis Types I, II, III, and IV. Tables that provide adjustment factors for free-flow speed estimation and those providing passenger-car equivalents for heavy vehicles are used to provide entries to the worksheet.
Updated December 1997
Page 3-25
Basic Freeway Sections
Highway Capacity Manual 1997 IV. EXAMPLE PROBLEMS
EXAMPLE PROBLEM 1 The Freeway Existing four-lane freeway, urban area, very restricted geometry, rolling terrain, 65-mph speed limit. The Question
What is the level of service during the peak hour?
The Facts √ Four lanes (two in each direction) √ 11-ft lanes √ 2-ft lateral clearance on left and right sides √ 2,000-vph peak-hour volume (one direction) √ Rolling terrain √ 5 percent trucks √ PHF = 0.92 √ Interchange density = 1.0/mi √ Mostly commuter traffic Comments √ Assume no buses and no RVs since none indicated. √ Assume ideal FFS of 70 mph considering freeway type and geometry. Outline of Solution All input parameters are known; thus no default values are required. Demand will be computed in terms of pcphpl, a free-flow speed will be estimated, and the level of service determined from the speed-flow graph. If desired, an estimate of passenger-car speed is directly available from the graph, and a value for density can be calculated using speed and flow rate. Steps 1. Convert volume (vph) to flow rate (pcphpl) fp = 1.0 (commuter traffic)
2. Find fHV (no buses or RVs) (use Table 3-2 for ET)
vp =
V (PHF)(N)(fHV)(fp)
vp =
2,000 0.92 × 2 × fHV × 1.0
fHV =
1 1 + PT (ET − 1)
fHV =
1 1 + 0.05(3 − 1)
fHV = 0.909 3. Find vp
vp =
2,000 (0.92)(2)(0.909)
vp = 1,196 pcphpl 4. Compute free-flow speed (using Tables 3-6, 3-7, 3-8, and 3-9)
FFS = FFSi−fLW−fLC−fN−fID FFS = 70 − 2.0 − 2.4 − 4.5 − 2.5 FFS = 58.6 mph (or round to 59 mph)
5. Determine level of service (using Table 3-1)
The Results
Level of service = C
Summary Other outputs are speed (S = 59 mph) and density (20.3 pc/mi/ln) calculated as vp /S, or 1,196/59.
Basic Freeway Sections
Page 3-26
Updated December 1997
Highway Capacity Manual 1997 Worksheet for Example Problem 1
80 120 1300
70
100
1600
60
1750
50
A
80
E
D
C
B
40
60
30 40 20
Average Passenger-Car Speed (km/hr)
Average Passenger-Car Speed (mph)
1450
Analysis Type
Input
Output
I
vP, FFS
LOS
II
vP, LOS, FFS
S
III
FFS, LOS
vp
IV
vP, LOS
N
20
10 0 0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
0 2400
Flow Rate (pcphpl)
General Information S. Stevens Analyst Binghamton Co. Agency or Company Site Information SR 210 Highway/Dir. Travel ___________ Adams St./Lincoln Ave. From/To ___________ Binghamton Co. Jurisdiction ___________ PM Peak Hour Analysis Time Period ___________ 1997 Analysis Year ___________ Traffic and Roadway Conditions 2,000 Volume, V ___________ vph Speed, S ___________ mph 11 Lane Width, LW ___________ ft 2 Number of Lanes, N ___________ 2 Rt-Shoulder Lat. Clear., LC ___________ ft Peak-Hour Factor, PHF Interchange Density, ID % Trucks and Buses, PT % RVs, PR General Terrain x Rolling Level
0.92 ___________ 1.0 ___________ 5 ___________ 0 ___________ Mountainous
Specific Grade Length
___________ mi
Up/Down
___________ %
Driver Type x Commuter/Wk Day
Updated December 1997
Date Performed Analysis Type
3/18/97 x I
III
II
IV
Flow Rate (vP ) ET Tables 3-2, 3-3, 3-5 3.0 ____________ ER ____________ Tables 3-2, 3-4 fHV ____________ 0.909 1
1 + PT(ET - 1) + PR(ER - 1)
fp vP
1.0 ____________ (1.0 - 0.85) V 1196 ____________ pcphpl (PHF x N x f
HV
x fp)
Free-Flow Speed (FFS) 70 FFSi _________mph 2.0 fLW _________mph Table 3-6 2.4 fLC _________mph Table 3-7 4.5 fN _________mph Table 3-81 2.5 fID _________mph Table 3-9 59 FFS _________mph (est.) FFSi - fLW - fN - fLC - fID or FFS _________mph (measured)
Level of Service (LOS) 20.3 Density, D ____________ C LOS __________
pc/mi/ln vP/S Table 3-1
1For rural freeway sections, f = 0 N
Recreational/Wk End
Page 3-27
Basic Freeway Sections
Highway Capacity Manual 1997 EXAMPLE PROBLEM 2 The Freeway The Question periods?
New suburban freeway being designed, level terrain. How many lanes are needed to provide LOS D during peak
The Facts √ 4,000-vph peak-hour volume (one direction) √ Level terrain √ 15 percent trucks √ 3 percent RVs √ PHF = 0.85 √ Interchange density = 1.50/mi √ Lane width and lateral clearance to be designed to high standards Comments √ Assume commuter traffic, since the freeway is suburban; thus, fp = 1.0. √ Assume ideal FFS of 70 mph considering the freeway type (i.e., suburban). Outline of Solution No default values are required. The flow rate per lane, vp, to be accommodated at LOS D for four-, six-, and eight-lane freeways will be determined and compared with the demand flow rate. Steps 1. Convert volume (vph) to flow rate (pcphpl)
vp =
V (PHF)(N)(fHV)(fp)
2. Find fHV (use Table 3-2 for ET and ER)
fHV =
1 1 + PT (ET − 1) + PR(ER − 1)
fHV =
1 1 + (0.15)(1.5 − 1) + 0.03(1.2 − 1)
fHV = 0.925 3. For four-lane freeway
vp =
4,000 (0.85)(2)(0.925)(1.0)
vp = 2,544 pcphpl 4. For six-lane freeway
vp =
4,000 (0.85)(3)(0.925)(1.0)
vp = 1,696 pcphpl 5. For eight-lane freeway
vp =
4,000 (0.85)(4)(0.925)
vp = 1,272 pcphpl 6. Eliminate the four-lane freeway since demand per lane exceeds capacity (2,400 pcphpl for an ideal section) 7. Compute free-flow speed for six-lane and eight-lane freeways (using Tables 3-6, 3-7, 3-8, and 3-9)
FFS = FFSi − fLW − fLC − fN − fID FFS = 70−0.0−0.0−3.0−5.0 (three lanes) FFS = 62 mph (three lanes) FFS = 70−0.0−0.0−1.5−5.0 (four lanes) fHV = 63.5 mph (four lanes) Table continues
Basic Freeway Sections
Page 3-28
Updated December 1997
Highway Capacity Manual 1997 8. Use Table 3-1 to determine that sixlane freeway operates at LOS D, eight-lane freeway at LOS C
The Results peak periods.
A six-lane freeway will meet operational objective of LOS D during
Summary Other outputs are speed = 61 mph and density = 27.8 pc/mi/ln (from 1,696/61). Also, an eight-lane design would operate at LOS C; speed = 63.5 mph, density = 20.0 pc/mi/ln (from 1,272/63.5).
Worksheet for Example Problem 2 80 120 1300
70
1750
50
A
E
D
C
B
80
40
60
30
N=3
40 20 10
20
0 0
200
400
600
800
1000
1200
1400
1600
1800
Analysis Type
Average Passenger-Car Speed (km/hr)
100
1600
60
N=4
Average Passenger-Car Speed (mph)
1450
2000
2200
Input
Output
I
vP , FFS
LOS
II
vP , LOS, FFS
S
III
FFS, LOS
vP
IV
vP, LOS
N
0 2400
Flow Rate (pcphpl)
General Information Analyst Agency or Company
MJM
2/7/96
Date Performed
TRANSCON
Analysis Type I
II
III
x IV
Flow Rate (v P)
Site Information Highway/Dir. Travel
WBWB SR 101 ____________
ET
1.5 __________________
Tables 3-2, 3-3, 3-5
From/To
I-10/I-17 ____________
ER
1.2 __________________
Tables 3-2, 3-4
Jurisdiction
____________
fHV
0.925 __________________
Analysis Time Period
Peak Period ____________
fp
Analysis Year
2015 ____________
vP
1.0 __________________ N= 2 3 4 2544 1696 1272 __________________
1 1 + PT(ET - 1) + PR(ER - 1)
(1.0 - 0.85)
pcphpl
Traffic and Roadway Conditions Volume, V
4,000 ____________ vph
Speed, S
____________ mph
Lane Width, LW
12 ____________ ft
Number of Lanes, N
2, 3, 4 ____________
Rt-Shoulder Lat. Clear., LC
10 ____________ ft
Peak-Hour Factor, PHF
0.85 ____________
Interchange Density, ID
1.5 ____________
% Trucks and Buses, PT
1.5 _______________
or
% RVs, PR
3 _______________
FFS
V (PHF x N x fHV x fp)
Free-Flow Speed (FFS) 70 mph FFSi ___________
fLW
0 ___________ mph Table 3-6
fLC
0 ___________ mph Table 3-7
fN
3.0 1.5 mph Table 3-81 ___________
fID
5.0 ___________ mph Table 3-9
N= 3 4
FFS
N= 3 4 62 63.5
mph
(est.) FFSi - fLW - fN - fLC - fID
___________mph (measured)
General Terrain x Level
Rolling
Mountainous
Level of Service (LOS) N= 3
Specific Grade Length
____________ mi
Up/Down
____________ %
Driver Type x Commuter/Wk Day
Updated December 1997
4
27.8 20.0 Density, D _______________ pc/mi/ln vP/S
LOS
N= 3 4 D C Table 3-1 _______________
1
For rural freeway sections, f = 0 N
Recreational/Wk End
Page 3-29
Basic Freeway Sections
Highway Capacity Manual 1997 EXAMPLE PROBLEM 3 The Freeway
Existing six-lane freeway, growing urban area, level terrain.
The Question What is the current LOS during peak periods? What LOS will occur in 3 years? To avoid the condition of demand exceeding capacity, when should a fourth lane be added in each direction? The Facts √ Six lanes √ 5,000-vph volume (in one direction) (existing) √ Level terrain √ 10 percent trucks √ PHF = 0.95 √ 5,600-vph volume (in one direction) (in 3 years) √ Beyond 3 years, traffic grows at 4 percent per year √ FFS = 65 mph (measured in field) Comments √ Since no information is given on possible changes over time, assume that percent trucks and PHF remain constant. √ This problem deals with a variety of demand levels and can most easily be solved by computing the maximum volume that can be accommodated for each level of service. √ Free-flow speed need not be estimated since it has been field measured. √ Assume no buses and no RVs. √ Assume familiar driver population given the freeway type and area type. Outline of Solution The maximum volume (vph) that can occur for each LOS will be computed. The demand volumes will then be compared and an LOS estimated. Steps 1. Convert the maximum service flow (pcphpl) for each LOS to vph
vp =
V (PHF)(N)(fHV)(fp)
or vp(PHF) (N) (fHV) (fp) = V 2. Find fHV
1 1 + PT (ET − 1) 1 = 1 + 0.10(1.5 − 1) = 0.952
fHV =
fHV fHV 3. Find vp (maximum for each LOS) from Table 3-1 (fp = 1.0)
LOS LOS LOS LOS LOS
A B C D E
vp = 650 pcphpl vp = 1,040 vp = 1,548 vp = 1,984 vp = 2,350
4. Compute V (vph)
LOS LOS LOS LOS LOS
A B C D E
V = 1,763 vph V = 2,822 V = 4,200 V = 5,383 V = 6,376
5. Compare 5,000 vph and 5,600 vph with above; determine LOS Table continues
Basic Freeway Sections
Page 3-30
Updated December 1997
Highway Capacity Manual 1997 5,600 (1.04n) = 6,376 n = 3.3 years
6. When traffic exceeds 6,376 vph, a fourth lane in each direction will be needed. A compounding equation is used
The Results
LOS D (existing) LOS E (in 3 years) 6.3 years (fourth lane needed)
Worksheet for Example Problem 3
80 120 1300
70
100
1600
60
1750
50
A
C
B
80
E
D
40
60
30 40 20
Average Passenger-Car Speed (km/hr)
Average Passenger-Car Speed (mph)
1450
Analysis Type
Input
Output
I
vP, FFS
LOS
II
vP, LOS, FFS
S
III
FFS, LOS
vP
IV
vP, LOS
N
20
10 0 0
200
400
600
1000
800
1200
1400
1600
1800
2000
2200
0 2400
Flow Rate (pcphpl)
General Information Analyst Agency or Company
Susan Collins
5/5/97
Date Performed
Arizona DOT
x I
Analysis Type
II
III
IV
Flow Rate (v P)
Site Information Highway/Dir. Travel
I-17 NB ____________ Dunlap Ave/Northern Ave ____________
From/To
ET
1.5 __________________
Tables 3-2, 3-3, 3-5
ER
__________________
Tables 3-2, 3-4
Jurisdiction
Arizona DOT ____________
fHV
0.952 __________________
Analysis Time Period
PM Peak Hour ____________
fp
1.0 __________________
Analysis Year
1997/2000 ____________
vP
LOS A 650 LOS D 1984 LOS B 1040 LOS E 2350 LOS C 1548
Traffic and Roadway Conditions
1 1 + PT(ET - 1) + PR(ER - 1)
(1.0 - 0.85)
pcphpl
V (PHF x N x fHV x fp)
Volume, V
1997-5000 2000-5600 ____________ vph
Speed, S
____________ mph
FFSi ___________mph
Lane Width, LW
____________ ft
fLW
___________mph Table 3-6
Number of Lanes, N
____________
fLC
___________mph Table 3-7
Rt-Shoulder Lat. Clear., LC
3 ____________ ft
fN
___________mph Table 3-81
Peak-Hour Factor, PHF
____________
fID
___________mph Table 3-9
Interchange Density, ID
0.95 ____________
FFS
___________mph (est.) FFSi - fLW - fN - fLC - fID
% Trucks and Buses, PT
10 _______________
or
% RVs, PR
_______________
FFS
Free-Flow Speed (FFS)
65 mph (measured) ___________
General Terrain x Level
Rolling
Mountainous
Level of Service (LOS) Density, D _______________ pc/mi/ln vP/S
Specific Grade Length
____________ mi
Up/Down
____________ %
LOS
1997 - D
_______________ Table 3-1 2000 - E
1
For rural freeway sections, f = 0 N
Driver Type x Commuter/Wk Day
Updated December 1997
Recreational/Wk End
Page 3-31
Basic Freeway Sections
Highway Capacity Manual 1997 EXAMPLE PROBLEM 4 The Freeway The Question periods?
Existing four-lane freeway, rural, ideal lane widths and clearances. What is the LOS for both upgrade and downgrade during peak
The Facts √ Four lanes √ 2,300 vph (in one direction) √ Composite grade, 3,000 ft at 3 percent and 2,500 ft at 5 percent √ 15 percent trucks √ PHF = 0.90 √ FFS = 75 mph (measured in field) Comments √ Assume no buses and no RVs. √ Free-flow speed need not be estimated since it has been field measured. √ The precise procedure for composite grades is used because there is a section steeper than 4 percent and the total length is greater than 4,000 ft. √ Since most drivers on a rural freeway section are generally unfamiliar with the area, a driver population factor of 0.95 is assumed. Outline of Solution The truck performance curves in Appendix I are used to develop an equivalent grade (i.e., a constant grade that has the same effect on heavy vehicles as does the composite grade). The equivalency tables for both upgrades and downgrades are used to define fHV. The flow rates, vp, are computed, and Table 3-1 is used to estimate LOS. Steps 1. Determine equivalent constant grade
2. Find vp 3. Find fHV (upgrade) (Table 3-3, use interpolation)
4. Find fHV (downgrade) (Table 3-5) 5. Compute vp (upgrade)
See detailed description in Appendix I. Answer = 4.8 percent (1.04 mi)
vp =
V (PHF)(N)(fHV)(fp)
fHV =
1 1 + PT (ET − 1)
fHV =
1 = 0.562 1 + 0.15(6.2 − 1)
fHV =
1 = 0.930 1 + 0.15(1.5 − 1)
vp =
2,300 (0.90)(2)(0.562)(0.95)
vp = 2,392 pcphpl 6. Compute vp (downgrade)
vp =
2,300 (0.90)(2)(0.930)(0.95)
vp = 1,447 pcphpl 7. Enter Table 3-1 or worksheet with vp, determine LOS
The Results Using the speed-flow curve of 75 mph, upgrade operates at LOS E (speed 53.5 mph, density 43.5 pc/mi/ln). Downgrade operates at LOS C (speed 69.5 mph, density 20.8 pc/mi/ln). Basic Freeway Sections
Page 3-32
Updated December 1997
Highway Capacity Manual 1997 Using Appendix I, enter Figure I.3-2 at 3,000 ft. Speed at top of 3 percent grade is 42.5 mph. Intersection of horizontal at 42.5 mph and 5 percent curve implies trucks have been on 5 percent grade for 1,200 ft. A vertical is drawn at 3,700 ft to the 5 percent deceleration curve and a horizontal shows a final truck speed of 27.5 mph.
Worksheet for Example Problem 4 80 120 1300
70
1750
50
A
E
D
C
B
80
40
60
30 20
Up
40
Average Passenger-Car Speed (km/hr)
100
1600
60
Down
Average Passenger-Car Speed (mph)
1450
Analysis Type
Input
Output
I
vP, FFS
LOS
II
vP, LOS, FFS
S
III
FFS, LOS
vP
IV
vP, LOS
N
20
10 0 0
200
400
600
1000
800
1200
1400
1600
1800
2000
2200
0 2400
Flow Rate (pcphpl)
General Information Analyst Agency or Company
J. Thompson
11/24/96
Date Performed
DJP Associates
x I
Analysis Type
II
III
IV
Flow Rate (v P)
Site Information Highway/Dir. Travel From/To Jurisdiction Analysis Time Period Analysis Year
I-405/SB ____________
ET
6.2 __________________
Tables 3-2, 3-3, 3-5
Genesee/Carmel Cyn. ____________
ER
__________________
Tables 3-2, 3-4
CALTRANS ____________
fHV
0.930 __________________
AM/PM Peak Hour ____________
fp
0.95 __________________
(1.0 - 0.85)
1996 ____________
vP
__________________ 2392 1447
pcphpl
Up Down
1 1 + PT(ET - 1) + PR(ER - 1)
Traffic and Roadway Conditions
V (PHF x N x fHV x fp)
Free-Flow Speed (FFS)
Volume, V
2,300 ____________ vph
Speed, S
____________ mph
Lane Width, LW
____________ ft
FFSi ___________mph fLW ___________mph Table 3-6
Number of Lanes, N
____________
fLC
___________mph Table 3-7
Rt-Shoulder Lat. Clear., LC
____________ ft
fN
___________mph Table 3-81
Peak-Hour Factor, PHF
____________
fID
___________mph Table 3-9
Interchange Density, ID
____________
FFS
___________mph (est.) FFSi - fLW - fN - fLC - fID
% Trucks and Buses, PT
_______________
or
% RVs, PR
_______________
FFS
75 mph (measured) ___________
General Terrain Level
Rolling
Mountainous
Level of Service (LOS) Up
Specific Grade Length
3,000/ 2,500 ft ____________
Up/Down
3/5 ____________ %
Driver Type Commuter/Wk Day
Updated December 1997
Down
44.7 20.8 Density, D _______________ pc/mi/ln vP/S
LOS
Up Down Table 3-1 _______________ E C
1
For rural freeway sections, f = 0 N
x Recreational/Wk End
Page 3-33
Basic Freeway Sections
Highway Capacity Manual 1997 EXAMPLE PROBLEM 5 The Freeway New urban facility being planned, forecast opening day AADT of 75,000 vpd, rolling terrain. The Question For opening day volumes, how many lanes will be needed to provide LOS D during peak periods? The Facts √ 75,000 vpd √ K = 0.09 √ D = 55/45 √ Rolling terrain Comments √ Several input variables (FFS, PHF, and percent trucks) are not given. Reasonable default values (for a moderately dense urban area) are selected as FFS = 65 mph, PHF = 0.90, and 10 percent trucks. √ Assume commuter traffic, given the urban characteristics of the area. Outline of Solution The flow rate, vp, is computed for four-, six-, and eight-lane alternatives. Table 3-1 is used to find LOS for each vp, using the 65-mph FFS curve. Steps 1. Convert AADT to design hour volume
DDHV = AADT × K × D DDHV = 75,000 × 0.09 × 0.55 DDHV = 3,713 vph
2. Find fHV (using Table 3-2)
fHV =
1 1 + PT (ET − 1)
=
1 1 + 0.10(3 − 1)
= 0.833 3. Find vp
vp = =
V (PHF)(N)(fHV)(fp) 3,713 (0.90)(2)(0.833)(1.0)
= 2,476 pcphpl (two lanes) = 1,651 pcphpl (three lanes) = 1,238 pcphpl (four lanes)
The Results
Three lanes in each direction will provide for LOS D.
Summary With two lanes in each direction, flows exceed capacity. The four-lane (each direction) option would provide LOS C.
Basic Freeway Sections
Page 3-34
Updated December 1997
Highway Capacity Manual 1997
Worksheet for Example Problem 5 80 120 1300
70
100
1600
60
1750
50
A
E
D
C
B
80
40
60
30 40 20
Average Passenger-Car Speed (km/hr)
Average Passenger-Car Speed (mph)
1450
Analysis Type
20
10 0 0
200
400
600
1000
800
1200
1400
1600
1800
2000
2200
Input
Output
I
vP, FFS
LOS
II
vP, LOS, FFS
S
III
FFS, LOS
vP
IV
vP, LOS
N
0 2400
Flow Rate (pcphpl)
General Information Analyst Agency or Company
N. Terry
7/97
Date Performed
TX DOT
Analysis Type I
II
x III
IV
Flow Rate (v P)
Site Information SR 805 ____________
ET
3.0 __________________
Tables 3-2, 3-3, 3-5
Caldwell Blvd/29th St ____________
ER
__________________
Tables 3-2, 3-4
Jurisdiction
TX DOT ____________
fHV
0.833 __________________
Analysis Time Period
Peak Hour ____________
fp
Analysis Year
2002 ____________
vP
1.0 __________________ N= 2 3 4 2476 1651 1238 __________________
Highway/Dir. Travel From/To
1 1 + PT(ET - 1) + PR(ER - 1)
(1.0 - 0.85)
pcphpl
Traffic and Roadway Conditions
V (PHF x N x fHV x fp)
Free-Flow Speed (FFS)
Volume, V
3,713 ____________ vph
Speed, S
____________ mph
Lane Width, LW
____________ ft
FFSi ___________mph fLW ___________mph Table 3-6
Number of Lanes, N
____________
fLC
___________mph Table 3-7
Rt-Shoulder Lat. Clear., LC
____________ ft
fN
___________mph Table 3-81
Peak-Hour Factor, PHF
0.90 ____________
fID
___________mph Table 3-9
Interchange Density, ID
____________
FFS
___________mph (est.) FFSi - fLW - fN - fLC - fID
% Trucks and Buses, PT
10 _______________
or
% RVs, PR
_______________
FFS
65 ___________ mph (measured)
General Terrain Level
x Rolling
Mountainous
Level of Service (LOS) Density, D _______________ pc/mi/ln vP/S
Specific Grade Length
____________ mi
Up/Down
____________ %
LOS
N=2 3 4
F D C _______________ Table 3-1
1
For rural freeway sections, f = 0 N
Driver Type x Commuter/Wk Day
Updated December 1997
Recreational/Wk End
Page 3-35
Basic Freeway Sections
Highway Capacity Manual 1997 V. REFERENCES The methodology in this chapter is based primarily on the results of a National Cooperative Highway Research Program (NCHRP) study completed in 1995 (1). Some adjustment factors, including those for lane width and heavy vehicles, were developed as part of an NCHRP study of traffic flow on multilane highways (2). 1. Schoen, J., May, A., Reilly, W., and Urbanik, T., Speed-Flow Relationships for Basic Freeway Sections. Final Report, NCHRP Project 3-45, JHK & Associates, Tucson, Ariz. (May 1995). 2. Reilly, W., Harwood, D., Schoen, J., et al., Capacity and Level of Service Procedures for Multilane Rural and Suburban Highways. Final Report, NCHRP Project 3-33, JHK & Associates, Tucson, Ariz. (1988). 3. ‘‘Basic Freeway Sections (Chapter 3).’’ Special Report 209: Highway Capacity Manual (third edition), Transportation Research Board, Washington, D.C. (1994). 4. Hall, F.L., Hurdle, V.F., and Banks, J.H., ‘‘Synthesis of Recent Work on the Nature of Speed-Flow and Flow-Occupancy (or Density) Relationships on Freeways.’’ Transportation Research Record 1365, Transportation Research Board, Washington, D.C. (1992). 5. Urbanik, T., Hinshaw, W., and Barnes, K., ‘‘Evaluation of High-Volume Urban Texas Freeways.’’ Transportation Research Record 1320, Transportation Research Board, Washington, D.C. (1991). 6. Banks, J.H., ‘‘Flow Processes at a Freeway Bottleneck.’’ Transportation Research Record 1287, Transportation Research Board, Washington, D.C. (1990). 7. Hall, F.L., and Hall, L.M. ‘‘Capacity and Speed-Flow Analysis of the Queen Elizabeth Way in Ontario.’’ Transportation Research Record 1287, Transportation Research Board, Washington, D.C. (1990). 8. Hall, F.L., and Agyemang-Duah, K., ‘‘Freeway Capacity Drop and the Definition of Capacity.’’ Transportation Research Record 1320, Transportation Research Board, Washington, D.C. (1991). 9. Chin, H.C., and May, A.D., ‘‘Examination of the Speed-Flow Relationship at the Caldecott Tunnel.’’ Transportation Research Record 1320, Transportation Research Board, Washington, D.C. (1991). 10. Banks, J., Evaluation of the Two-Capacity Phenomenon as a Basis for Ramp Metering. Final Report, San Diego State University, San Diego, Calif. (1991).
Basic Freeway Sections
Page 3-36
Updated December 1997
Highway Capacity Manual 1997 APPENDIX I PRECISE PROCEDURE FOR DETERMINING PASSENGER-CAR EQUIVALENTS OF TRUCKS ON COMPOSITE UPGRADES In a capacity analysis, an overall average grade can be substituted for a series of grades if no single portion of the grade is steeper than 4 percent or the total length of the grade is less than 4,000 ft. For grades outside these limits, that is, those having both a total length greater than 4,000 ft and portions steeper than 4 percent, the following technique is recommended. It estimates the continuous grade that would result in the same final truck speed as the actual series of composite grades. The solution for this equivalent grade uses performance curves for trucks on grades, which are included in this appendix. As noted elsewhere in the chapter, the truck acceleration and deceleration curves presented and used in this appendix are for a vehicle with an average weight-tohorsepower ratio of 200 lb/hp. This is a somewhat heavier vehicle than the usual mix of trucks found on a typical freeway, which averages between 125 and 150 lb/hp. A conservative approach is taken to reflect the fact that heavier vehicles will have a greater influence on operations than those that are lighter. The 200-lb/hp vehicle is used only to determine the equivalent of a composite grade and the passenger-car equivalent values for trucks are based on the 125- to 150-lb/hp range. The technique for determining composite grade equivalents is best illustrated by an example. Consider a composite grade with 5,000 ft of 2 percent grade followed by 5,000 ft of 6 percent grade. If the average grade technique (which is not valid in this case) were applied, the following results would be obtained: Total rise = (5,000 × 0.02) + (5,000 × 0.06) = 400 ft Average grade = 400 4 10,000 = 0.04 or 4 percent
The more precise method recommended in this appendix determines a percent grade of 10,000 ft that results in the same final speed of trucks as the actual sequence of grades. The solution for this point is illustrated in Figure I.3-1. A blank set of truck performance curves is included as Figure I.3-2. To find the truck speed at the end of the first 5,000 ft of 2 percent upgrade, a vertical line is drawn from the 5,000-ft point on the horizontal axis to its intersection with the 2 percent deceleration curve. This is Point 1 in Figure I.3-1. The truck speed is found by drawing a horizontal line from this point to the vertical axis, which intersects at Point 2, 47 mph. This is also the speed at which trucks enter the second 5,000 ft of 6 percent grade. FIGURE I.3-1. SAMPLE SOLUTION FOR COMPOSITE GRADE.
Updated December 1997
Page 3-37
Basic Freeway Sections
FIGURE I.3-2. PERFORMANCE CURVES FOR STANDARD TRUCKS (200
LB/HP).
Highway Capacity Manual 1997
Basic Freeway Sections
Page 3-38
Updated December 1997
Highway Capacity Manual 1997 The intersection of the horizontal line between Points 1 and 2 and the 6 percent deceleration curve is found and labeled Point 3. A vertical line is constructed from this point to the horizontal axis, locating Point 4. This point indicates that at 47 mph, trucks enter the 6 percent grade as if they had already been on it for 750 ft, starting from level terrain. Because trucks will now travel another 5,000 ft on the 6 percent grade, this distance is added to the 750 ft determined by Point 4 to find Point 5 at 5,750 ft. A vertical is constructed from this point to the intersection with the 6 percent deceleration curve (Point 6) to find the final truck speed after the second 5,000 ft of 6 percent upgrade. A horizontal line drawn from this point intersects the vertical axis at Point 7, 23 mph, the final truck speed. To find a single constant grade of 10,000 ft that will result in a final truck speed of 23 mph, a horizontal line is drawn from 23 mph to its intersection with a vertical line drawn from 10,000 ft, Point 8. The equivalent grade is found to be 6 percent, not the 4 percent indicated by the average grade technique. The value of ET would now be selected for a 6 percent grade of 10,000 ft. In general terms the following steps describe the solution for equivalent grade: 1. Enter the truck performance curves of Figure I.3-2 with initial grade and length of grade. Find the truck speed at the end of the first grade, which is also the speed at which trucks enter the second segment. 2. Find the length along the second grade that results in the same speed as that found in Step 1. Use this point as the starting point along the second grade. 3. Starting with the length found in Step 2, add the length of the second grade, and find the speed at the end of the second grade. 4. If there are additional grade segments, repeat Steps 1 through 3 for each subsequent grade until a final speed is found. 5. Enter the truck performance curves with a final truck speed and the total length of the composite grade to find the equivalent uniform grade percent, which may be used in finding ET. Note that this analysis can be applied to any number of successive grades. A given series of grades may even include downgrade portions, or segments of level terrain. Such points should not be used as points of demarcation between analysis segments unless the truck speed can be shown to have returned to 55 mph under free-flow conditions. For any given set of consecutive grades, it is important to identify the point at which truck speeds are lowest. The deleterious effect of trucks is most severe at this point. Thus, the appropriate point at which to evaluate a composite grade may not be at its end, but at the point of minimum truck speed. For example, if a 4 percent upgrade of 1 mi were followed by 1⁄2 mi of 2 percent upgrade, the point of minimum truck speed will be the end of the 4 percent grade, not the subsequent 2 percent grade. Note also that the procedure uses discrete grade segments and ignores the vertical curves that join them. This simplifies computations and results in sufficient accuracy for capacity analysis purposes.
Updated December 1997
Page 3-39
Basic Freeway Sections
Highway Capacity Manual 1997 APPENDIX II WORKSHEET FOR ANALYSIS OF BASIC FREEWAY SECTIONS 80 12 130
70
10
160
60
Average Passenger-Car Speed (km/hr)
Average Passenger-Car Speed (mph)
145
175
50
A
80
E
D
C
B
40
60
30 40 20
Analysis Type
Input
Output
I
vP, FFS
LOS
II
vP, LOS, FFS
S
III
FFS, LOS
vP
IV
vP, LOS
N
20
10 0 0
200
400
600
800
100
1200
1400
1600
1800
2000
2200
0 2400
Flow Rate (pcphpl)
General Information Analyst Agency or Company
Date Performed Analysis Type I
Site Information Highway/Dir. Travel ____________ From/To ____________ Jurisdiction ____________ Analysis Time Period ____________ Analysis Year ____________ Traffic and Roadway Conditions Volume, V ____________ vph Speed, S ____________ mph Lane Width, LW ____________ ft Number of Lanes, N ____________ Rt-Shoulder Lat. Clear., LC ____________ ft Peak-Hour Factor, PHF ____________ Interchange Density, ID ____________ % Trucks and Buses, PT _______________ % RVs, PR _______________ General Terrain Level Rolling Mountainous
II
Flow Rate (vP) ET
__________________
Tables 3-2, 3-3, 3-5
ER
__________________
Tables 3-2, 3-4
fHV
__________________
fp
__________________
vP
__________________
1 1 + PT(ET - 1) + PR(ER - 1)
(1.0 - 0.85)
pcphpl
V (PHF x N x fHV x fp)
Free-Flow Speed (FFS) FFSi ___________mph fLW ___________mph Table 3-6 fLC
___________mph Table 3-7
fN
___________mph Table 3-81
fID
___________mph Table 3-9
FFS
___________mph (est.) FFSi - fLW - fN - fLC - fID
or FFS
___________mph (measured)
Length
____________ mi
Density, D _______________ pc/mi/ln vP/S
Up/Down
____________ %
LOS
Basic Freeway Sections
IV
Level of Service (LOS)
Specific Grade
Driver Type Commuter/Wk Day
III
_______________ Table 3-1
1
Recreational/Wk End
For rural freeway sections, f = 0 N
Page 3-40
Updated December 1997
chapter 4
WEAVING AREAS
CONTENTS i.
introduction .......................................................................................................................................................................... Weaving Length .................................................................................................................................................................... Configuration ......................................................................................................................................................................... Type A Weaving Areas ................................................................................................................................................... Type B Weaving Areas.................................................................................................................................................... Type C Weaving Areas.................................................................................................................................................... Determining Configuration Type..................................................................................................................................... Weaving Width and Type of Operation ............................................................................................................................... Weaving Area Parameters.....................................................................................................................................................
4-2 4-2 4-2 4-2 4-4 4-4 4-4 4-4 4-5
ii.
methodology.......................................................................................................................................................................... Prediction of Weaving and Nonweaving Speeds ................................................................................................................. Determination of Type of Operation .................................................................................................................................... Limits on Weaving Area Operations .................................................................................................................................... LOS Criteria ..........................................................................................................................................................................
4-6 4-6 4-7 4-8 4-9
iii.
procedures for application ................................................................................................................................................ Simple Weaving Areas.......................................................................................................................................................... Step 1—Establish Roadway and Traffic Conditions ...................................................................................................... Step 2—Convert All Traffic Volumes to Peak Flow Rates Under Ideal Conditions ................................................... Step 3—Construct Weaving Diagram ............................................................................................................................. Step 4—Compute Unconstrained Weaving and Nonweaving Speeds ........................................................................... Step 5—Check for Constrained Operation...................................................................................................................... Step 6—Compute Average (Space Mean) Speed and Density of All Vehicles in Weaving Area .............................. Step 7—Check Weaving Area Limitations..................................................................................................................... Step 8—Determine Level of Service .............................................................................................................................. Multiple Weaving Areas .......................................................................................................................................................
4-9 4-9 4-9 4-10 4-10 4-10 4-10 4-10 4-10 4-11 4-11
iv.
sample calculations ............................................................................................................................................................ Calculation 1—Analysis of Major Weaving Area ............................................................................................................... Calculation 2—Analysis of Ramp-Weave Section .............................................................................................................. Calculation 3—Constrained Operation ................................................................................................................................. Calculation 4—Design Application ...................................................................................................................................... Calculation 5—Multiple Weaving Area ............................................................................................................................... Calculation 6—Sensitivity Analysis with Design Application ............................................................................................
4-12 4-12 4-13 4-14 4-16 4-17 4-19
v.
references .............................................................................................................................................................................. 4-20
4-1
Updated December 1997
freeways
4-2
I. INTRODUCTION Weaving is defined as the crossing of two or more traffic streams traveling in the same general direction along a significant length of highway without the aid of traffic control devices. Weaving areas are formed when a merge area is closely followed by a diverge area, or when an on-ramp is closely followed by an offramp and the two are joined by an auxiliary lane. Weaving areas require intense lane-changing maneuvers as drivers must access lanes appropriate to their desired exit point. Thus, traffic in a weaving area is subject to turbulence in excess of that normally present on basic highway sections. This turbulence presents special operational problems and design requirements that are addressed by the procedures in this chapter. Figure 4-1 shows the formation of a weaving area. If entry and exit roadways are referred to as ‘‘legs,’’ vehicles traveling from Leg A to Leg D must cross the path of vehicles traveling from Leg B to Leg C. Flows A-D and B-C are, therefore, referred to as weaving flows. Flows A-C and B-D may also exist in the section, but these need not cross the path of other flows, and are referred to as nonweaving flows. Figure 4-1 shows a simple weaving area, formed by a single merge point followed by a single diverge point. Multiple weaving areas, formed by one merge followed by two diverges or two merges followed by a single diverge, are discussed later in this chapter. Weaving areas may exist on any type of facility: freeways, multilane highways, two-lane highways (in interchange areas), or arterials. The methodology presented in this chapter is based on research focusing on freeway facilities. This methodology was developed using research conducted in four widely separated studies: by the Bureau of Public Roads in the early 1960s (published in an appendix to the 1965 HCM, but not used therein); by the Polytechnic University in the early 1970s (1–3); by Leisch in the 1970s (4), and by JHK & Associates in the early 1980s (5). The procedures herein have been updated to reflect recent research on basic freeway sections (6) and ramp junctions (7) as they affect weaving areas. No new data base, however, has been established, and the updating is based on logical extensions of the freeway and ramp research. Some of these updated procedures were developed for a text by Roess et al. (8) and are used herein with the permission of the publisher. NCHRP Project 3-55(5) is expected to result in an improved and expanded methodology by the year 2000. Although this chapter is primarily intended for use in analyzing freeway weaving areas, suggestions are made for its application to weaving on uninterrupted flow segments of multilane highways.
Figure 4-2. Measuring length of a weaving section.
Application of these procedures to arterial weaving areas is not recommended. WEAVING LENGTH
The requirement that drivers execute lane changes to complete many weaving movements introduces a new geometric parameter for consideration—weaving length. The length of the weaving section constrains the time and space in which the driver must make all required lane changes. Thus, as the length of a weaving area decreases (all other factors being constant), the intensity of lanechanging, and the resulting level of turbulence, increases. The measurement of weaving area length is shown in Figure 4-2. Length is measured from the merge gore area at a point where the right edge of the freeway shoulder lane and the left edge of the merging lane(s) are 2 ft apart to a point at the diverge gore area where the two edges are 12 ft apart. Procedures in this chapter generally apply to weaving sections of up to 2,500 ft in length. Weaving may exist in longer sections, but merging and diverging movements are often separated, with lane-changing tending to concentrate near merge and diverge gore areas. For longer sections, merge and diverge areas may be separately analyzed using the procedures of Chapter 5. Weaving turbulence may exist throughout a long section to some degree, but operations are approximately the same as those for a basic freeway section. CONFIGURATION
Because lane-changing is the critical operational feature of weaving areas, another critical geometric characteristic can drastically affect performance: configuration. Configuration refers to the relative placement and number of entry lanes and exit lanes for the section, and it can have a major impact on how much lanechanging must take place in the section. The procedures in this chapter deal with three primary types of weaving configuration. These are referred to as Type A, Type B, and Type C sections, and are shown in Figures 4-3, 4-4, and 4-5, respectively. The types are defined in terms of the minimum number of lane changes that must be made by weaving vehicles as they travel through the section. Type A Weaving Areas
Figure 4-1. Formation of a weaving section. Updated December 1997
Type A weaving areas require that each weaving vehicle make one lane change in order to execute the desired movement. Figure 4-3 shows two examples of Type A weaving areas. In Figure 4-3(a),
weaving areas
4-3
Figure 4-3. Type A weaving areas: (a) ramp-weave/one-sided weave, and (b) major weave.
an on-ramp is followed by an off-ramp, with a continuous auxiliary lane between the ramps. All on-ramp vehicles must make a lane change out of the auxiliary lane into the shoulder lane of the freeway, and all off-ramp vehicles must make a lane change from the shoulder lane of the freeway to the auxiliary lane. Lane changes to and from the outer lanes of the freeway may also take place within the section, but these are not mandated or required by the weaving movement. Sections formed by on-ramp/off-ramp sequences joined by continuous auxiliary lanes are often referred to as ramp-weave sections. They may also be referred to as one-sided weaving sections,
Figure 4-4. Type B weaving areas: (a) major weave with lane balance at exit gore, (b) major weave with merging at entrance gore, and (c) major weave with merging at entrance gore and lane balance at exit gore.
Figure 4-5. Type C weaving areas: (a) major weave without lane balance or merging, and (b) two-sided weave.
because all weaving movements take place on one side of the roadway. It should be noted that on-ramps followed by off-ramps that are not joined by a continuous auxiliary lane are not considered to be weaving areas. They are treated as separate merge and diverge areas and analyzed using the procedures of Chapter 5. Figure 4-3(b) illustrates a major weaving section. Major weaving sections are characterized by three or more entry and exit roadways having multiple lanes. In Figure 4-3(b), two two-lane sections join to form a four-lane roadway, only to separate into two two-lane sections again at the diverge point. Note that all weaving vehicles must make at least one lane change, regardless of the direction in which they are weaving. Figure 4-3(a) and 4-3(b) are similar in that each has a crown line, that is, a lane line that connects the nose of the entrance gore area to the nose of the exit gore area. The lane change that each weaving vehicle must make is across this crown line. The two sections illustrated differ primarily in the impact of ramp geometrics on speed. For many ramp-weave sections, the design speed of ramps is significantly lower than that of the freeway. Thus, on- or off-ramp vehicles must accelerate or decelerate as they traverse the weaving section. For major weaving sections, the design of multilane entry and exit legs is more compatible with the design of the freeway mainline, and the impact of acceleration and deceleration in the section is minimal. It should be noted, however, that this difference is not reflected in the procedures in this chapter because of the relative scarcity of major weave sites with crown lines and the lack of data concerning operations in such sites. Because weaving vehicles in a Type A weaving area must cross the crown line, weaving vehicles are usually confined to occupying the two lanes adjacent to the crown line while in the weaving section. Normally, some nonweaving vehicles will also remain in lanes adjacent to the crown line. Lanes adjacent to the crown line are, therefore, generally shared by weaving and nonweaving vehicles. One of the most significant effects of configuration on Updated December 1997
4-4
freeways
operations is to limit the maximum number of lanes that weaving vehicles may occupy while traversing the section.
Table 4-1. Configuration Type Versus Minimum Number of Required Lane Changes
}a
Type B Weaving Areas
All weaving areas classified as Type B may also be referred to as major weaving sections, because all involve multilane entry legs or exit legs or both. Two critical characteristics distinguish Type B weaving areas from all others: 1. One weaving movement may be accomplished without making any lane changes. 2. The other weaving movement requires at most one lane change. Figure 4-4(a) and (b) show two such weaving areas. In both illustrations, movement B-C can be made without executing any lane changes, whereas movement A-D requires only one lane change. In Figure 4-4(a), this is accomplished by providing a diverging lane at the exit gore. From this lane, a vehicle may proceed on either exit leg without making a lane change. This type of design is also referred to as lane balanced, that is, the number of lanes leaving the diverge is one greater than the number of lanes approaching it. In Figure 4-4(b), a lane from Leg A is merged with a lane from Leg B at the entrance gore area. Type B weaving areas are extremely efficient in carrying large weaving volumes, primarily because of the provision of a through lane for one of the weaving movements. Weaving maneuvers can be accomplished with a single lane change from the lane or lanes adjacent to this through lane. Thus, weaving vehicles can occupy a substantial number of lanes in the weaving section and are not as restricted in this regard as in Type A sections. Figure 4-4(c) shows an unusual configuration in which both a merge of two lanes at the entrance gore and lane balance at the exit gore are provided. In this case, both weaving movements can be made without a lane change. Again, weaving movements can be made with a single lane change from the two lanes adjacent to the through lane. Such configurations are usually found on collector-distributor roadways. Although some weaving movements are accomplished as a merge followed by a diverge, lane changes to and from lanes adjacent to the through lane yield real weaving activity, and these sections are analyzed as weaving areas.
}b minimum number of req’d lane changes for weaving mvt. a 0 1 ≥2
minimum number of req’d lane changes for weaving mvt. b 0 1 ≥2 Type B Type B Type C
Type B type A —
Type C — —
lane balance at the exit gore and no crown line exists. Although such a section is relatively efficient for weaving movements in the direction of the through lane, it cannot efficiently handle large weaving volumes in the other direction. Figure 4-5(b) shows a two-sided weaving area. It is formed when a right-hand on-ramp is followed by a left-hand off-ramp or vice versa. In such cases, the through volume on the freeway is functionally a weaving movement. Ramp-to-ramp vehicles must cross all lanes of the freeway to execute their desired maneuver. Freeway lanes are, in effect, through weaving lanes. Ramp-toramp drivers must execute three lane changes in Figure 4-5(b). Although it is technically a Type C configuration, there is little information concerning the operation of such sections, and the methodology of this chapter is only a rough approximation of their characteristics. They should generally be avoided in cases where there is any significant ramp-to-ramp volume. Determining Configuration Type
Figures 4-3, 4-4, and 4-5 show the three basic types of weaving area configuration. Weaving configuration is determined on the basis of the number of required lane changes that must be performed by the two weaving flows in the section. This determination ignores lane changes that are not necessary to the completion of a particular weaving movement. Table 4-1 identifies the configuration type on the basis of lane-changing characteristics.
Type C Weaving Areas WEAVING WIDTH AND TYPE OF OPERATION
Type C weaving areas are similar to Type B sections in that one or more through lanes are provided for one of the weaving movements. The distinguishing feature between Type B and Type C sections is the number of lane changes required for the other weaving movement. A Type C weaving area is characterized as follows: 1. One weaving movement may be accomplished without making a lane change. 2. The other weaving movement requires two or more lane changes. Figure 4-5 shows two Type C weaving areas. In Figure 4-5(a), movement B-C does not require lane-changing, whereas movement A-D requires two lane changes. This type of section is formed when there is neither a merging of lanes at the entrance gore nor Updated December 1997
The third geometric characteristic with a significant impact on weaving area operations is the width of the weaving area, measured as the number of lanes in the section. It is, however, not only the total number of lanes that affects weaving area operations, but the proportional use of those lanes by weaving and nonweaving vehicles. The nature of weaving movements creates traffic stream turbulence and results in the consumption of more of the available roadway space by a weaving vehicle than by a nonweaving vehicle. The exact nature of relative space use depends on the relative weaving and nonweaving volumes using the weaving area and the number of lane changes that weaving vehicles must make. The latter is, as discussed, dependent on the configuration of the weaving section. Thus, the proportional use of space is dependent not
weaving areas only on relative volumes, but also on the configuration of the weaving area. Configuration has a further impact on proportional use of available lanes. The configuration can limit the ability of weaving vehicles to use outer lanes in the section. This limitation is most severe in Type A sections, in which all weaving vehicles must cross a crown line, and is least severe in Type B sections. In general, vehicles in a weaving area will make use of available lanes in such a way that all component flows achieve approximately the same average running speed, with weaving flows somewhat slower than nonweaving flows. Occasionally, the configuration limits the ability of weaving vehicles to occupy the proportion of available lanes required to achieve this equivalent or balanced operation. In such cases, weaving vehicles occupy a smaller proportion of the available lanes than desired, and nonweaving vehicles occupy a larger proportion of lanes than for balanced operation. When this occurs, the operation of the weaving area is classified as constrained by the configuration. The result of constrained operation is that nonweaving vehicles will operate at significantly higher speeds than weaving vehicles.
4-5
Where configuration does not restrain weaving vehicles from occupying a balanced proportion of available lanes, the operation is classified as unconstrained. Average running speeds of weaving and nonweaving vehicles generally differ by less than 5 mph, except in short Type A sections, where acceleration and deceleration of ramp vehicles limit their average speed regardless of the use of available lanes. A major component of the procedure presented in this chapter is the determination of whether operations in a given section are constrained or unconstrained. This is discussed in the Methodology section.
WEAVING AREA PARAMETERS
The introductory portions of this chapter have discussed a number of parameters that may affect the operation of weaving areas. For convenience, Table 4-2 presents these measures and defines the symbols that will be used to depict them.
Table 4-2. Parameters Affecting Weaving Area Operation symbol L................................................................
definition Length of weaving area, in ft.
LH ..............................................................
Length of weaving area, in hundreds of ft.
N ...............................................................
Total number of lanes in the weaving area.
Nw ..............................................................
Number of lanes used by weaving vehicles in the weaving area.
Nnw.............................................................
Number of lanes used by nonweaving vehicles in the weaving area.
v ................................................................
Total flow rate in the weaving area, in passenger car equivalents, in pcph.
vw...............................................................
Total weaving flow rate in the weaving area, in passenger car equivalents, in pcph.
vw1 .............................................................
Weaving flow rate for the larger of the two weaving flows, in passenger car equivalents, in pcph.
vw2 .............................................................
Weaving flow rate for the smaller of the two weaving flows, in passenger car equivalents, in pcph.
vnw .............................................................
Total nonweaving flow rate in the weaving area, in passenger car equivalents, in pcph.
VR .............................................................
Volume ratio vw /v.
R ...............................................................
Weaving ratio vw2/vw.
Sw ..............................................................
Average (space mean) speed of weaving vehicles in the weaving area, in mph.
Snw .............................................................
Average (space mean) speed of nonweaving vehicles in the weaving area, in mph.
Updated December 1997
freeways
4-6
II. METHODOLOGY The methodology presented in this chapter has four distinct components: 1. Equations predicting the average running speed of nonweaving and weaving vehicles in a weaving area based on known roadway and traffic conditions. Equations are specified for each configuration type, and for unconstrained and constrained operations. 2. Equations describing the proportional use of available lanes by weaving and nonweaving vehicles, used to determine whether operations are constrained or unconstrained. 3. Definitions of limiting values of key parameters for each type of weaving configuration, beyond which equations do not apply. 4. Definition of LOS criteria based on average running speeds of weaving and nonweaving vehicles. These components are discussed in the sections that follow.
PREDICTION OF WEAVING AND NONWEAVING SPEEDS
The heart of the weaving area analysis procedure is the prediction of speeds and density of vehicles within the weaving area. Because weaving and nonweaving vehicles may travel at speeds that are similar or at speeds that are markedly different, average (space mean) speeds are predicted separately for weaving and nonweaving vehicles. An average speed and density for all vehicles is then estimated, and level of service is based on the estimated density. The algorithm for prediction of weaving and nonweaving speeds may be stated in general terms as Si = Smin +
Smax − Smin 1+W
(4-1)
where Si = speed of weaving (i = w) or nonweaving (i = nw) vehicles (mph), Smin = minimum speed expected in section (mph), Smax = maximum speed expected in section (mph), and W = weaving intensity factor. For the purposes of these procedures, the minimum speed, Smin, is taken to be 15 mph. The maximum speed, Smax, is taken to be the average of the free-flow speeds of freeway segments entering and leaving the section plus 5 mph. The addition of 5 mph to the freeflow speed adjusts for the tendency of the algorithm to underpredict high speeds. Setting the maximum and minimum speeds in this way constrains the prediction range of the algorithm to reasonable values. With the assumed maximum and minimum speeds defined, the algorithm becomes Si = 15 +
SFF − 10 1+W
(4-2)
where SFF is the average free-flow speed of the freeway segments entering and leaving the weaving area. The weaving intensity factor, W, is a measure of weaving activity and its intensity. It is computed as Updated December 1997
W=
a (1 + VR)b (v/N)c Ld
(4-3)
where VR = volume ratio, vw /v; v = total flow rate in weaving area (equivalent pcph); vw = weaving flow rate in weaving area (equivalent pcph); N = number of lanes in weaving area; and L = length of weaving area (ft). Constants a, b, c, and d are given in Table 4-3. They vary on the basis of three factors: 1. Whether a weaving speed, Sw, or a nonweaving speed, Snw, is being predicted; 2. Configuration type (A, B, or C) of the weaving area; and 3. Whether operations are constrained or unconstrained. In the case of Item 3, initial computations always assume unconstrained operations. The assumption is subsequently tested for validity. Equations 4-2 and 4-3 yield sensitivities that are consistent with observed operations of weaving areas. Specifically, 1. As the length of the weaving section increases, speeds also increase as the intensity of lane-changing declines. 2. As the proportion of weaving vehicles in the total flow, VR, increases, speeds decrease, reflecting the increased turbulence caused by higher proportions of weaving vehicles in the traffic stream. 3. As the total average flow per lane, v/N, increases, speeds decrease, reflecting more intense demand. 4. Constrained operations will have lower weaving speeds and higher nonweaving speeds than similar unconstrained operations because weaving vehicles are constrained to less space than they would need for unconstrained operation, whereas nonweaving vehicles have more. 5. Type B sections are the most efficient for handling large weaving flow rates. For high flow rates, weaving speeds are higher than for similar Type A and C sections. 6. The sensitivity of weaving speed to increasing VR is greatest for Type A configurations and least for Type B configurations, illustrating the greater efficiency of B sections in handling large proportions of weaving vehicles in the traffic stream. It also suggests that Type A sections are effective where the proportion of weaving vehicles in the traffic stream is relatively low. 7. The sensitivity of weaving speed to increasing length is greatest for Type A sections, because vehicles are often accelerating or decelerating through the section in this configuration. The sensitivity of weaving speed is less for Type B and C configurations, where at least one weaving movement is made without a lane change. It is important to note that Type A configurations are quite different from Type B and Type C configurations. Because all weaving vehicles must cross a crown line in Type A sections, weaving and nonweaving flows tend to become segregated in such segments; weaving vehicles become concentrated in lanes adjacent to the crown line, and nonweaving vehicles gravitate to outer lanes.
weaving areas
4-7
Table 4-3. Constants of Prediction for Weaving Intensity Factor, W general form: a (1 + VR)b (v/N)c W= Ld
type of configuration
a
constants for weaving speed, Sw b c
constants for nonweaving speed, Snw b c
d
a
1.00 1.00
0.90 0.90
0.020 0.020
4.0 4.0
1.30 0.88
1.00 0.60
1.2 1.2
0.77 0.77
0.50 0.50
0.020 0.015
2.0 2.0
1.42 1.30
0.95 0.90
1.8 2.0
0.80 0.85
0.50 0.50
0.015 0.013
1.8 1.6
1.10 1.00
0.50 0.50
Type A Unconstrained Constrained
0.226 0.280
2.2 2.2
Type B Unconstrained Constrained
0.100 0.160
Type C Unconstrained Constrained
0.100 0.100
d
NOTE: All variables are as defined in Table 4-2.
In Type B and C configurations, there is substantial mixing of weaving and nonweaving vehicles across a number of lanes. This difference makes Type A sections behave somewhat differently from Type B or C sections. Speeds tend to be higher in Type A sections than in Type B or C sections with the same flows, length, and number of lanes. This does not, however, suggest that Type A sections always operate better than Type B or C configurations with similar lengths, widths, and flows. Restrictions on the amount of weaving flow that Type A sections can accommodate are more severe than those for other configurations. These restrictions are discussed in a subsequent section (see Table 4-5). DETERMINATION OF TYPE OF OPERATION
The determination of whether a particular section is operating in a constrained or unconstrained state is based on the comparison of two variables: Nw = number of lanes that must be used by weaving vehicles in order to achieve balanced or unconstrained operation; and Nw (max) = maximum number of lanes that may be used by weaving vehicles for a given configuration. Fractional values for lane requirements of weaving vehicles may occur because lanes are shared with nonweaving vehicles. Cases for which Nw ≤ Nw (max) will be unconstrained, because there are no impediments to weaving vehicles using the required number of lanes. Where Nw > Nw (max), the configuration constrains weaving vehicles to a smaller number of lanes than that required for balanced operation. Such cases are constrained and will result in average nonweaving vehicle speeds significantly higher than average weaving vehicle speeds. Table 4-4 contains equations for the computation of Nw and values for Nw (max), both of which vary with the type of configuration. The equations for Nw are based on weaving and nonweaving speeds for unconstrained operation. Computed values are compared with the maximum values shown in the third column of Table 4-4 to determine whether operations are constrained or unconstrained. Values of Nw (max) in Table 4-4 reflect observations
in the data bases reported by Pignataro et al. (1), Roess et al. (2), and Reilly et al. (5). Type A sections are the most restrictive in terms of the maximum number of lanes that can be used by weaving vehicles. As noted previously, weaving vehicles must, in general, confine themselves to the two lanes adjacent to the crown line in order to execute their desired maneuvers. However, nonweaving vehicles will also remain in these lanes, and full use of them by weaving vehicles is not a reasonable expectation. For Type A sections, weaving vehicles generally use at most 1.4 lanes, regardless of the total number of lanes available. Type B sections do not greatly restrict weaving vehicles in their use of available lanes. Weaving vehicles may occupy up to 3.5 lanes in a Type B section. This is based on the full use of through weaving lanes and lanes immediately adjacent to the through lane, as well as partial use of outer lanes. Such configurations are most efficient when weaving flows compose substantial portions of the traffic stream. Because weaving vehicles may filter through most of the lanes in the segment, nonweaving vehicles tend to share lanes and are generally unable to segregate themselves from weaving flows. Type C sections are similar to Type B sections in the provision of a through weaving lane. The multiple lane-changing required of one weaving movement, however, restricts the ability of weaving vehicles to use outer lanes of the sections. Thus, in Type C sections, weaving vehicles can use no more than 3.0 lanes. One exception to this rule is a two-sided weaving area [see Fig. 4-5(b)]. For twosided configurations, all freeway lanes are through weaving lanes, and weaving vehicles may therefore use all lanes without restriction. The proportional use of available lanes by weaving vehicles is again quite different for Type A sections as compared with Type B and C sections. In Type A sections, more lanes are required by weaving vehicles for balanced operation as length increases. This is primarily due to the substantial segregation of weaving and nonweaving flows in such sections, and the higher speeds of weaving vehicles that result. As length increases, weaving speeds become quite high, and more space is required by weaving vehicles to maintain these speeds. This characteristic produces, however, Updated December 1997
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4-8
Table 4-4. Criteria for Unconstrained Versus Constrained Operation of Weaving Areas type of configuration
no. of lanes req’d for unconstrained operation, Nw
max. no. of weaving lanes, Nw (max)
Type A
2.19 N VR0.571 LH0.234/Sw0.438
1.4
Type B
N [0.085 + 0.703VR + (234.8/L) − 0.018(Snw − Sw)]
3.5
Type C
N [0.761 − 0.011LH − 0.005(Snw − Sw) + 0.047VR]
3.0 a
NOTE: All variables are as defined in Table 4-2. When Nw ≤ Nw (max), operation is unconstrained. When Nw > Nw (max), operation is constrained. a For two-sided weaving areas, all freeway lanes may be used as weaving lanes.
an interesting result. For any given set of flows and number of lanes, it is more likely for a Type A section to operate in the constrained mode as length is increased. Type B and Type C sections show an opposite trend. Increasing length has a much smaller impact on weaving speed than for Type A sections, primarily because of the mixing of weaving and nonweaving flows. As length increases, the proportion of lanes required by weaving vehicles for balanced operation decreases, and it is less likely that constrained operation will occur.
LIMITS ON WEAVING AREA OPERATIONS
Table 4-5 gives a number of limitations on the application of this methodology that may not be obvious from either the speed or lane use equations described previously. These include weaving capacity, maximum flow rate per lane, and maximum volume and weaving ratios at which the various configuration types generally operate, as well as length limits beyond which merge and diverge areas may operate independently. The interpretation of each of these limitations varies. In the case of limitations on weaving flow rate, vw, and total flow rate per lane, v/N, acceptable operations are unlikely beyond these values. They are therefore maximum values that may be accommodated in a weaving section, within the maximum lengths shown in Table 4-5. Limits on volume ratio, VR, and weaving ratio, R, represent values beyond which weaving operations are rarely observed. Higher values may occur, but these fall outside the prediction range of the methodology, and results should be taken as approximate. Length limitations, L, represent the range of the calibration data base. As noted previously, weaving may occur in longer sections. In such cases it is generally considered that merging and
diverging maneuvers tend to become segregated, and that the procedures of Chapter 5 may be applied. Speeds in longer sections tend to approach those that would be achieved in a basic freeway section, even where some weaving turbulence exists. The weaving capacity of a Type A section is limited to a flow rate of 2,000 pcph because all weaving vehicles must cross a single crown line, restricting the number of vehicles that can cross from one side of the roadway to the other. Type B and C sections can accommodate up to 3,500 pcph and 3,000 pcph, respectively. This is primarily due to the existence of a through lane for weaving vehicles and the flexibility in lane use provided by such configurations. It is critical to note that weaving flow rates higher than these values cannot normally be sustained within a weaving area within the length limitations of Table 4-5. As length increases beyond the maximum limits shown, weaving capacity is difficult to define. When the length increases to a point where weaving lane-changing is no greater than the normal lane-changing that would occur on a basic freeway segment, weaving flow rates are constrained only by the total capacity of the freeway. The length required to achieve this, however, is not precisely defined. Analysts and designers should view with caution any weaving flow rates in excess of the Table 4-5 values. Changes in the basic design of the freeway system, including provision of grade separations, may be considered to accommodate higher flows. A maximum limitation on v/N should also be observed in weaving areas within the length limits of Table 4-5. This limitation is based on the per-lane capacity of the basic freeway section entering the freeway, and is expressed in Table 4-5 as c-100 for Type A and B configurations, and c-200 for Type C configurations, which are more restrictive, where c is the capacity per lane under ideal conditions for a basic freeway or multilane highway segment.
Table 4-5. Limitations on Weaving Sections weaving capacity vw (max),a pcph
maximum v/N,b pcphpl
Type A
2,000
c-100
Type B
3,500
c-100
Type C
3,000
c-200
configuration
a
maximum Rd
maximum weaving length L,e ft
0.50
2,000
0.80
0.50
2,500
0.50
0.40
2,500
maximum VRc N
VR
2 3 4 5
1.00 0.45 0.35 0.22
Section likely to fail at higher weaving flows. b Section likely to fail at higher average per-lane flows. c Section will likely operate at lower speeds than predicted if VR limit is exceeded. d Section will likely operate at lower speeds than predicted if R limit is exceeded. e When length exceeds these limits, merge and diverge are treated as isolated junctions and analyzed accordingly.
Updated December 1997
weaving areas The capacity per lane is found from the procedures in Chapter 3 and is related to the average free-flow speed of the freeway sections entering and leaving the weaving area. Limitations on volume ratio, VR, reflect the character of each configuration type. Type A sections are intended to handle small weaving flows comprising a minority of the traffic stream. Because weaving vehicles do not normally use more than 1.4 lanes in such sections, the limiting VR depends on the total number of lanes available and decreases as N increases. Freeway weaving areas with Type A configurations generally should not be used where weaving traffic includes a proportion of total flow larger than that shown in Table 4-5. Type C configurations are more generous in handling larger proportions of weaving traffic, but are still not efficient where weaving flows dominate total flow. Only Type B configurations effectively handle situations in which VR > 0.50 and N > 2. The weaving ratio, R, is the ratio of the smaller weaving flow to the total weaving flow. Its maximum value is 0.50, which occurs when the two weaving flows are equal. Neither Type A nor Type B configurations have any practical limitation on R, because both can accommodate equal weaving flows without operational problems. Type C configurations, however, are most efficient where weaving flows are unequal because one weaving movement requires no lane-changing, whereas the other requires two or more lane changes. Such sections generally do not operate efficiently when the weaving ratio exceeds 0.40, with the larger flow in the direction requiring no lane changes. LOS CRITERIA
Level of service in weaving areas is related to the average density of all vehicles in the section. Average density in the weaving area is computed by finding the average (space mean) speed of all vehicles in the weaving section and then estimating density as total flow divided by average (space mean) speed: S=
vw + vnw vw Sw
+
vnw
(4-4)
Snw
4-9
Table 4-6. LOS Criteria for Weaving Areas maximum density (pc/mi/ln) level of service
freeway weaving area
multilane and c-d weaving areas
A B C D E F
10 20 28 35 ≤43 >43
12 24 32 36 ≤40 >40
where S is the average (space mean) speed of all vehicles in the weaving section in miles per hour, and all other variables are as previously defined. The density is then found: D=
v/N S
(4-5)
where D is the density in passenger cars per mile per lane. Table 4-6, contains LOS criteria based on density in the weaving area. Note that criteria are shown for freeways as well as for multilane highways and collector-distributor (C-D) roadways. The procedures in this chapter can be applied to weaving sections on multilane highways by using an appropriate free-flow speed in the prediction of nonweaving and weaving vehicle speeds. Chapter 7 contains procedures for the estimation of free-flow speed on a multilane highway if field measurements are not available. Multilane criteria may be cautiously applied to C-D roadway weaving areas, but it is recommended that free-flow speed be measured or roughly estimated from design speed or speed limit information. In general, these criteria allow for slightly higher densities at any given LOS threshold than on a comparable basic freeway or multilane highway section. This follows the philosophy that drivers expect higher densities in weaving areas relative to those on basic freeway or multilane highway segments. The LOS EF boundary does not apply this approach. Rather, it is thought that breakdown will occur at slightly lower densities than on basic sections because of the additional turbulence resulting from weaving movements.
III. PROCEDURES FOR APPLICATION SIMPLE WEAVING AREAS
Procedural steps for the analysis of simple weaving areas are given below. Computations are performed in the operational analysis mode; that is, a known or projected situation is analyzed for the probable level of service. All roadway and traffic conditions must be specified, including weaving length, type of configuration, number of lanes, lane widths, terrain or grade, weaving and nonweaving flow rates by movement, peak-hour factor, and traffic composition. Weaving analysis is made easier through the use of a weaving diagram, which is a schematic drawing showing weaving and nonweaving flows in a weaving area. Figure 4-6 shows such a diagram. Note that the weaving diagram depicts actual flows in
a straight-line form. The relative placement of entry and exit points (A, B, C, D) in the diagram matches the actual site to ensure proper placement of weaving and nonweaving flows relative to each other. Flows on the weaving diagram should represent flow rates for the peak 15 min under ideal conditions, expressed in passenger cars per hour. It is also convenient to use the weaving diagram as a guide in computing the parameters used during an analysis. The level of service in an existing or projected weaving area is evaluated using the following computational steps. Step 1—Establish Roadway and Traffic Conditions
All existing or projected roadway and traffic conditions must be specified. Roadway conditions include the length, number of Updated December 1997
freeways
4-10
v=
V PHF × fHV × fw × fp
(4-6)
where v = flow rate for peak 15 min under ideal conditions (pcph); V = hourly volume under prevailing condition (veh/hr); PHF = peak-hour factor; fHV = heavy-vehicle adjustment factor, determined using the procedures in Chapter 3 or 7; and fp = driver population adjustment factor, determined using the procedures in Chapter 3. Step 3—Construct Weaving Diagram
A weaving diagram of the type illustrated in Figure 4-6 is now constructed, with all flows indicated as peak flow rates under ideal conditions in passenger cars per hour. Critical analysis variables are identified and computed as shown in Figure 4-6. Step 4—Compute Unconstrained Weaving and Nonweaving Speeds
Using weaving intensity factors for the appropriate configuration from Table 4-3, compute the average (space mean) speed for weaving and nonweaving vehicles. Unconstrained operation is assumed for this step. Figure 4-6. Construction and use of weaving diagrams. Step 5—Check for Constrained Operation
lanes, and type of configuration for the weaving area under study. Table 4-1, should be consulted in assigning the type of configuration. Other roadway features of importance are lane widths and the general terrain or grade conditions for the section. Traffic conditions include the distribution of vehicle types in the traffic stream, as well as the peak-hour factor, or peak-hour factors where the component flows have differing peaking characteristics. Because the weaving area should be analyzed on the basis of peak flow rates for a 15-min interval within the hour of interest, hourly volumes must be adjusted by dividing by the peak-hour factor. Such a conversion, however, ignores the fact that the four component flows in a weaving area may not all peak during the same interval. Where possible, weaving flows should be observed and recorded for 15-min intervals so that critical periods may be identified for analysis. Where hourly volumes are available or projected, it will be assumed that all component flows peak simultaneously—a conservative procedure. The predicted speeds of weaving and nonweaving vehicles will be lower than those actually occurring in such cases. It should also be noted that the component movements in a weaving area may not have the same peak-hour factor. Where possible, each flow and its peaking characteristics should be considered separately. Step 2—Convert All Traffic Volumes to Peak Flow Rates Under Ideal Conditions
Because all of the speed and lane-use algorithms presented earlier are based on peak flow rates under ideal conditions, expressed in passenger cars per hour, all component flows must be converted to this basis: Updated December 1997
Using the speeds computed in Step 4, estimate the number of lanes needed by weaving vehicles to achieve unconstrained operation using the equations in Table 4-4. Compare the computed value of Nw with the tabulated value of Nw (max) to determine whether operation is constrained or unconstrained. If Nw ≤ Nw (max), the operation is unconstrained, and the speeds computed in Step 4 are accurate. If Nw > Nw (max), the operation is constrained. Values of Sw and Snw must be recomputed using Equation 4-3 and the constrained weaving intensity factor for the appropriate configuration given in Table 4-3. Step 6—Compute Average (Space Mean) Speed and Density of All Vehicles in Weaving Area
Use Equation 4-4 to compute the average (space mean) speed of all vehicles in the weaving section. The result may be used in Equation 4-5 to compute the density in weaving section. Then S=
vw + vnw vw Sw
D=
+
vnw Snw
v/N S
Step 7—Check Weaving Area Limitations
Table 4-5 should be consulted to ensure that none of the limitations specified are exceeded. Where one or more of these limits are exceeded, consult the Methodology section of this chapter for the appropriate interpretation.
weaving areas Care should be taken in applying the limiting values given in Table 4-5. Where the weaving capacity is exceeded, it is likely that breakdowns will occur and that LOS F will prevail, at least for weaving vehicles. Where limitations on VR or R are exceeded, breakdowns need not occur, but speeds would be lower than those anticipated by the equations of Table 4-3. Maximum lengths reflect the limits of the predictive equations. Lengths beyond the values shown may be analyzed as separate merge and diverge areas using the procedures in Chapter 5. It would not be expected that speeds within the section would be significantly lower than those for a basic freeway section serving the same volume. Step 8—Determine Level of Service
The estimated value of density, D, in the weaving area is compared with the criteria in Table 4-6 to determine the prevailing level of service. MULTIPLE WEAVING AREAS
Multiple weaving areas are formed when one merge point is followed closely by two diverge points or where two merge points are closely followed by a single diverge point. In such cases, several sets of weaving movements take place over the same segments of freeway, and lane-changing turbulence may be higher than that found in simple weaving areas. Drivers will carefully select where to execute their required lane changes in a manner that minimizes interference with other
4-11
weaving movements. Figures 4-7 and 4-8 show the two types of multiple weaving areas and where weaving movements are most likely to take place. Weaving diagrams may be developed for each subsegment of the weaving area, each of which can be analyzed as a simple weaving area using the procedures specified earlier. Figure 4-7 depicts a single merge area followed by two diverge areas. The weaving of Movement 5 with Movements 3 and 4 must take place in the first segment, because vehicles in Movement 5 leave at the first diverge point. The weaving of Movement 2 with Movement 3 may take place anywhere in either segment of the section. However, to avoid the turbulence of weaving that must take place in the first segment, these latter weaving movements will tend to concentrate in the second segment of the section. Figure 4-8 depicts two merge areas followed by a single diverge area. In this case, the weaving of Movements 3 and 4 with Movement 5 must take place in the second segment of the section, because Movement 5 enters at the second merge. Although the weaving of Movements 2 and 3 could take place anywhere in the section, it will tend to be concentrated in the first segment, because drivers seek to avoid the turbulence of other weaving movements in the second segment. Thus, the analysis of multiple weaving areas involves the construction of appropriate weaving diagrams for each subsegment of the area using Figures 4-7 and 4-8. Once these diagrams are established, each subsegment may be analyzed as a simple weaving area, according to the procedures in this chapter. Limits established in Table 4-5 would apply to the individual subsegments.
Figure 4-7. Weaving flows in a multiple weave formed by a single merge followed by two diverges. Updated December 1997
freeways
4-12
Figure 4-8. Weaving flows in a multiple weave formed by two merge points followed by a single diverge.
IV. SAMPLE CALCULATIONS The following sample calculations illustrate the application and interpretation of the methodology presented in this chapter.
CALCULATION 1—ANALYSIS OF MAJOR WEAVING AREA
Solution
The calculation is conducted according to the steps outlined in the Procedures for Application section of this chapter. Step 1—Establish Roadway and Traffic Conditions
Description
The weaving area illustrated in Figure 4-9 serves the following traffic volumes: A–C = 1,815 veh/hr; A–D = 692 veh/hr; B–C = 1,037 veh/hr; B–D = 1,297 veh/hr. Traffic volumes include 10 percent trucks, and the PHF is 0.91. The section is located in generally level terrain, and lane widths are 12 ft. There are no lateral obstructions. The driver population is composed primarily of commuters. The observed free-flow speed of the freeway, SFF, is 65 mph. At what level of service will the section operate?
The existing geometrics and traffic volumes are stated in the description. Note that the section is a Type B configuration (see Table 4-1). Weaving Movements B and C may be made without a lane change, whereas Movements A–D can be made with a single lane change. Step 2—Convert All Traffic Volumes to Peak Flow Rates Under Ideal Conditions
All volumes must be converted to peak flow rates under ideal conditions expressed in passenger cars per hour: v=
V PHF × fHV × fp
where PHF = 0.91 (given); ET = 1.5 (Table 3-3); fHV = 0.95 (computed as 1/[1 + 0.10(1.5 − 1)]; and fp = 1.00. SFF = 65 mph
Figure 4-9. Weaving area for Calculation 1. Updated December 1997
Then A–C = 1,815/(0.91 × 0.95 × 1.00) = 2,100 pcph A–D = 692/(0.91 × 0.95 × 1.00) = 800 pcph
weaving areas B–C = 1,037/(0.91 × 0.95 × 1.00) = 1,200 pcph B–D = 1,297/(0.91 × 0.95 × 1.00) = 1,500 pcph Step 3—Construct Weaving Diagram
A weaving diagram for the calculation is now constructed using the converted flow rates of Step 2:
4-13
As 2.4 lanes is less than Nw (max), which is 3.5 lanes for a Type B section, the operation is unconstrained, and the predicted speeds of Step 4 stand without modification. Step 6—Compute Average (Space Mean) Speed and Density of All Vehicles in Weaving Area
Level of service is found by first computing the average (space mean) speed of all vehicles and then the average density of all vehicles in the weaving section: S=
vw + vnw vw Sw
S= Critical ratios may also be computed for use in analysis: vw = 1,200 + 800 = 2,000 pcph v = 2,000 + 2,100 + 1,500 = 5,600 pcph R = 800/2,000 = 0.400 VR = 2,000/5,600 = 0.357 Step 4—Compute Unconstrained Weaving and Nonweaving Speeds
The unconstrained speeds of weaving and nonweaving vehicles may be estimated using Equation 4-3 and the weaving intensity factors computed from Table 4-3:
+
vnw Snw
2,000 + 3,600 = 42.2 mph 2,000 3,600 + 42.7 42.0
D=
v/N S
D=
5,600/4 = 33.2 pc/hr/ln 42.2
From the density criteria in Table 4-6, this is LOS D. Step 7—Check Weaving Area Limitations
All limiting values of Table 4-5 are met. The results are therefore expected to be valid as indicated.
a (1 + VR)b (v/N)c Ld
CALCULATION 2—ANALYSIS OF RAMP-WEAVE SECTION
Ww =
0.10 (1 + 0.357)1.2 (5,600/4)0.77 = 0.9855 1,5000.5
Description
Wnw =
0.02 (1 + 0.357)2.0 (5,600/4)1.42 = 1.0385 1,5000.95
W=
Then, on the basis of a free-flow speed of 65 mph for the freeway, weaving and nonweaving speeds may be computed as follows: Si = 15 +
SFF − 10
The weaving section shown in Figure 4-10 serves the traffic flows indicated. Lane widths are 12 ft and the section is located in level terrain. There are no lateral obstructions. For convenience, all traffic flows are given in terms of peak flow rates for ideal conditions, expressed in passenger cars per hour. The free-flow speed of the freeway is observed to be 70 mph through field evaluation. At what level of service will the section operate?
1+W
Sw = 15 +
65 − 10 = 42.7 mph 1 + 0.9855
Snw = 15 +
65 − 10 = 42.0 mph 1 + 1.0385
Step 5—Check for Constrained Operation
Using the unconstrained estimates of weaving and nonweaving vehicle speeds, the assumption of unconstrained operation is checked using the criteria in Table 4-4. From this table, the number of lanes required by weaving vehicles for unconstrained operation is computed as follows:
SFF = 70 mph
Nw = N [0.085 + 0.703VR + (234.8/L) − 0.018(Snw − Sw)] Nw = 4[0.085 + 0.703(0.357) + (234.8/1,500) − 0.018(42.0 – 42.7)] = 2.4 lanes
Figure 4-10. Weaving area and flows for Calculation 2. Updated December 1997
freeways
4-14 Solution
Step 1—Establish Roadway and Traffic Conditions
All prevailing traffic and roadway conditions are specified in the calculation description and in Figure 4-10. Note that this is a Type A configuration because both weaving movements are required to make one lane change. Step 2—Convert All Traffic Volumes to Peak Flow Rates Under Ideal Conditions
weaving and nonweaving speeds occurs even though there is no constraint present and reflects the short length of the section and the fact that most weaving vehicles will be accelerating or decelerating within the confines of the section. Step 6—Compute Average (Space Mean) Speed and Density of All Vehicles in Weaving Area
The level of service is found by computing the average (space mean) speed and then estimating the average density in the section:
No conversions of stated traffic demands are required, because they are given in terms of peak flow rates under ideal conditions, expressed in passenger cars per hour.
S=
Step 3—Construct Weaving Diagram
S=
Sw
The weaving diagram is shown in Figure 4-10. Critical ratios may be computed as follows: vw = 600 + 300 = 900 pcph v = 900 + 4,000 + 100 = 5,000 pcph VR = 900/5,000 = 0.18 R = 300/900 = 0.33 Step 4—Compute Unconstrained Weaving and Nonweaving Speeds
Weaving intensity factors are computed from Table 4-3 for assumed unconstrained conditions on a Type A weaving section: W=
a (1 + VR)b (v/N)c Ld
Wnw =
0.02 (1 + 0.18) (5,000/4) 1,0001.0
= 0.4117
SFF − 10 1+W
Sw = 15 +
70 − 10 = 48.1 mph 1 + 0.8110
Snw = 15 +
70 − 10 = 57.5 mph 1 + 0.4117
Step 5—Check for Constrained Operation
The assumption of unconstrained operation is checked using the equations and criteria of Table 4-4: Nw = Nw =
Vnw Snw
900 + 4,100 = 55.5 mph 900 4,100 + 48.1 57.5
D=
v/N S
D=
5,000/4 = 22.5 pc/hr/ln 55.5
From the density criteria of Table 4-6, this is LOS C. Step 7—Check Weaving Area Limitations
None of the limitations indicated in Table 4-5 have been violated, and the results seem to be appropriate.
Description
1.3
Then, on the basis of a free-flow speed, SFF, of 70 mph, the weaving and nonweaving vehicle speeds can be estimated: Si = 15 +
+
CALCULATION 3—CONSTRAINED OPERATION
0.226 (1 + 0.18)2.2 (5,000/4)1.0 Ww = = 0.8110 1,0000.9 4.0
vw + vnw vw
The ramp-weave section shown in Figure 4-11 serves the following demand volumes. A–C = 975 veh/hr; A–D = 650 veh/hr; B– C = 520 veh/hr; B–D = 0 veh/hr. Traffic includes 15 percent trucks, is composed of daily commuters, and the PHF is 0.85. Twelvefoot lanes are provided with no lateral obstructions, and the section is located in generally rolling terrain. Through field evaluation, the free-flow speed is observed to be 65 mph. What is the expected level of service for the section? Solution
Step 1—Establish Roadway and Traffic Conditions
All roadway and traffic conditions are specified in the calculation description and Figure 4-11. Note that this is a Type A configuration because both Movements A–D and B–C require one lane change.
2.19N VR0.571L 0.234 H S 0.438 w 2.19(4)(0.180.571)(100.234) = 1.1 lanes 48.10.438
Because this is less than the maximum value of 1.4 lanes, the section may be assumed to be unconstrained. The speeds computed in Step 4 stand without modification. The large difference between Updated December 1997
SFF = 65 mph
Figure 4-11. Weaving area for Calculation 3.
weaving areas Step 2—Convert All Traffic Volumes to Peak Flow Rates Under Ideal Conditions
The given demand volumes must be converted to peak flow rates under ideal conditions expressed in passenger cars per hour:
4-15
The estimated speed of weaving and nonweaving vehicles (assuming unconstrained operation) may now be computed as follows: Si = 15 +
V v= PHF × fHV × fp
1+W
Sw = 15 +
65 − 10 = 40.0 mph 1 + 1.292
Snw = 15 +
65 − 10 = 42.1 mph 1 + 1.028
where PHF = 0.85 (given); ET = 3 (Table 3-3); fHV = 0.77 = 1/[1 + 0.15(3 − 1)]; and fp = 1.00.
SFF − 10
Step 5—Check for Constrained Operation
The assumption of unconstrained operation is now checked using the equations and limits of Table 4-4:
Then A–C = 975/(0.85 × 0.77 × 1.00) = 1,490 pcph A–D = 650/(0.85 × 0.77 × 1.00) = 993 pcph B–C = 520/(0.85 × 0.77 × 1.00) = 794 pcph B–D = 0 pcph
Step 3—Construct Weaving Diagram
A weaving diagram for the calculation is now constructed using the converted flow rates of Step 2:
Nw = Nw =
2.19N VR 0.571L 0.234 H S 0.438 w 2.19(3)(0.550.571)(100.234) = 1.6 lanes 40.00.438
As this is greater than Nw(max) of 1.4 lanes for a Type A weaving section, the section operates in a constrained mode. The weaving intensity factors and speeds must therefore be recomputed for the constrained case: Ww =
0.28 (1 + 0.55)2.2 (3,277/3)1.0 = 1.600 1,0000.9
Wnw =
0.02 (1 + 0.55)4.0 (3,277/3)0.88 = 0.863 1,0000.6
and Sw = 15 +
65 − 10 = 36.2 mph 1 + 1.600
Snw = 15 +
65 − 10 = 44.5 mph 1 + 0.863
Critical ratios may be computed as follows: vw v VR R
= = = =
Step 6—Compute Average (Space Mean) Speed and Density of All Vehicles in Weaving Area
993 + 794 = 1,787 pcph 1,787 + 1,490 = 3,277 pcph 1,787/3,277 = 0.55 794/1,787 = 0.44
The level of service is found by computing the average (space mean) speed in the weaving area and then the density. The resultant density is compared with the criteria of Table 4-6: S=
Step 4—Compute Unconstrained Weaving and Nonweaving Speeds
vw + vnw vw Sw
From Table 4-3, the weaving intensity factors, W, for assumed unconstrained flow for a Type A weaving section are
W=
Ww =
a (1 + VR)b (v/N)c Ld 0.226(1 + 0.55)2.2 (3,277/3)1.0 = 1.292 1,0000.9 4.0
Wnw =
0.02 (1 + 0.55) (3,277/3) 1,0001.0
1.3
= 1.028
S=
+
vnw Snw
1,787 + 1,490 = 39.6 mph 1,787 1,490 + 36.2 44.5
D=
v/N S
D=
3,277/3 = 27.6 pc/hr/ln 39.6
From Table 4-6, this is LOS C, though barely. Updated December 1997
4-16
freeways Step 1—Establish Roadway and Traffic Conditions
All required roadway and traffic conditions are specified in the description. Step 2—Convert All Traffic Volumes to Peak Flow Rates Under Ideal Conditions
Figure 4-12. Weaving area for Calculation 4. Note: Free-flow speed for a design case is generally estimated from the design speed or speed limit. Step 7—Check Weaving Area Limitations
In consulting the limiting values of Table 4-5, it is seen that the volume ratio (VR) of 0.55 exceeds the maximum value of 0.45 in the table. This means that it is likely that the operation is worse than that indicated by this analysis, although a breakdown is not necessarily going to occur. A possible solution is to add one lane to the exit ramp, creating a Type 8 configuration that can better serve high volume ratios.
No conversions are required because all demands are stated as peak flow rates under ideal conditions, in passenger cars per hour. Step 3—Construct Weaving Diagram
A weaving diagram and critical ratios are shown in Figure 4-12. Step 4—Compute Unconstrained Weaving and Nonweaving Speeds
The unconstrained weaving and nonweaving speeds are expressed for the Type C configuration by using equations from Table 4-3: W=
CALCULATION 4—DESIGN APPLICATION
Ww =
0.100 (1 + 0.385)1.8 (6,500/5)0.8 = 1.438 1,5000.50
Wnw =
0.015 (1 + 0.385)1.8 (6,500/5)1.1 = 1.853 1,5000.5
Description
A weaving area is being considered at a major junction between two urban freeways. The configuration of entry and exit roadways is expected to be as shown in Figure 4-12, which also shows the expected demand flow rates, expressed as peak flow rates under ideal conditions in passenger cars per hour. Design constraints limit the section length to a maximum of 1,500 ft. LOS C design is desired for the section.
a (1 + VR)b (v/N)c Ld
and Si = 15 +
1+W
Sw = 15 +
70 − 10 = 39.6 mph 1 + 1.438
Snw = 15 +
70 − 10 = 36.1 mph 1 + 1.853
Solution
Design of weaving areas is best achieved by trial-and-error analysis of likely design scenarios. Because the length of the section is limited to 1,500 ft, trial designs will start with this assumed length. Given the anticipated design of entry and exit roadways, the most obvious design would be a five-lane section as shown below:
SFF − 10
Step 5—Check for Constrained Operation
Using these estimates, the type of operation is checked using equations and values given in Table 4-4: Nw = N [0.761 − 0.011LH − 0.005(Snw − Sw) + 0.047VR] Nw = 5 [0.761 − 0.011(15) − 0.005(36.1 − 39.6) + 0.047(0.385)] Nw = 3.2 lanes > 3.00 lanes
This design results from simply connecting each of the five entry lanes with the five exit lanes. Note that the resulting configuration is Type C, because Movement B–C may be made without lane changing, whereas Movement A–D requires a minimum of two lane changes. The resulting section is now analyzed for the anticipated level of service. Updated December 1997
Because the number of lanes required by weaving vehicles for unconstrained operation is greater than the maximum number of lanes that can be achieved in a Type C configuration, the operation will be constrained, and the speeds must be recomputed. Ww =
0.100 (1 + 0.385)2.0 (6,500/5)0.85 = 2.200 1,5000.50
Wnw =
0.013 (1 + 0.385)1.6 (6,500/5)1.0 = 0.735 1,5000.5
weaving areas and Sw = 15 + Snw = 15 +
70 − 10 = 33.8 mph 1 + 2.200 70 − 10 = 49.6 mph 1 + 0.735
4-17 Ww =
0.100 (1 + 0.385)1.2 (6,500/5)0.77 = 0.954 1,5000.50
Wnw =
0.02 (1 + 0.385)2.0 (6,500/5)1.42 = 0.974 1,5000.95
and
Step 6—Compute Average (Space Mean) Speed and Density of All Vehicles in Weaving Area
The level of service is computed by finding the average (space mean) speed and density in the weaving area. The resulting density is compared with the criteria in Table 4-6: S=
vw + vnw vw Sw
S=
+
vnw Snw
2,500 + 4,000 = 42.2 mph 2,500 4,000 + 33.8 49.6
D=
v/N S
D=
6,500/5 = 30.8 pc/hr/ln 42.2
From Table 4-6, this is LOS D. This does not meet the design objective of LOS C. Further, the dramatic difference in speed of weaving and nonweaving vehicles suggests that this design is inappropriate for the demand shown. In particular, it is inappropriate to have 1,000 vehicles in the minor weaving direction making two lane changes in 1,500 ft. Since the length of the section is limited to 1,500 ft (problem statement), and it is difficult to see how lanes could be added within the section, a change of configuration seems to be in order. A Type B configuration can be created by adding one lane to exit leg D. This also solves the principal problem in the section, because the 1,000 veh/hr in the minor weaving direction must now only make a single lane change. The resulting section is shown below:
Sw = 15 +
70 − 10 = 45.7 mph 1 + 0.954
Snw = 15 +
70 − 10 = 45.4 mph 1 + 0.974
Step 5: The type of operation is now checked using equations and values from Table 4-4: Nw = N [0.085 + 0.703VR + (234.8/L) − 0.018(Snw − Sw)] Nw = 5 [0.085 + 0.703(0.385) + (234.8/1,500) − 0.018 (45.4 – 45.7)] Nw = 2.6 lanes < 3.50 lanes The operation is therefore unconstrained. Step 6: None of the limiting values of Table 4-5 are exceeded by the trial design. Step 7: The level of service is found by computing the average (space mean) speed and density in the weaving area. The density is compared with the criteria of Table 4-6: S=
D=
2,500 + 4,000 = 45.5 mph 2,500 4,000 + 45.7 45.4 6,500/5 = 28.6 pc/hr/ln 45.5
From Table 4-6, this is still LOS D, just missing the maximum of 28 pc/ml/ln for LOS C, the target level of service. Given the limitation on length, however, there are no practical alternatives that would improve operations. The design level of service is almost achieved. This calculation illustrates, however, the significant improvement in operation that can be achieved by providing an appropriate configuration. In both trial designs, the demand on and length and width of the weaving section were exactly the same. The provision of a Type B configuration, however, resulted in better balance between weaving and nonweaving vehicles and improved density. CALCULATION 5—MULTIPLE WEAVING AREA Description
Figure 4-13 shows a multiple weaving area. Peak flow rates for the sections are This revised trial design may now be analyzed using the procedures of this chapter.
A–X = 900 pcph
Step 1: All roadway and traffic conditions have been stated. Step 2: All flows are expressed in peak flow rates under ideal conditions, in passenger cars per hour. Step 3: Figure 4-12 includes a weaving diagram. Step 4: Speed equations are now selected from Table 4-3 for unconstrained operation on a Type B configuration:
A–Y = 1,000 pcph
B–X = 400 pcph
B–Y = 200 pcph C–X = 300 pcph C–Y = 100 pcph Updated December 1997
freeways
4-18
All geometric conditions are ideal, and the terrain is generally level. At what level of service would the section operate? SFF = 60 mph (field measurement)
and Snw = 15 +
SFF − 10 1 + 0.02(1 + VR)2.0(v/N)1.42/L0.95
Snw = 15 +
60 − 10 1 + 0.02(1 + 0.56)2.0(2,500/3)1.42/1,0000.95
Snw = 40.4 mph
Figure 4-13. Weaving area for Calculation 5.
The number of lanes required by weaving vehicles for unconstrained operation is computed using the appropriate equation from Table 4-4 and compared with the maximum value of 3.5 lanes, also obtained from Table 4-4, for Type B configurations: Nw = N [0.085 + 0.703 VR + (234.8/L) − 0.018(Snw − Sw)]
Solution
A multiple weaving section is analyzed as two separate simple weaving areas. The initial step in the analysis is to construct weaving diagrams for the two subsegments of the multiple weaving area. Because all demands are stated in peak flow rates under ideal conditions and no conversion computations are required, this is done immediately. The weaving area under study is of the type illustrated in Figure 4-8, that is, two merge areas followed closely by a diverge area. Weaving diagrams are constructed in accordance with Figure 4-8, as follows:
Nw = 3 [0.085 + 0.703(0.56) + (234.8/1,000) − 0.018(40.4 – 40.5)] Nw = 2.2 lanes < 3.5 lanes The section is therefore unconstrained. None of the limitations of Table 4-5 are exceeded. The harmonic average speed and density are computed to find level of service: S=
D=
1,400 + 1,100 = 40.5 mph 1,400 1,100 + 40.5 40.4 2,500/3 = 20.6 pc/hr/ln 40.5
From Table 4-6, this is LOS C, just missing the LOS B boundary. Segment 2
Using the same equations as for Segment 1, because both are Type B configurations, Sw = 15 +
60 − 10 1 + 0.10(1 + 0.517)1.2(2,900/3)0.77/1,5000.5
Sw = 42.1 mph Note that both segments of the weaving area are Type B configurations. In Segment 1, Movement A–Y may be made with no lane changes, whereas Movement B–X requires one lane change. In Segment 2, Movements A–Y and B–Y may be made with no lane changes, but Movement C–X requires a single lane change. Computations for speed are now done for each segment. Note that the first three steps of the procedure have been completed in the establishment of weaving diagrams for the two segments.
Snw = 15 +
60 − 10 1 + 0.02(1 + 0.517)2.0(2,900/3)1.42/1,5000.95
Snw = 43.3 mph The number of lanes required by weaving vehicles is Nw = 3 [0.085 + 0.703(0.517) + (234.8/1,500) − 0.018(43.3 – 42.1)]
Segment 1
Unconstrained speed predictions are obtained from Table 4-3 for a Type B configuration. To save space, the equation for the weaving intensity factor, W, is inserted directly into the speed prediction equation: Sw = 15 +
SFF − 10 1 + 0.10(1 + VR)1.2(v/N)0.77/L0.5
Sw = 15 +
60 − 10 1 + 0.10(1 + 0.56)1.2(2,500/3)0.77/1,0000.5
Sw = 40.5 mph Updated December 1997
Nw = 1.8 lanes < 3.5 lanes Operation is unconstrained. None of the limitations of Table 4-5 are exceeded. The harmonic average speed and density are computed to find level of service: S=
D=
1,500 + 1,400 = 42.7 mph 1,500 1,400 + 42.1 43.3 2,900/3 = 22.6 pc/hr/ln 42.7
weaving areas
4-19
Table 4-7. Results of Weaving Analysis: Sample Calculation 6 type a configurations
type b configurations
type c configurations
no. of lanes
length (ft)
S, mph
D, pc/ mi/ln
los
cons. ?
S, mph
D, pc/ mi/ln
los
cons. ?
S, mph
D, pc/ mi/ln
los
cons. ?
3
500 750 1,000 1,500 2,000 2,500 500 750 1,000 1,500 2,000 2,500 500 750 1,000 1,500 2,000 2,500
36.7 40.9 44.0 48.5 51.7 — 40.3 44.8 48.0 52.4 55.4 — 43.4 47.9 51.0 55.3 58.0 —
38.2 34.3 31.8 28.8 27.1 — 26.0 23.4 21.9 20.0 19.0 — 19.4 17.6 16.5 15.2 14.5 —
E D D D C — C C C B B — B B B B B —
Yes Yes Yes Yes Yes — Yes Yes Yes Yes Yes — Yes Yes Yes Yes Yes —
32.0 36.1 39.2 43.9 47.2 49.7 36.3 40.9 44.2 48.8 52.0 54.3 40.1 44.8 48.1 52.5 55.4 57.5
43.8 38.8 35.7 31.9 29.7 28.2 28.9 25.7 23.8 21.5 20.2 19.4 21.0 18.8 17.5 16.0 15.2 14.6
F E E D D D D C C C C B C B B B B B
No No No No No No No No No No No No No No No No No No
29.3 31.6 33.4 36.0 38.0 39.6 32.6 35.2 37.2 40.0 42.2 43.8 35.4 38.2 40.3 47.0 49.1 50.6
47.8 44.3 42.0 38.9 36.8 35.3 32.2 29.9 28.3 26.2 24.9 24.0 23.7 21.9 20.9 17.8 17.1 16.6
F F E E E E D D D C C C C C C C C C
No No No No No No No No No No No No No No No Yes Yes Yes
4
5
From Table 4-6, this is LOS C. The analysis shows that the section will operate at speeds in the 40- to 43-mph range, producing densities that are in the upper portion of LOS C. CALCULATION 6—SENSITIVITY ANALYSIS WITH DESIGN APPLICATION
Description
A major interchange is to be built to join two major freeways in a suburban area. The issue of handling some of the interchanging movements in a weaving section is to be investigated. The flows in question are shown below, and are given in terms of flow rates in passenger cars per hour under ideal conditions.
Because the interchange joins two future facilities, there is substantial flexibility in both the length and width that may be considered for the section. LOS C operation is desired. Solution
Since the length, width, and configuration to be used are open to question, as is the issue of whether or not to use a weaving section, many trial computations must be made. Speeds can be computed for weaving and nonweaving vehicles for a range of
conditions covering three, four, or five lanes; lengths from 500 to 2,500 ft; and all three types of configuration. Although this is a time-consuming process, it is easily set up on a programmable calculator, microcomputer spreadsheet, or any type of computer. The results of such computations are shown in Table 4-7. A number of points should be made concerning these results and their impact on a final design decision: 1. Before all the potential solutions that yield LOS C are examined, the configuration of entry and exit legs should be considered. To provide for LOS C on each of the entry and exit legs, using the criteria for basic freeway sections, each leg would have the following number of lanes, based on a service flow rate of 1,644 pcphpl: Leg A B C D
Volume (pcph) 2,200 2,000 2,500 1,700
No. of Lanes for LOS C 2 2 2 2
With this number of entry and exit legs, all five-lane solutions are impractical and are therefore eliminated from serious consideration. Five lanes is excessive, given that four lanes is adequate to handle all input and output flows. 2. If the lanes from the above legs are simply connected, a fourlane Type A configuration results. All of the four-lane Type A configurations produce LOS C or better. On the other hand, they are also all constrained, indicating a serious imbalance between weaving and nonweaving flows. Further, for four- and five-lane configurations, the VR of 0.405 for this problem exceeds the maximum indicated in Table 4-5. Thus, the results may be misleading, and poorer operating conditions would likely result. 3. There is no easy way to create a Type C configuration given the number of lanes on entry and exit legs. A Type B configuration could be created by adding a lane to Leg C. If this were done, a four-lane section with a length between 750 and 2,500 ft could be provided, because all would result in Updated December 1997
4-20
freeways
LOS C or better. No length provides LOS C in a three-lane design. The final design result would be in this range, with the exact length being determined by economics and specifics of
geometry. The additional lane on Leg C would most likely be dropped at some downstream point, because it is not needed to provide for LOS C on that leg.
V. REFERENCES 1. Pignataro, L., et al. NCHRP Report 159: Weaving Areas— Design and Analysis. Transportation Research Board, Washington, D.C. (1975). 2. Roess, R.P., et al. Freeway Capacity Analysis Procedures. Final Report, Project No. DOT-FH-11-9336, Polytechnic University, Brooklyn, N.Y. (1978). 3. Roess, R.P. ‘‘Development of Weaving Procedures for the 1985 Highway Capacity Manual.’’ Transportation Research Record 1112, Transportation Research Board, Washington, D.C. (1988). 4. Leisch, J. Completion of Procedures for Analysis and Design of Traffic Weaving Areas. Final Report, Vols. 1 and 2, Federal Highway Administration, Washington, D.C. (1983).
Updated December 1997
5. Reilly, W., et al. Weaving Analysis Procedures for the New Highway Capacity Manual. Technical Report, JHK & Associates, Tucson, Ariz. (1983). 6. Schoen, J., et al. Speed-Flow Relationships for Basic Freeway Sections. Final Report, NCHRP Project 3-45, Catalina Engineering, Tucson, Ariz. (1995). 7. Roess, R., and Ulerio, J. Capacity of Ramp-Freeway Junctions. Final Report, NCHRP Project 3-37, Polytechnic University, Brooklyn, N.Y. (1993). 8. Roess, R.P., McShane, W.R., and Prassas, E.S. Traffic Engineering, 2nd ed. Prentice-Hall, Simon & Schuster, Salt Lake City, Utah (Jan. 1998).
chapter 5
RAMPS AND RAMP JUNCTIONS
CONTENTS i.
introduction .......................................................................................................................................................................... Ramp Components ................................................................................................................................................................ Operational Characteristics.................................................................................................................................................... Length of Acceleration and Deceleration Lanes ..................................................................................................................
5-1 5-2 5-2 5-3
ii.
methodology.......................................................................................................................................................................... Prediction of Flow Entering Lanes 1 and 2 (V12) ................................................................................................................ General Model Structure ................................................................................................................................................... Specific Models ................................................................................................................................................................. Capacity Values..................................................................................................................................................................... Merge Areas ...................................................................................................................................................................... Diverge Areas .................................................................................................................................................................... Level-of-Service Criteria....................................................................................................................................................... Prediction of Density......................................................................................................................................................... Prediction of Speed ...........................................................................................................................................................
5-3 5-3 5-4 5-4 5-4 5-4 5-7 5-7 5-8 5-8
iii.
procedures for application ................................................................................................................................................ Single-Lane On- and Off-Ramps .......................................................................................................................................... Special Applications .............................................................................................................................................................. Two-Lane On-Ramps ........................................................................................................................................................ Two-Lane Off-Ramps........................................................................................................................................................ Lane Additions and Lane Drops....................................................................................................................................... Effects of Ramp Control ................................................................................................................................................... Ramps on 10-Lane Freeway Sections (5 Lanes in Each Direction) ............................................................................... Left-Hand Ramps .............................................................................................................................................................. Effects of Ramp Geometry ............................................................................................................................................... Major Merge Sites............................................................................................................................................................. Major Diverge Sites .......................................................................................................................................................... Capacity of Ramp Roadways................................................................................................................................................
5-9 5-9 5-9 5-9 5-11 5-11 5-12 5-12 5-12 5-12 5-12 5-13 5-14
iv.
sample calculations ............................................................................................................................................................ Calculation 1: Isolated On-Ramp.......................................................................................................................................... Calculation 2: Consecutive Off-Ramps on Six-Lane Freeway............................................................................................ Calculation 3: On-Ramp–Off-Ramp Pair on Eight-Lane Freeway...................................................................................... Calculation 4: Two-Lane On-Ramp...................................................................................................................................... Calculation 5: Off-Ramp on 10-Lane Freeway.................................................................................................................... Calculation 6: Left-Side On-Ramp .......................................................................................................................................
5-14 5-14 5-16 5-19 5-23 5-23 5-24
v.
references .............................................................................................................................................................................. 5-27
I. INTRODUCTION A ramp may be described as a length of roadway providing an exclusive connection between two highway facilities. Analysis of ramp-freeway junctions is the focus of this chapter, and some material on ramp roadways is provided. Ramp-freeway junction analysis procedures presented herein may be applied to approxi-
mately analyze ramp junctions on nonfreeway facilities, such as expressways, multilane highways, and two-lane highways, provided that the junctions involve merging or diverging movements not controlled by traffic signals or stop or yield signs. For rampstreet junctions controlled by such devices, the procedures of 5-1
Updated December 1997
5-2
freeways
Chapter 9, Signalized Intersections, or Chapter 10, Unsignalized Intersections, should be applied.
RAMP COMPONENTS
A ramp may consist of up to three geometric elements of interest: 1. The ramp-freeway junction, 2. The ramp roadway, and 3. The ramp-street junction. A ramp-freeway junction is generally designed to permit highspeed merging or diverging to take place with a minimum of disruption to the adjacent freeway traffic stream. The geometric characteristics of ramp-freeway junctions vary. Elements such as the length and type (taper, parallel) of acceleration or deceleration lane, free-flow speed of the ramp in the immediate vicinity of the junction, and sight distances may all influence ramp operations. The procedures in this chapter are primarily applicable to hightype designs. Nevertheless, some of the models used account explicitly for the effect of acceleration or deceleration lane length and the free-flow speed of the ramp and can therefore be applied to a range of geometric designs, including some that might be considered substandard. Geometric design standards for ramps and ramp junctions are given by AASHTO (1). Geometric characteristics of ramp roadways also vary from location to location. Ramps may vary in terms of number of lanes (usually one or two), design speed, grade, and horizontal curvature. The design of a ramp roadway is seldom a source of operational difficulty unless a traffic incident causes disruption along its length. Ramp-street terminal problems can cause queueing along the length of a ramp, but this queueing is generally not related to the design of the ramp roadway. Freeway-to-freeway ramps have two ramp-freeway terminals and do not have a ramp-street terminal. Many ramps, however, connect limited-access facilities to local arterials and collectors. For such ramps, the ramp-street terminal is often a critical element in the overall design. Ramp-street junctions can permit uncontrolled merging and diverging movements or take the form of an at-grade intersection. Procedures in this chapter allow for the identification of likely breakdowns at ramp-freeway terminals [Level-of-Service (LOS) F] and for the analysis of operations at ramp-freeway junctions and on ramp roadways at LOS A through E. For analysis of rampstreet junctions involving an at-grade intersection, consult Chapter 9, Signalized Intersections, or Chapter 10, Unsignalized Intersections. Sections addressing special applications, including metered ramps, ramps on five-lane (one-direction) freeway sections, twolane ramps, major merge areas, and major diverge areas, are contained in this chapter.
upstream freeway demand is a composite of upstream trip generation patterns from a variety of sources. In the merge area, individual on-ramp vehicles attempt to find gaps in the traffic stream of the adjacent freeway lane. Since most ramps are on the right side of the freeway, the freeway lane in which on-ramp vehicles seek gaps is the shoulder lane, designated herein as Lane 1. In this chapter, lanes are numbered 1 to N from the shoulder to the median. The action of individual merging vehicles entering the Lane 1 traffic stream creates turbulence in the traffic stream in the vicinity of the ramp. Approaching freeway vehicles move toward the left to avoid this turbulence. Recent studies (2) have shown that the operational effect of merging vehicles is heaviest in freeway Lanes 1 and 2 and the acceleration lane for a distance extending from the physical merge point to 1,500 ft downstream. Figure 5-1 shows the ‘‘influence area’’ for on-ramp junctions. Models presented in this chapter focus on operational characteristics within this defined influence area. Interactions are dynamic. Approaching freeway vehicles will move left as long as there is capacity to do so. Whereas the intensity of ramp flow generally influences the behavior of freeway vehicles, general freeway congestion can also limit ramp flow, causing diversion to other interchanges or routes. At off-ramps the basic maneuver is a diverge, that is, a single traffic stream separating into two separate streams. Exiting vehicles must occupy the lane adjacent to the off-ramp, Lane 1 for a right-hand off-ramp. Thus, as the off-ramp is approached, exiting vehicles move right. This movement brings about a redistribution of other freeway vehicles, which move left to avoid the turbulence of the immediate diverge area. Again, recent studies (2) show that the area of most intense turbulence is the deceleration lane plus Lanes 1 and 2 over 1,500 ft extending upstream from the physical diverge point (Figure 5-1). Procedures in this chapter treat both ramp and freeway flow rates as inputs to an operational analysis of the merge or diverge influence area. Thus, design and planning applications become trial-and-error computations using the operational analysis techniques as specified. This procedure is logical, because the ramp is a point location on an overall facility for which flows are either known or specified. The procedures in this chapter assume that the behavior of merging or diverging vehicles is unaffected by downstream or upstream constrictions or disruptions. Downstream problems, for example, can easily propagate upstream through a merge or diverge area. In such cases operations reflect the characteristics of the downstream
OPERATIONAL CHARACTERISTICS
A ramp-freeway junction is an area of competing traffic demands for space. Upstream freeway traffic competes for space with entering on-ramp vehicles in merge areas. On-ramp demand is usually generated locally, although arterials and collectors may bring some drivers to the ramp from more distant origins. The Updated December 1997
Figure 5-1. On- and off-ramp influence areas.
ramps and ramp junctions breakdown and would not be expected to conform to the models presented herein. LENGTH OF ACCELERATION AND DECELERATION LANES
A critical geometric parameter influencing operations at a merge or diverge area is the length of the acceleration (LA) or
5-3
deceleration (LD) lane. The length of such lanes is measured from the point at which the left edge of the ramp lanes and the right edge of the freeway lanes converge to the end of the taper segment connecting the ramp to the freeway. The point of convergence is typically defined by painted markings or physical barriers, or both.
II. METHODOLOGY As shown in Figure 5-1, the basic approach to the modeling of merge and diverge areas focuses on an influence area of 1,500 ft including the acceleration or deceleration lane and Lanes 1 and 2 of the freeway. The methodology has three major steps: 1. The flow entering Lanes 1 and 2 immediately upstream of the merge influence area or the beginning of the deceleration lane at an off-ramp is determined. This flow is designated V12. It must be known, because it is a major determinant of operating characteristics within the ramp influence area. 2. Critical capacity values are determined, and demand flows are compared with these values. The comparison determines whether the merge or diverge area is likely to break down. Capacity is evaluated at two points: (a) the maximum total flow departing from the merge or diverge area (VFO for on-ramps; VFO + VR for off-ramps) and (b) the maximum total flow that can reasonably enter the merge or diverge influence area (VR12 for on-ramps; V12 for off-ramps). If demand exceeds either of these two capacity values, breakdown is likely. 3. The density within the merge or diverge influence area (DR) and the level of service based on this value are determined. For some situations, the average speed of vehicles within the merge or diverge area (SR) may also be predicted. Figure 5-2 shows these key variables and their relationship to each other. All aspects of the model and LOS criteria are expressed in equivalent maximum flow rates in passenger cars per hour for the peak 15 min of the hour of interest. Therefore, before any of these procedures are applied, all relevant freeway and ramp flows
Figure 5-2. Critical ramp junction values.
must be converted to equivalent passenger cars per hour under ideal conditions for the peak 15 min of the hour of interest. Equation 51 is used to convert any hourly flow rate in vehicles per hour to the desired format: Vpcph =
Vveh/hr
(5-1)
PHF fHV fp
where Vpcph = maximum 15-min flow rate in passenger cars per hour (pcph) under ideal conditions, Vveh/hr = hourly volume in vehicles per hour (veh/hr) under prevailing conditions, PHF = peak-hour factor, fHV = adjustment factor for heavy vehicles, and fp = adjustment factor for driver population. The following sections detail the three steps of the ramp-freeway junction operational model. PREDICTION OF FLOW ENTERING LANES 1 AND 2 (V12)
Studies have shown that the principal influences on lane distribution of freeway vehicles immediately upstream of merge or diverge areas are the following: T VF, total freeway flow approaching the merge or diverge area (pcph); T VR, total ramp flow (pcph); T LA or LD, total length of the acceleration or deceleration lane (ft); and T SFR, free-flow speed of ramp at point of merge or diverge (mph). Of these, total freeway flow is easily the dominant factor. Models are structured to account for this phenomenon without distorting other relationships. Total ramp flow plays a major role in lane distribution immediately upstream of off-ramps, because all of the ramp traffic must be in Lane 1 to access the ramp. For on-ramps, this parameter has surprisingly little influence on flow entering Lanes 1 and 2. The length of the acceleration or deceleration lane also influences lane distribution. In merge areas, longer acceleration lanes contribute to lower turbulence levels and lower densities in the merge influence area. Thus, approaching freeway vehicles are less likely to move left to avoid the turbulence, and V12 tends to increase. The influence of deceleration lane length is less pronounced Updated December 1997
freeways
5-4
in diverge areas. Higher ramp free-flow speeds tend to push drivers further left to avoid high-speed merging or diverging. Lane distribution at a given ramp may also be influenced by flows on adjacent upstream and downstream ramps. When nearby ramps inject vehicles into or remove them from Lane 1, the lane distribution of total vehicles may be seriously altered. Several variables are critical: T T T T
VU, total flow on an upstream adjacent ramp (pcph), VD, total flow on a downstream adjacent ramp (pcph), DU, distance to the adjacent upstream ramp (ft), and DD, distance to the adjacent downstream ramp (ft).
Whether upstream or downstream adjacent ramps have a significant influence on lane distribution depends on the size of the freeway, the specific combination of upstream or downstream ramp (or both), and the distances and flows involved. General Model Structure
The model form for prediction of V12 immediately upstream of single-lane, right-hand on-ramps is V12 = VF × PFM
(5-2)
where PFM is the proportion of freeway vehicles remaining in Lanes 1 and 2 immediately upstream of an on-ramp and V12 and VF are as previously defined. This form allows the model to retain the importance of total freeway flow in determining flow in Lanes 1 and 2, and PFM expresses the behavioral choices of drivers selecting lanes. In essence, the model focuses on predicting the proportion of vehicles in Lanes 1 and 2 and applies this to the freeway flow, which is known or designated. The model for single-lane, right-hand off-ramps must take a different form. V12 for off-ramps is defined immediately upstream of the beginning of the deceleration lane. Thus, V12 must include VR, the off-ramp flow. The real issue is the proportion of through vehicles remaining in Lanes 1 and 2 at this point. A model expressing this logic is V12 = VR + (VF − VR)PFD
(5-3)
This model focuses on predicting the choice to be made by approaching freeway drivers not exiting at the ramp (i.e., drivers with a choice to make). Specific Models
The methodology is based on the results of a National Cooperative Highway Research Program study (2) in which equations for PFM and PFD were calibrated for different possible configurations, including width of freeway and upstream and downstream ramp configurations. The data base for the study included 58 sites from seven regions of the United States, each studied for 2 to 4 hr. Figures 5-3 and 5-4 provide an index to predictive models for V12. Figure 5-3 shows the models used in conjunction with singlelane right-hand on-ramps and provides a matrix for determining which model applies for a given configuration. Figure 5-4 provides similar information for single-lane right-hand off-ramps. Prediction of V12 for four-lane freeways is trivial, since Lanes 1 and 2 compose the entire freeway in a given direction. Drivers Updated December 1997
must traverse the ramp influence area, because there are no lanes that avoid it. The form of each equation in Figures 5-3 and 5-4 is indicative of causal interactions among operational and geometric variables in merge and diverge areas. Equation 2 (Figure 5-3), the general equation for six-lane freeways covering single-lane on-ramps, is quite simple. It suggests that the only variable affecting the proportion of flow remaining in Lanes 1 and 2 immediately upstream of the merge is the length of the acceleration lane. By reducing merge turbulence, a longer acceleration lane allows more freeway vehicles to remain in Lanes 1 and 2. Equations 3 and 4 (Figure 5-3) deal with merging on six-lane freeways but take into account the effect of upstream adjacent offramps and downstream adjacent off-ramps on the subject ramp. These equations should be used only when all variables fall within the limits shown in Figure 5-3. When input variables fall outside these limits, the general equation for six-lane freeways, Equation 2, should be applied. The general equation is also applied where upstream or downstream adjacent on-ramps exist; there is no recent evidence that they affect behavior at the on-ramp in question. Equation 5 (Figure 5-3) is used for all single-lane right-hand onramps on eight-lane freeways. No separate equations are applied to account for upstream and downstream adjacent ramp effects. Equation 5 indicates that higher ramp flows have a negative impact on V12, whereas the proportion of traffic remaining in Lanes 1 and 2 increases with increasing length of acceleration lane (as in the case of six-lane freeways) and decreasing free-flow speed of the ramp. The latter suggests that ramp vehicles entering the freeway at higher speeds cause more approaching freeway vehicles to move out of Lanes 1 and 2. Equation 7 (Figure 5-4) is the general diverge equation for sixlane freeways. Equation 8 applies to six-lane freeway off-ramps where an upstream adjacent on-ramp is present, whereas Equation 9 is used where a downstream adjacent off-ramp is present. These equations should be used only when all variables fall within the ranges indicated in Figure 5-4. When they do not, the general Equation 7 should be used. Equation 7 is also used for six-lane freeway off-ramps where upstream adjacent off-ramps or downstream adjacent on-ramps exist. They do not have any significant influence on off-ramp behavior. Equation 10 is used for all single-lane right-hand off-ramps on eight-lane freeways. It suggests that the proportion of nonexiting traffic remaining in Lanes 1 and 2 is a constant. Thus, V12 is influenced only by VF and VR, which are part of the general model used. CAPACITY VALUES
Merge Areas
The capacity of merge areas is controlled by either of the following two criteria: (a) the total flow leaving the merge area on the downstream freeway (VFO) and (b) the maximum flow entering the merge influence area (VR12). The total flow leaving the merge area is subject to the constraints of the downstream freeway section. There is no evidence that the turbulence of the merge area causes the downstream freeway capacity to be less than that of a basic freeway segment. Thus, for stable flow operations to exist, the sum of the merging flows cannot exceed the capacity of the downstream freeway segment.
ramps and ramp junctions
5-5
Figure 5-3. Models for predicting V12 for on-ramps.
Updated December 1997
5-6
freeways
Figure 5-4. Models for predicting V12 for off-ramps.
Updated December 1997
ramps and ramp junctions
5-7
Table 5-1. Capacity Values for Merge and Diverge Areas
freeway free-flow speed (mph) 70 65 60 55
2
3
4
>4
max flow entering merge influence area (VR12) (pcph)
4,800 4,700 4,600 4,500
7,200 7,050 6,900 6,750
9,600 9,400 9,200 9,000
2,400/ln 2,350/ln 2,300/ln 2,250/ln
4,600 4,600 4,600 4,600
maximum upstream (VF) or downstream (VFO) freeway flow (pcph) by no. of lanes in one direction
max flow entering diverge influence area (V12) (pcph) 4,400 4,400 4,400 4,400
NOTE: For capacity of ramp roadways, see Table 5-6.
It is possible, however, to experience congestion in the merge influence area even if the capacity of the downstream freeway segment is adequate. Studies (2) have shown that there is a practical maximum flow that may enter the merge influence area and still maintain stable operations. In a ramp merge junction, both the flow in Lanes 1 and 2 and the flow in the on-ramp enter the merge influence area. Thus,
ramp-street junction should also be checked using the procedures for signalized intersections (Chapter 9) or those for unsignalized intersections (Chapter 10) to ensure that queues will not form and spread upstream on the ramp, affecting traffic operations on the diverge area. LEVEL-OF-SERVICE CRITERIA
VR12 = VR + V12 Table 5-1 shows capacity values for the downstream freeway flow (VFO) and the merge influence area (VR12). If the demand expected at either point exceeds the capacity values shown, failure, or LOS F, is expected to exist. When this is the case, the analysis ends, and solutions are sought to alleviate the problem. Where stable operations are expected (i.e., demand does not exceed capacity at either point), the next step of the analysis—estimation of density in the merge influence area—is implemented to find the level of service. Diverge Areas
Three capacity values should be checked in a diverge area: (a) the total flow that may leave the diverge area, (b) the maximum flow that may enter Lanes 1 and 2 immediately before the deceleration lane, and (c) the capacity of each of the exiting legs of the freeway. The total flow that can leave the diverge area is generally limited by the capacity of the freeway lanes approaching the diverge junction. In all appropriate diverge designs, the number of lanes leaving the diverge area is either equal to or one greater than the number entering. This departing flow is designated VFO. The flow entering Lanes 1 and 2 just upstream of the deceleration lane is simply the flow in Lanes 1 and 2 (V12). This flow includes the off-ramp flow. Table 5-1 gives capacity values for the first two capacity checks. The third limit is most important because it is the primary reason for failure of diverge areas. Failure at a diverge is most often related to the capacity of one of the exit legs, usually the ramp. The capacity of each exit leg must be checked against the expected demand. For a downstream freeway leg (at a major diverge area there may be two), capacity values may be drawn from Table 5-1 for the appropriate number of freeway lanes. The capacity of ramp roadways is discussed later in the chapter. The failure of any of these capacity checks, that is, an expected demand that exceeds the capacities given, indicates that the merge area will fail. In such cases, breakdown and formation of queues are expected to occur. Where an off-ramp terminates at an at-grade intersection (either signalized or unsignalized), the capacity of the
LOS A through E for ramp-freeway terminals are based on the density in the influence area of the ramp and the expectation that no breakdown will occur. LOS F signifies that a breakdown condition exists or is expected to exist. LOS F occurs whenever demand exceeds the limits indicated in Table 5-1. When none of these limits is exceeded, no breakdown is expected, and the level of service is based on density, as indicated in Table 5-2. Table 5-2 also gives average speed of vehicles in the ramp influence area as a secondary LOS parameter. This is particularly useful in comparing these criteria with field data, since density is rarely measured directly. The density values shown for LOS A through E assume stable, nonbreakdown operations. Studies (2) have shown that there is an overlap in the density range such that some breakdown operations may actually have lower densities than those achieved under stable operation. This is due to the wavelike movement of vehicles in a queue and the rather short length of the defined ramp influence area. The model first calls for determination of whether LOS F exists using the maximum flow levels of Table 5-1. Then density is estimated and the level of service assigned if flow is stable. Except for LOS A, each of the density boundaries is higher than that of a similar basic freeway section (Chapter 3). This is because (a) drivers expect increased turbulence and greater proximity of other vehicles in a merge or diverge area and (b) drivers are generally traveling at somewhat lower speeds at any given per-lane flow rate in the merge or diverge area than on open freeway.
Table 5-2. Level-of-Service Criteria for Ramp-Freeway Junction Areas of Influence level of service A B C D E F a
maximum density (primary measure) (pc/mi/ln)
minimum speed (secondary measure) (mph)
10 20 28 35 >35
58 56 52 46 42
a
a
Demand flows exceed limits of Table 5-1.
Updated December 1997
freeways
5-8
LOS A represents unrestricted operations. Density is low enough to permit merging and diverging maneuvers without disruption to through vehicles. There is virtually no noticeable turbulence in the ramp influence area, and speeds remain close to the expected basic freeway section level. At LOS B, merging and diverging maneuvers become noticeable to through drivers, and minimal levels of turbulence exist. Merging drivers must adjust their speeds to smoothly fill available gaps, as do diverging drivers making lane changes within the ramp influence area. Speeds of vehicles in the influence area begin to decline slightly. At LOS C, average speed within the ramp influence area begins to decline as the level of merging or diverging turbulence becomes noticeable. Both freeway and on-ramp vehicles begin to adjust their speeds to accommodate smooth merging maneuvers. In diverge areas, vehicles begin to slow to allow lane-changing as offramp vehicles approach the diverge. Driving conditions are still relatively comfortable at this level. At LOS D, turbulence levels become intrusive, and virtually all vehicles slow to accommodate merging or diverging maneuvers. Some ramp queues may form at heavily used on-ramps, but freeway operation remains stable. LOS E represents conditions approaching and reaching capacity operation. Speeds reduce to the low 40s (mph), and the turbulence of merging and diverging maneuvers becomes intrusive to all drivers in the influence area. Flow levels approach capacity limits, and small changes in demand or disruptions within the traffic stream can cause both ramp and freeway queues to begin forming. LOS F represents breakdown, or unstable, operation. At this level, approaching demand flows exceed the discharge capacity of the downstream freeway (and ramp, in the case of diverge areas). Queues are visibly formed on the freeway and on-ramps and continue to grow as long as approaching demand exceeds the discharge capacity of the section. Freeway queues are not the same as intersection or other stopped queues. Consult Chapter 3 for a more complete description. Prediction of Density
Table 5-3 gives models for prediction of density in merge or diverge influence areas. Independent variables include flows entering the influence area and length of acceleration or deceleration lane. Such lanes have an important effect on density, because they
Table 5-3. Models for Prediction of Density in Ramp Influence Areas item
equation or value Single-Lane On-Ramp Merge Area
Model R2 Std. error (pc/mi/ln) Data periods (no.)
DR = 5.475 + 0.00734VR + 0.0078V12 − 0.00627LA 0.88 2.68 167
Single-Lane Off-Ramp Diverge Areas Model R2 Std. error (pc/mi/ln) Data periods (no.) Updated December 1997
DR = 4.252 + 0.0086V12 − 0.009LD 0.93 1.75 86
Table 5-4. Models for Prediction of Speed in Ramp Influence Areas item
equation or value Single-Lane On-Ramps, Stable Flow
Model
SR = SFF − (SFF − 42) MS
2
R SE (mph) Data periods (no.)
1
LASFR MS = 0.321 + 0.0039 e(VR12 /1,000) − 0.002 1,000 0.60 2.20 132
2
Single-Lane Off-Ramps, Stable Flow Model R2 SE (mph) Data periods (no.)
SR = SFF − (SFF − 42) DS DS = 0.883 + 0.00009 VR − 0.013 SFR 0.44 2.46 73
provide additional lane length over which to disperse the total flow in the influence area. The density models of Table 5-3 apply only to cases where no breakdown is occurring or is expected to occur on the basis of demand flows. Thus, all densities predicted by these models are, by definition, in the range of LOS A through E. No models are available for directly predicting the density of a ramp influence area operating under LOS F. Values of VR, LA, and LD are known inputs. Values of V12 are predicted using the models of Figures 5-3 and 5-4, as previously discussed. Prediction of Speed
Where desired, models are also available for the prediction of average travel speed (space mean speed) within the ramp influence area. This may be useful information, but it should not be used as a primary measure of level of service unless density is unavailable. It is not necessary to estimate the speed of vehicles traversing the ramp influence area to use this methodology. As in the case of density models, reliable speed predictors are not available for unstable flow conditions. Table 5-4 gives models for the prediction of average speed of vehicles within the ramp influence area defined in this chapter. Speed models are obviously approximate. The R2 values do not indicate strong correlations, but the standard errors (SEs) are reasonable enough for rough estimates of speed. Predicted speeds from these equations should never be used to establish level of service, because the SEs are larger than some of the LOS speed ranges. The equations are all based on the concept of maximum and minimum speeds under stable and unstable operation. For stable flow, the maximum speed is the free-flow speed of the freeway (SFF). Because 42 mph has been found to be the dividing line between stable and unstable flow, it becomes the minimum speed in stable flow models. M and D are merging and diverging intensity factors used to scale the drop from maximum to minimum speed. No unstable flow model is presented, but the practical range of speeds under LOS F is from a minimum of 10 to 12 mph to a maximum of 42 mph.
ramps and ramp junctions
5-9
III. PROCEDURES FOR APPLICATION SINGLE-LANE ON- AND OFF-RAMPS
Models for the analysis of single-lane on- and off-ramp terminals on freeways were presented and discussed in the previous section. This section provides simple step-by-step procedures for their application. Figure 5-5 shows a worksheet on which the results of such an analysis may be summarized. As noted, all ramp computations are done in the operational analysis mode—that is, the geometry and all demand volumes are specified. The operational analysis determines the likely density in the ramp influence area and therefore the expected level of service for the operation specified. Design alternatives are analyzed through trial-and-error application of this process. Various designs may be proposed and operational analysis performed to determine the expected level of service that would result. Step 1: Specify geometry and demand volumes. To conduct an operational analysis, both the geometry and demand volumes must be fully specified. A sketch of the geometry of the ramp under analysis is entered into the upper portion of the worksheet of Figure 5-5. It should show all lanes and their configuration, lane widths, the ramp volume (VR) in vehicles per hour, and the upstream approaching freeway volume (VF) in vehicles per hour. Where upstream adjacent or downstream adjacent ramp information is available, it is entered in the areas to the left and right of the sketch on the worksheet. Step 2: Convert all demand volumes to flow rates (in passenger cars per hour) under ideal conditions. All demand volumes specified in mixed vehicles per hour for the full hour under consideration must be converted to flow rates (for the peak 15 min of the hour) in passenger cars per hour under equivalent ideal conditions. This is done according to Equation 5-1: Vpcph =
Vveh/hr PHF fHV fp
The following volumes must be converted in this way: VF, VR, VU, and VD. The peak-hour factor, PHF, is specified on the basis of local demand characteristics. The two adjustment factors are found using the methods specified in Chapter 3, Basic Freeway Sections. Step 3: Estimate V12. The flow rate of freeway vehicles remaining in Lanes 1 and 2 immediately upstream of the merge point or beginning of the deceleration lane is critical. The appropriate model is selected from Figure 5-3 (merge areas) or 5-4 (diverge areas) and applied. All input flow rates used in these equations must be converted to passenger cars per hour under ideal conditions (i.e., they are taken from the ‘‘conversion’’ section of the worksheet). The results of this computation are entered into the third section of the worksheet as shown. The appropriate equation number (from Figure 5-3 or 5-4) is also shown so that it may be checked later. Where a configuration may be covered by more than one equation, such as when both an upstream and a downstream adjacent ramp fall within the appropriate ranges for application, both computations should be made. The higher resulting value of V12 should be used. Equations dealing with the effects of upstream or downstream adjacent ramps are used only when all variables fall within the
calibration ranges indicated in Figures 5-3 and 5-4. For all other cases, the general equations for the size of freeway under consideration are used, regardless of whether all variables are within the calibration ranges of these equations. Some caution should be exercised when the general equations are used outside their calibration ranges. The accuracy of predictions outside these ranges cannot be statistically assessed. Nevertheless, given no alternative models, they must be used. The user should, however, check the reasonableness of the results. Step 4: Find checkpoint flow rates. Once the value of V12 is estimated, it can be combined with known values of VF and VR to find the checkpoint flow rates needed to compare with the capacity values of Table 5-1. For merge areas, VFO = VF + VR VR12 = VR + V12 For diverge areas, four checkpoints are needed. The limit on total flow is the capacity of the approaching freeway (VF). Other checkpoints include the expected demand at the diverge influence area (V12 ) and the capacity of each exit leg of the diverge (i.e., VFO, VR). Checkpoint flow rates are compared with the capacity values of Table 5-1. If existing or expected flows exceed these capacities, LOS F is indicated, and a Y is noted in the appropriate cell. If existing or expected flows do not exceed these capacities, stable flow in the range LOS A through E is expected, and an N is entered in the ‘‘LOS F?’’ cell. Step 5: Determine level of service. If Step 4 has already resulted in a determination of LOS F, this step is eliminated. If Step 4 has determined that the level of service is in the range A through E, the expected density in the ramp influence area is computed using the equations of Table 5-3, which are shown on the worksheet. These equations are valid only when the level of service is in the A through E range. Input flow rates must be in passenger cars per hour under ideal conditions. An LOS determination is made by comparing the resultant density with the criteria in Table 5-2. For additional information, the average speed in the ramp influence area may be roughly approximated using the equations in Table 5-4.
SPECIAL APPLICATIONS
The procedures outlined in the previous section apply to standard one-lane, right-hand on- and off-ramp freeway terminals. There are a number of special situations requiring modifications of the basic procedure. Each is discussed in the following subsections.
Two-Lane On-Ramps
Figure 5-6 shows a typical two-lane freeway on-ramp. It is characterized by two separate acceleration lanes, each successively forcing merging maneuvers to the left. Whereas the general intent of such ramps is to allow higher ramp flows to merge more smoothly into the traffic stream, studies (2) have not clearly demUpdated December 1997
5-10
freeways
Figure 5-5. Worksheet for the analysis of ramp-freeway terminals. Updated December 1997
ramps and ramp junctions onstrated whether two-lane on-ramps can effectively serve higher on-ramp flow rates than similar one-lane ramps. Two-lane on-ramps entail two modifications of the basic methodology: (a) the flow remaining in Lanes 1 and 2 immediately upstream of the on-ramp is generally somewhat higher than that for one-lane on-ramps in similar situations, and (b) densities in the merge area are lower than in similar one-lane on-ramp situations. The latter modification is primarily due to the existence of two acceleration lanes and the generally longer distance over which the two acceleration lanes extend. The effectiveness of two-lane on-ramps, then, is that higher ramp flows are handled more smoothly and at better levels of service than if the same flows were carried on a one-lane ramp with a conventional merge design. In computing V12 for two-lane on-ramps, the standard expression is used:
5-11
Figure 5-7. Common geometries for two-lane off-ramps.
V12 = VF (PFM) However, the formula for PFM given in Figure 5-3 is replaced by the following: T For four-lane freeways, PFM = 1.0000. T For six-lane freeways, PFM = 0.5550. T For eight-lane freeways, PFM = 0.2093.
V12 = VR + (VF − VR)PFD However, PFD is not found from the equations in Figure 5-4. It is determined as follows:
In computing the expected density in the ramp influence area, the standard equation of Table 5-3 is applied, except that the length of the acceleration lane, LA, is replaced by the effective length of the acceleration lane, LAeff, as follows; LAeff = 2LA1 + LA2
In computing V12, the general equation for diverge areas is used:
(5-4)
where LA1 and LA2 are as defined in Figure 5-6. The capacity values governing maximum flow rates for VFO and VR12 are not affected by the use of a two-lane on-ramp. The capacity of the downstream freeway section continues to control the total output capacity of the merge, and the number of vehicles that may enter the influence area on Lanes 1 and 2 of the freeway is not enhanced by the existence of a two-lane on-ramp. The capacity values of Table 5-1 apply unchanged. Two-Lane Off-Ramps
Two-lane off-ramps have two general types of geometry, as shown in Figure 5-7. In the first, two deceleration lanes are successively introduced. In the second, only a single deceleration lane is used, with drivers in Lane 1 of the freeway permitted to directly access the second lane of the ramp without a deceleration lane. As in the case of two-lane on-ramps, the existence of a twolane off-ramp influences the flow rate in Lanes 1 and 2, and the resulting density in the influence area is reduced if the geometry shown in Figure 5-7(a) is used.
T For four-lane freeways, PFD = 1.000. T For six-lane freeways, PFD = 0.450. T For eight-lane freeways, PFD = 0.260. In estimating the density in the ramp influence area, the standard equation of Table 5-3 is still applied. Where the geometry is of the type shown in Figure 5-7(a), the length of the deceleration lane, LD, is replaced by the effective length of the deceleration lane, LDeff, as follows: LDeff = 2LD1 + LD2
(5-5)
Where the geometry is of the type shown in Figure 5-7(b), the standard density equation is applied without modification. As in the case of two-lane on-ramps, the basic capacity limitations for two-lane off-ramps are not different from those of one-lane off-ramps. The control on total output (VFO + VR) is the capacity of the upstream basic freeway section, since this capacity limits the total flow that can be delivered to the diverge. No evidence suggests that the maximum value of V12 is affected by whether the off-ramp has one or two lanes. Thus, the capacity values of Table 5-1 are applied without modification. Whereas the total flow that can be discharged through a twolane off-ramp section is not different from that of a one-lane offramp, the distribution of the discharge flow between freeway and ramp is most certainly affected. A two-lane off-ramp can handle significantly greater ramp flows than a one-lane off-ramp. Assuming that there is no more stringent limitation at the other ramp terminus, a two-lane off-ramp can accommodate flows of up to 4,000 pcph. One-lane off-ramps have a significantly lower capacity, as is detailed in a later section. One-lane off-ramps most often fail because of insufficient ramp capacity, not because of any factor related to the diverge area itself. Lane Additions and Lane Drops
Figure 5-6. Typical two-lane on-ramp.
Sometimes on-ramps are associated with lane additions and offramps with lane drops. Where a single-lane ramp results in a lane Updated December 1997
freeways
5-12
addition or deletion, the capacity of the ramp is governed by its geometry, as indicated in Table 5-6 in a later section of this chapter. Where a two-lane ramp results in a lane addition or deletion, the section should usually be treated as a major merge or diverge according to procedures described later.
Effects of Ramp Control
For the purposes of this chapter, procedures are not modified in any way to account for the local effect of ramp control, except for the limitation the ramp meter may have on VR.
Ramps on 10-Lane Freeway Sections (5 Lanes in Each Direction)
Although they are not common, sections of 10-lane freeway do exist in parts of the United States, and procedures must be developed for handling the right-hand on- and off-ramps that may be placed on such sections. The general approach is a simple one: the flow rate in Lane 5 of the freeway (V5) is estimated and deducted from the total approaching freeway flow. This becomes the effective approaching freeway flow (VFeff) for an equivalent eightlane freeway section. The analysis proceeds using the standard procedures for eight-lane freeways. VFeff = VF − V5
(5-6)
where V5 is estimated using the criteria of Table 5-5. Values for V5 in advance of on-ramps are taken from a recent study (2). Values estimated in advance of off-ramps are taken from a 1974 report (3). The values may appear somewhat incongruous in that Lane 5 flows are predicted to be heavier in advance of onramps than off-ramps. Whereas this is partially due to the time difference between the two studies, off-ramp values reflect the fact that none of the off-ramp flow will be in Lane 5, which will lower the expected proportion of total approaching freeway flow in Lane 5. Off-ramp values are, however, somewhat more conservative, particularly at freeway flows under 4,000 pcph, where no Lane 5 flow is anticipated.
Table 5-5. Determination of V5 for Right-Hand Ramps on 10-Lane Freeways total freeway flow, VF (pcph)
flow in lane 5, V5 (pcph)
Left-Hand Ramps
Although not normally recommended, left-hand ramps do exist on some freeways and occur frequently on collector-distributor roadways. When this happens, the ramp influence area covers the same length as that for right-hand ramps but now encompasses the two left lanes plus an acceleration or deceleration lane. Whereas for right-hand ramps a critical computation is the estimation of V12, for left-hand ramps the two left lanes are of interest. For a four-lane freeway, this remains V12 and there is no difficulty. For a six-lane freeway, the entering flow of interest is V23, and for an eight-lane freeway it is V34. Although no direct method is available for the analysis of left-hand ramps, some rational modifications can be applied to right-hand ramp methodologies to produce reasonable results. The following procedure is suggested: compute V12 using standard procedures for right-hand ramps. Then T T T T T
For left-hand ramps on four-lane freeways, V12 = V12. For left-hand on-ramps on six-lane freeways, V23 = 1.12V12. For left-hand off-ramps on six-lane freeways, V23 = 1.05V12. For left-hand on-ramps on eight-lane freeways, V34 = 1.20V12. For left-hand off-ramps on eight-lane freeways, V34 = 1.10V12.
The remaining computations for density or speed (or both) may continue; V12 is replaced with V23 or V34 as appropriate. All capacity values remain unchanged. These procedures have been adapted from Leisch (3) using judgment.
Effects of Ramp Geometry
The procedures in this chapter explicitly consider the effect of the length of the acceleration or deceleration lane and the freeflow speed of the ramp roadway on the performance of rampterminal influence areas. The latter is a surrogate variable that is affected by many related factors, including design speed of various segments of the ramp roadway, relative grades, sight distance, and others. No models are available that explicitly consider each of these factors as an operational variable. Drew (4) demonstrated, using gap acceptance models, that the gap acceptance capacity of an on-ramp vehicle would be reduced by as much as 90 percent when a 2-degree angle of convergence and a 1,200-ft acceleration lane were worsened to 10 degrees and 400 ft, respectively. The user is cautioned that Drew’s use of ‘‘gap acceptance capacity’’ is in no way related to the definition of capacity used in these procedures. More recent studies (2) show that improved geometric details do not influence capacity at all, but rather help create better and smoother merging and diverging operations.
Approaching Right-Hand On-Ramps >8,500 7,500–8,499 6,500–7,499 5,500–6,499 7,000 5,500–7,000 4,000–5,499 50 41-50 31-40 21-30 1 0–1⁄4 1 ⁄4–1⁄3 1 ⁄3–1⁄2 1 ⁄2–3⁄4 3 ⁄4–1 >1 0–1⁄4 1 ⁄4–1⁄3 1 ⁄3–1⁄2 1 ⁄2–3⁄4 3 ⁄4–1 >1
3
4
5
6
ETa 2
4
5
6
8
10
15
20
25
1.5 1.5 1.5 1.5 2.5 4.0 4.5 1.5 3.0 6.0 7.5 8.0 8.5 1.5 5.5 9.5 10.5 11.0 2.0 6.0 9.0 12.5 13.0 13.0 4.5 9.0 12.5 15.0 15.0 15.0
1.5 1.5 1.5 1.5 2.0 3.0 3.5 1.5 2.5 4.0 5.5 6.0 6.0 1.5 4.0 7.0 8.0 8.0 2.0 4.5 7.0 9.0 9.5 9.5 3.5 6.5 9.5 11.0 11.0 11.0
1.5 1.5 1.5 1.5 2.0 3.0 3.0 1.5 2.5 4.0 5.0 5.5 5.5 1.5 4.0 6.5 7.0 7.5 1.5 4.0 6.0 8.5 9.0 9.0 3.0 6.0 8.5 10.0 10.0 10.0
1.5 1.5 1.5 1.5 2.0 3.0 3.0 1.5 2.0 3.5 4.5 5.0 5.0 1.5 3.5 6.0 6.5 7.0 1.5 4.0 6.0 8.0 8.0 8.0 3.0 6.0 8.0 9.5 9.5 9.5
1.5 1.5 1.5 1.5 1.5 2.5 2.5 1.5 2.0 3.5 4.0 4.5 4.5 1.5 3.0 5.5 6.0 6.0 1.5 3.5 5.5 7.0 7.5 7.5 3.0 5.0 7.0 9.0 9.0 9.0
1.5 1.5 1.5 1.5 1.5 2.5 2.5 1.5 2.0 3.0 4.0 4.0 4.5 1.5 3.0 5.0 5.5 6.0 1.5 3.0 5.0 7.0 7.0 7.0 2.5 5.0 6.5 8.0 8.5 8.5
1.5 1.5 1.5 1.5 1.5 2.0 2.0 1.5 2.0 2.5 3.5 4.0 4.0 1.5 3.0 4.5 5.0 5.0 1.5 3.0 4.5 6.0 6.5 6.5 2.5 4.0 6.0 8.0 8.0 8.0
1.5 1.5 1.5 1.5 1.5 2.0 2.0 1.5 1.5 2.5 3.0 3.5 3.5 1.5 2.5 4.0 4.5 5.0 1.5 2.5 4.0 6.0 6.0 6.0 2.0 3.5 6.0 7.5 7.5 7.5
1.5 1.5 1.5 1.5 1.5 2.0 2.0 1.5 1.5 2.0 3.0 3.0 3.0 1.5 2.5 3.5 4.0 4.5 1.5 2.0 3.5 5.0 5.5 5.5 2.0 3.0 5.5 6.5 6.5 6.5
NOTE: If a length of grade falls on a boundary condition, the equivalent from the longer-grade category is used. a Four- or six-lane highways.
Table 7-9. Passenger-Car Equivalents for Recreational Vehicles on Uniform Upgrades grade (%)
length (mi)
percent rvs ≤2 3 4
5
6
All 0–1⁄2 >1⁄2 0–1⁄4 1 ⁄4–1⁄2 >1⁄2 0–1⁄4 1 ⁄4–1⁄2 >1⁄2 0–1⁄4 1 ⁄4–1⁄2 >1⁄2
ERa 2
4
5
6
8
10
15
20
25
1.2 1.2 2.0 1.2 2.5 3.0 2.5 4.0 4.5 4.0 6.0 6.0
1.2 1.2 1.5 1.2 2.5 2.5 2.0 3.0 3.5 3.0 4.0 4.5
1.2 1.2 1.5 1.2 2.0 2.5 2.0 3.0 3.0 2.5 4.0 4.0
1.2 1.2 1.5 1.2 2.0 2.0 2.0 3.0 3.0 2.5 3.5 4.0
1.2 1.2 1.5 1.2 2.0 2.0 1.5 2.5 3.0 2.5 3.0 3.5
1.2 1.2 1.5 1.2 2.0 2.0 1.5 2.5 2.5 2.0 3.0 3.0
1.2 1.2 1.2 1.2 1.5 2.0 1.5 2.0 2.5 2.0 2.5 3.0
1.2 1.2 1.2 1.2 1.5 1.5 1.5 2.0 2.0 2.0 2.5 2.5
1.2 1.2 1.2 1.2 1.5 1.5 1.5 2.0 2.0 1.5 2.0 2.0
NOTE: If a length of grade falls on a boundary condition, the equivalent from the longer-grade category is used. a Four- or six-lane highways.
Updated December 1997
rural and suburban highways
7-14
Table 7-10. Passenger-Car Equivalents for Trucks on Downgrades downgrade (%)
length (mi)
percent trucks 4 ≤4 >4 ≤2 >2
ETa 5
10
15
20
1.5 1.5 2.0 1.5 5.5 1.5 7.5
1.5 1.5 2.0 1.5 4.0 1.5 6.0
1.5 1.5 2.0 1.5 4.0 1.5 5.5
1.5 1.5 1.5 1.5 3.0 1.5 4.5
Four- or six-lane highways.
D = vp /S
(7-5)
where: D = density (pc/mi/ln), vp = service flow rate (pcphpl), and S = average passenger-car travel speed (mph).
Table 7-7. For grades of at least 4 percent and longer than 2 mi, use the specific values shown in Table 7-10. For RVs on downgrades, use the passenger-car equivalents for level terrain given in Table 7-7 in all cases. Computing the Heavy-Vehicle Adjustment Factor
Once values for ET and ER have been determined, the adjustment factor for heavy vehicles may be computed as follows: fHV = 1/[1 + PT (ET − 1) + PR(ER − 1)]
Step 3. Find the point on the horizontal axis corresponding to the appropriate flow rate (vp) in pcphpl. Step 4. Read up to the FFS curve identified in Step 2 and determine the average passenger-car travel speed corresponding to that point. Step 5. Determine the level of service by determining the density region within which the point on the FFS curve falls. These regions are labeled in Figure 7-3. The density can also be computed as
(7-4)
where: fHV = adjustment factor for the presence of heavy vehicles in the traffic stream, ET, ER = passenger-car equivalents for trucks and buses and for RVs, respectively, and PT, PR = proportion of trucks and buses and RVs, respectively, in the traffic stream (expressed as a decimal).
The level of service can then be determined from the density ranges shown in Table 7-1. A graphic example of these steps is given in Figure 7-4 for a multilane highway with a free-flow speed equal to 52 mph and a flow rate equal to 1,700 pcphpl. A free-flow speed curve for 52 mph has been shown with a dashed line; at this speed, capacity is approximately 2,040 pcphpl. Reading up to this curve from a flow rate of 1,700 pcphpl, one finds that the average travel speed is approximately 50 mph and that the highway is operating at LOS D. If the user does not need to know the average travel speed but only the level of service, this can be accomplished by determining from Table 7-1 the MSF for each level of service for the appropriate FFS (or by interpolation between adjacent FFS columns, if necessary) and then the level of service within which the flow rate falls.
SEGMENTING THE ROADWAY VOLUME DISTRIBUTION BY LANE
It is not necessary to know the volume distribution by lane to determine the capacity and level of service of a multilane highway; nevertheless, there may be situations in which this lane distribution would be useful. Field data show that under high-volume conditions (equivalent to LOS D and E), the right lane of a multilane highway is underutilized. For one direction of flow on a four-lane highway, the user can expect 40 percent of the traffic to be moving in the right lane and 60 percent in the left lane. With three lanes in one direction, the user can expect 25 percent of the traffic in the right lane, 37.5 percent in the center lane, and 37.5 percent in the left lane. DETERMINATION OF LEVEL OF SERVICE
The level of service on a multilane highway can be determined directly from Figure 7-3 on the basis of the free-flow speed (FFS) and the service flow rate (vp) in pcphpl. The procedure is as follows: Step 1. Define and segment the highway as appropriate. Step 2. On the basis of the actual free-flow speed on a highway segment, an appropriate speed-flow curve of the same shape as the typical curves in Figure 7-3 is drawn. The curve should intercept the y-axis at the free-flow speed. Updated December 1997
The procedures described in this chapter are best applied to homogeneous sections of roadway where the variables that affect travel speeds are constant. Therefore, it may sometimes be necessary for the analyst to divide a roadway into separate sections for analysis. The following conditions should generally indicate that segmenting of the roadway is necessary: T A change in the basic number of travel lanes along the highway, T A change in the median treatment along the highway, T A change of grade of 2 percent or more or a constant upgrade over 4,000 ft long, T The presence of a traffic signal along the multilane highway, T A significant change in the density of access points within a defined area on the route, T Different speed limits along the highway, and T The presence of a bottleneck condition. Some judgment must be applied when a roadway is segmented for analysis. In general, the minimum length of a study section should be 2,500 ft. Also, the limits of study sections should be no closer than 1⁄4 mi to a signalized intersection. The procedures in this chapter are based on average conditions observed over an extended highway section with generally consistent physical characteristics.
multilane rural and suburban highways
7-15
Figure 7-4. Example of graphic solution using speed-flow curves.
V. PROCEDURES FOR APPLICATION The procedures for capacity analysis of multilane rural and suburban highways are divided into three analysis types: operational, design, and planning.
OPERATIONAL ANALYSIS
For these applications, traffic and geometric conditions must be known for an existing highway or estimated for a future highway. The analysis focuses on the determination of a level of service and on estimates of travel speed and density of the traffic stream along the highway. The typical situations that can be resolved through this type of analysis include the comparison of flow conditions for different volume levels and number of lanes. This type of analysis might also be used to establish the impacts of a change in the number of access points along a given section of multilane highway. Another typical application of an operational analysis might be to develop several alternative packages that would be used to improve the level of service or travel speed along a multilane highway.
Data Requirements
The following information must be available as inputs to the operational analysis procedure: 1. Geometrics—The geometrics of the highway should be specified in detail, including (a) number of lanes, (b) lane widths,
(c) lateral clearances, (d) grades, (e) length of grades, and (f) type of terrain. 2. Volume—The existing traffic volume or the projected future volume must be known in vehicles per hour (vph) for the hour of interest (usually the peak hour). 3. Speed—The existing free-flow speed for passenger cars either measured directly or estimated must be known for the hour of interest. 4. Traffic Characteristics—Detailed traffic characteristics are needed for operational analysis, including (a) the PHF, (b) percent of trucks and buses, and (c) percent of RVs. 5. Roadway Environment—The multilane highway must be classified as either divided or undivided and the total number of access points (driveways plus unsignalized intersections) along each side of the highway should be known.
Segmenting the Roadway
As described in Section IV, Methodology, the analysis procedures are best applied to multilane highway segments of relatively uniform characteristics. Therefore, significant changes in roadway or traffic characteristics require the roadway to be divided into separate segments for analysis. Signalized intersections should be located at least 1⁄4 mi from the segment ends because they can affect speed and volume. Signalized intersections cannot be analyzed using the procedure in this chapter; the procedure contained in Chapter 9 should be used instead. It is inappropriate to classify Updated December 1997
7-16
rural and suburban highways
a long segment at a single level of service when various subsegments are experiencing different levels of service and different operating conditions. Careful division of the roadway into uniform analysis segments will avoid this inadequacy. Computational Steps
The general approach taken in operational analysis for which field-measured speeds are unavailable is to use Equations 7-1 and 7-3 to solve for the free-flow speed (FFS) and the service flow rate (vp). The resulting values are used to find the density and level of service in Figures 7-2 and 7-3 and in Table 7-1. The following computational steps are used. 1. The segment’s free-flow speed is determined by either direct field measurements of passenger-car speeds or by using data from a similar roadway. If the free-flow speed is estimated, Equation 7-1 must be used to convert the ideal free-flow speed to an actual free-flow speed. The adjustments needed can be found in the appropriate tables: FM, median type (Table 7-2) FLW, lane width (Equation 7-2 and Table 7-3) FLC, lateral clearance (Table 7-4) FA, access-point density (Table 7-5 or 7-6) 2. The hourly flow rate in pcphpl is calculated for each direction of flow by using Equation 7-3. The heavy-vehicle adjustment factor is calculated by using Equation 7-4 and Tables 7-7 through 7-10. 3. Figure 7-3 is used to set a speed-flow curve at the appropriate free-flow speed. Then the travel speed and level of service can be determined by reading up from the flow rate (pcphpl). 4. Density is determined by using either Table 7-1 and Figure 7-2 or more accurately by using Equation 7-5. 5. The maximum service flow rate (Mvp), maximum v/c ratio, and maximum density for a given level of service can be determined by using Table 7-1. A worksheet for operational analysis is shown in Figure 7-5. It provides a useful format for the organization and display of computations and can also be used for design applications as described in the following section.
is built into the access-point adjustment. The ability of drivers to change lanes on multilane facilities and the presence of shoulders and turn lanes play a large role in minimizing the delay associated with turning vehicles. On multilane highway segments, in which turning volumes significantly affect traffic flow, either because of poor geometric conditions or unusually high turning movement volumes, a field study should be performed to determine an appropriate speed adjustment attributable to a particular access point or points. However, any adjustments should replace those already in the procedure so as not to double-count the effect of turning movements. Use of posted speed limits to determine free-flow speeds should be undertaken with extreme care. The research on which these analysis procedures are based indicates that speed limits are generally lower than 85th-percentile speeds. Speed limits, which are set unusually low, should not be relied on to determine free-flow speed. It also must be realized that a change in speed limit will not necessarily cause a change in free-flow speeds or level of service. When the analysis of a segment suggests the existence of LOS F conditions, it may be useful to estimate the propagation of queues upstream of the breakdown. A detailed technique for such analysis is included in Chapter 6.
DESIGN ANALYSIS
To use the procedures in this chapter for design, a forecast of future traffic volumes has to be made and the general geometric and traffic control conditions, such as speed limits, must be estimated. With these data and a threshold level of service, an estimate of the number of lanes required for each direction of travel can be made. Another application for design involves identification of the level of service achievable if the design used a minimum number of lanes (rather than increased the lanes to maintain the objective level of service). The design application might also be used in conjunction with Chapter 8 to assess the traffic flow characteristics of a four-lane road compared with a two-lane cross section.
Data Requirements Interpretation of Results
Operational analysis results in an estimate of the operating characteristics of the traffic stream for the road segment under study. The densities and travel speeds estimated on the basis of Figures 7-2 and 7-3 represent average U.S. conditions; local conditions may vary somewhat from these values. The densities drawn from Figure 7-2 are expressed in passenger cars per mile per lane. When field measurements of density are used to determine level of service, data expressed in vehicles per mile per lane must be converted to passenger cars per mile per lane using heavy-vehicle equivalencies before they are compared with the density criteria in Table 7-1. The average travel speeds drawn from Figure 7-3 are based on passenger cars in the traffic stream. Although the effect of turning volumes is not explicitly considered in the analysis procedures, some effect of turning movements Updated December 1997
The design analysis requires less-detailed data than does the operational analysis. Data are required on general geometric conditions, future traffic volumes, and roadway environment. 1. Geometric Conditions: (a) lane width, (b) lateral clearance and median type, (c) type of terrain, (d) grade, and (e) grade length. 2. Volume: (a) directional design-hour volume, (b) traffic composition, and (c) PHF. 3. Roadway Environment: development environment, rural or suburban. The desired or expected level of service is normally input into the design analysis. Many of the preceding adjustments can be controlled in the design process, and the varying geometric or environmental conditions may affect the number of lanes necessary to reach a desired level of service.
7-17
Figure 7-5. Worksheet for operational and design analysis.
multilane rural and suburban highways
Updated December 1997
7-18
rural and suburban highways
Relationship to AASHTO Design Criteria
The LOS values used in the AASHTO Policy on Geometric Design of Highways and Streets (1990) are not directly applicable to this chapter. The AASHTO design criteria for multilane highways may, however, be related to using the following v/c values: 1. Rural design—0.50 (i.e., LOS B, 1,000 pcphpl maximum). 2. Suburban design—0.75 (i.e., LOS C, 1,500 pcphpl maximum).
Segmenting the Roadway
The roadway undergoing design must be separated into uniform segments. Changes in terrain, significant grades, major junctions at which demand volume changes significantly, changes in the development environment, and similar conditions would indicate the need to begin a new segment for design analysis. Along significant grades, the upgrade and downgrade must be considered separately. Computational Steps
The general approach to design analysis involves determination of the number of lanes, N, required to carry the expected traffic volumes at a desired level of service. The following computational steps are used: 1. An ideal free-flow speed is estimated, based on either local conditions or an anticipated speed limit. As stated throughout these procedures, however, care must be exercised when speed limit is used as a basis for free-flow speed estimation. 2. By using Equation 7-1, the actual free-flow speed is determined on the basis of anticipated geometric and environmental conditions. The adjustments necessary are FM, median type (Table 7-2) FLW, lane width (Table 7-3) FLC, lateral clearance (Equation 7-2 and Table 7-4) FA, access-point density (Table 7-5 or 7-6) 3. By using Figure 7-3, the appropriate speed-flow curve is drawn corresponding with the actual free-flow speed. 4. By using Figure 7-3, the service flow rate necessary to reach the desired level of service is determined. This flow rate may be maximum, minimum, or at some midpoint within the LOS range depending on the design goals. 5. By using Equation 7-3, the number of lanes, N, necessary to reach the desired level of service is calculated. The heavy-vehicle adjustment factor is determined by using Equation 7-4 and Tables 7-7 through 7-10. Figure 7-5 is a worksheet that may be used for design as well as operational analysis. It is a useful form for performing and summarizing the results of design computations. Interpretation of Results
Design computation for N generally results in a fraction. Because the number of lanes must be an integer value, the designer is faced with deciding whether to reduce or increase the computed value to the nearest integer, a decision with economic conseUpdated December 1997
quences. Although there are no set guidelines for such decisions, designers should perform an operational analysis on the possible choices for N to determine the level of service and approximate speed and density that would result. This allows such decisions to be made with some knowledge of the operational impacts— knowledge that must be weighed against the relative costs involved. The decision on number of lanes in a specific segment of a multilane highway also depends on their continuity with lanes in adjacent segments and with the rest of the highway system. Frequent adding or dropping of lanes along a highway is not practical, although either may be considered at critical locations. On specific grades, a larger number of lanes may be required on the upgrade than on the downgrade. This is a clear indication that a climbing lane is required. For a more precise treatment of such cases, Chapter 3 contains a detailed procedure for the design and evaluation of climbing lanes.
PLANNING ANALYSIS
A planning analysis is directed toward estimating the number of lanes required to accommodate given traffic conditions. It differs from the design application in that the analyst usually has available a value for annual average daily traffic (AADT) and a minimal definition of the facility being planned. In the planning stage, details of specific grades and other geometric features usually do not exist. Further, traffic forecasts are not precise. Thus, at the planning level, capacity analysis is approximate and serves to give a general idea of the highway geometrics required.
Data Requirements
The planning methodology assumes that ideal geometrics exist and that traffic streams consist of only passenger cars and trucks. The access-point density assumed is applicable to fringe urban and suburban conditions. The required input data include 1. A forecast of the AADT for the design year, 2. A forecast percent of trucks, 3. The anticipated ideal free-flow speed of the roadway segment, and 4. A general classification of terrain type. Table 7-11 was developed using free-flow speeds of 60 and 50 mph under ideal conditions. Using Equation 7-1, the free-flow speed was adjusted for 20 access points per mile (all other conditions are ideal). The limiting flows (in pcphpl) for LOS A through E were found from Figure 7-3 and multiplied by the peak-hour factor (0.9). These are the values in vehicles per hour per lane when there are no trucks. The vehicle volumes with varying percents of trucks were found by applying the appropriate heavy-vehicle factor. The AADT is a necessary input for the planning of any highway and will generally be available for capacity analysis. Vertical alignment and truck presence may only be estimates on the part of the analyst, based on the general terrain conditions of the area through which the highway will pass and on the anticipated character of traffic it is intended to serve.
multilane rural and suburban highways
7-19
Table 7-11. Service Flow Rates in Vehicles per Lane for Use in Planning Analysis type of terrain
level of service
percent trucks Level
Rolling
Mountainous
A B C D E A B C D E A B C D E
free-flow speed (ideal conditions) = 60 mph
free-flow speed (ideal conditions) = 50 mph
0
5
10
15
20
0
5
10
15
20
590 990 1,360 1,620 1,890 590 990 1,360 1,620 1,890 590 990 1,360 1,620 1,890
580 970 1,330 1,580 1,840 540 900 1,240 1,470 1,720 480 790 1,090 1,300 1,510
570 940 1,290 1,540 1,800 500 830 1,130 1,350 1,580 400 660 910 1,080 1,260
550 920 1,260 1,510 1,760 460 760 1,050 1,250 1,450 340 570 780 930 1,080
540 900 1,240 1,470 1,720 420 710 970 1,160 1,350 300 500 680 810 950
490 810 1,130 1,350 1,710 490 810 1,130 1,350 1,710 490 810 1,130 1,350 1,710
470 790 1,110 1,320 1,670 440 740 1,030 1,230 1,550 390 650 910 1,080 1,370
460 770 1,080 1,290 1,630 410 680 950 1,130 1,430 320 540 760 900 1,140
450 750 1,050 1,260 1,590 370 620 870 1,040 1,320 280 460 650 770 980
440 740 1,030 1,230 1,550 350 580 810 960 1,220 240 410 570 680 860
NOTE: Lane widths are 12 ft. Shoulder width is 6 ft. PHF = 0.9. Number of access points = 20 per mi. Divided highway.
Computational Steps
The following steps are involved in conducting a planning analysis: 1. AADT is converted to DDHV using the following equation: DDHV = AADT × K × D
(7-6)
where: AADT = forecast average annual daily traffic (vpd), DDHV = directional design hourly volume (vph), K = percent of AADT occurring in the peak hour, and D = percent of peak-hour traffic in the heaviest direction. Values of K and D should be based on local or regional characteristics. Further discussion of these parameters appears in Section VI, Sample Calculations, Calculation 5. 2. An appropriate maximum service flow rate in vehicles, Mvv, is selected from Table 7-11 for the prevailing truck percent and terrain and for the desired level of service. 3. The number of lanes that would be required in each direction of the highway is computed using the following equation: N = DDHV/(Mvv)
(7-7)
Figure 7-6 is a worksheet that may be used for planning analysis. Interpretation of Results
Planning analysis results in an estimate of N, the number of lanes required in each direction, for the multilane highway in question. This estimate is based on general information, and planning computations must be refined during the design phase of the project. Multilane highways with more than three lanes in each direction are rare, and those with more than four lanes are virtually nonexistent. Computations resulting in more than four lanes in each
direction offer a good indication that a multilane highway may be inappropriate for the anticipated conditions and that a limitedaccess highway should be considered. SIGNALIZED INTERSECTIONS ON MULTILANE HIGHWAYS
Multilane highways will generally have signalized intersections at widely spaced intervals, occurring at major junction points that are not grade separated. These intersections may be subjected to a detailed analysis using the methodology of Chapter 9. THREE-LANE HIGHWAYS WITH PERMANENTLY ASSIGNED THIRD LANES
Use of three-lane highways, which declined in the late 1960s, has recently increased. Three-lane highways may be operated in a number of ways, the most common of which include 1. Use of the center lane as a continuous left-turn lane (more common in suburban settings). 2. Alternate assignment of the center lane to one direction, then to the other, providing alternating, exclusive passing lanes for each direction of flow. 3. Permanent operation of a long segment of three-lane highway with two lanes in one direction and one in the other. The added lane in the preferred direction on a three-lane highway is generally less efficient than a full four-lane facility, because the added lane exists for distances of less than 1 to 2 mi. The added lane is used primarily to pass slower-moving vehicles (particularly on long upgrades) and to make left turns. This added lane increases the capacity of the two-lane highway by providing for more efficient passing and reducing left-turn conflicts but such a three-lane highway would not approach the capacity of a four-lane highway even in the preferred direction. Updated December 1997
7-20
rural and suburban highways
Figure 7-6. Worksheet for planning analysis.
Updated December 1997
multilane rural and suburban highways
7-21
VI. SAMPLE CALCULATIONS CALCULATION 1—OPERATIONAL ANALYSIS OF AN UNDIVIDED HIGHWAY
1. Description—A 3.25-mi section of undivided highway in generally level terrain has a free-flow speed of 46 mph measured at a flow rate of 1,000 pcphpl. At a distance of 6,000 ft from one end of the section is a 3,200-ft segment with a 2.5 percent grade. There are 14 driveways on each side of the road in the 3,200-ft segment and approximately 21 driveways per mile throughout the rest of the section. The cross section for the entire roadway is composed of four 11-ft lanes with a 4-ft shoulder on either side. The afternoon peak-hour traffic volume throughout is 1,900 vph in each direction with 8 percent trucks, 3 percent buses, and 2 percent RVs. The peak-hour factor is 0.90. 2. Objective—Determine the overall average travel speed for passenger cars, the density of traffic, and the level of service for each direction of flow. Are there any potential problem areas? 3. Solution—Free-flow speed has been measured under lowvolume conditions for this road. No adjustments to free-flow speed will be made. The value for free-flow-speed is 46 mph. A 46-mph curve is sketched onto a copy of Figure 7-3 (as shown in Figure 7-7). The only calculation required is for service flow rate. An initial solution is obtained using a general level terrain segment. Equation 7-3 is used to calculate the service flow rate: vp =
V (N)(PHF)(fHV)
The heavy-vehicle adjustment factor, fHV, is calculated using Equation 7-4. fHV = 1/[1 + PT (ET − 1) + PR (ER − 1)] ET, the passenger-car equivalent for trucks and buses, is determined to be 1.5 from Table 7-7 on the basis of an extended level terrain segment. Similarly, from Table 7-7, ER is 1.2. The resulting heavyvehicle factor, fHV, is 0.94. The service flow rate is calculated as vp = (1,900 vph)/(2 × 0.90 × 0.94) = 1,123 pcphpl As shown in Figure 7-4, the average travel speed on the total section is 46.0 mph and the level of service is C. The density is calculated as 24.4 pc/mi/ln. Figure 7-7 shows this part of the solution and the calculations as worked on the operational analysis worksheet. The only segment that might have a different result is the 3,200-ft 2.5 percent grade, analyzed as an upgrade in one direction and a downgrade in the other. For the 2.5 percent upgrade over approximately 0.6 mi, the value of ET is 2.2 from Table 7-8 by interpolation for 11 percent trucks and buses on an upgrade between 2 and 3 percent over 1⁄2 to 3⁄4 mi. ER is 2.0 from Table 7-9 for 2 percent RVs on a grade between 2 and 3 percent and more than 1⁄2 mi long. By using Equation 7-5, fHV is determined to be 0.87. The service flow rate on the upgrade is vp = (1,900 vph)/(2 × 0.90 × 0.87) = 1,213 pcphpl.
On the free-flow speed curve, the average speed is still 46.0 mph with LOS C and a density of 26.4 pc/mi/ln. For the 2.5 percent downgrade over the same distance, a different value of fHV results. Because the grade is less than 4 percent, the values of ET and ER are those used in the general terrain analysis for level terrain. The heavy-vehicle factor, fHV, has been determined above as 0.94, and vp as 1,123 pcphpl. The average travel speed on the downgrade is 46.0 mph with LOS C and a density of 24.4 pc/mi/ln. Figure 7-8 shows the solution for the downgrade. CALCULATION 2—OPERATIONAL ANALYSIS OF A DIVIDED HIGHWAY
1. Description—An east-west multilane highway has a fivelane cross section and is composed of two travel lanes in each direction separated by a two-way left-turn lane (TWLTL). Lane widths are 12 ft and there is sufficient lateral clearance on each side of the roadway. The study area is about 2 mi long and contains a 6,000-ft-long, 4 percent upgrade westbound, followed by level terrain for 5,000 ft. The section has a volume of 1,500 vph in each direction with 4 percent trucks and 2 percent buses. The north side of the highway has 27 access points evenly distributed approximately 400 ft apart throughout the section. The south side has only 10 access points, all located in the level terrain section. Data are available on current travel speeds along the roadway. The 85thpercentile speed of passenger cars on the upgrade (westbound) is 48 mph and 54 mph on the downgrade (eastbound). On the level section, the 85th-percentile speed is 52 mph in both directions. The PHF is 0.90. 2. Objective—Determine the level of service in the study area. 3. Solution—Proper analysis requires the 2-mi study area to be separated into two segments, the level segment and the segment with sustained grade. Note that because the number of access points varies by direction, the level segment must be evaluated in both directions. Figures 7-9 and 7-10 present the worksheets used for this problem. The first step in determining the level of service for each segment is to calculate the free-flow speed for ideal conditions for each segment on the basis of the rule of thumb for 85th-percentile speeds. These speeds are Level segment (both directions): 50 mph; Sustained-grade segment: Westbound (upgrade), 46 mph; Eastbound (downgrade), 52 mph. The free-flow speed can then be calculated using Equation 7-1: FFS = FFSI − FM − FLW − FLC − FA FM, the adjustment for median type, is determined using Table 7-2. Because a TWLTL is considered to have the same effect as a median, FM = 0.0. FLW, the lane width adjustment, and FLC, the lateral clearance adjustment, are both 0.0, as determined from Tables 7-3 and 7-4, respectively. FA, the adjustment for accesspoint density, is determined using Table 7-5. The access-point densities for each segment are Updated December 1997
7-22
rural and suburban highways
Figure 7-7. Illustration of solution to Calculation 1—general segment.
Updated December 1997
multilane rural and suburban highways
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Figure 7-8. Illustration of solution to Calculation 1—grade segment.
Updated December 1997
7-24
rural and suburban highways
Level segment: Westbound, 13 access points per mile; Eastbound, 10 access points per mile. Sustained-grade segment: Westbound (upgrade), 13 access points per mile; Eastbound (downgrade), 0 access points per mile. From Table 7-5, the access-point adjustments for the level segment are 3.3 and 2.5 mph in the westbound and eastbound directions, respectively, or a 0.25-mph reduction per access point. On the grade segment, FA for the upgrade (westbound) is 3.3 mph and 0.0 mph for the downgrade (eastbound). The free-flow speeds that result after appropriate adjustments are 46.7 and 47.5 in the westbound and eastbound directions of the level segment, 42.7 on the upgrade (westbound), and 52.0 on the downgrade (eastbound). The appropriate free-flow speed curves can then be drawn on Figure 7-3. Next the service flow rate is calculated for each segment by direction using Equation 7-3. The heavy-vehicle adjustment factor is calculated using Equation 7-4. For the level segment, ET is 1.5 from Table 7-7. In the upgrade direction, Table 7-8 provides an ET of 7.0, and Table 7-10 provides an ET of 1.5 in the downgrade direction. The service flow rates are calculated as Level segment (both directions): 859 pcphpl; Sustained-grade segment: Westbound (upgrade), 1,126 pcphpl; Eastbound (downgrade), 859 pcphpl. On the basis of these flow rates and the free-flow speeds, it is determined from the speed-flow curves that the level segment operates at LOS B in both directions. On the sustained-grade section, the upgrade operates at LOS C and the downgrade section at LOS B.
CALCULATION 3—DESIGN OF A MULTILANE HIGHWAY
1. Description—A 2-mi section of a multilane highway must be designed to carry an average daily traffic volume of 60,000 vehicles at LOS D. On the basis of local data from other multilane highways, the design-hour volume should be 10 percent with a 55/45 directional split, a PHF of 0.9, and 5 percent trucks. The highway is expected to have a 50-mph speed limit and approximately 10 access points per mile and to be located in rolling terrain. Existing right-of-way consists of a 90-ft corridor. 2. Objective—Determine the cross section that must be provided to meet the design criteria and find the expected travel speed for passenger cars on this highway. 3. Solution—A design analysis allows the designer to determine, by trial and error, the appropriate geometrics that are necessary to provide a given level of service. Initially, it is assumed that an ideal facility will be provided. The resulting cross section will have 12-ft lanes, a raised median, and shoulders 6 ft or more in each direction. The restrictions imposed by available rightof-way can then be investigated. Figure 7-11 shows the worksheet for this problem.
In the absence of better information, the free-flow speed under ideal conditions is estimated using the rule of thumb in Section IV, Determination of Free-Flow Speed. Updated December 1997
By using Equation 7-1, the free-flow speed is calculated as 52.5. A speed-flow curve is drawn at a free-flow speed of 52.5 mph. From the speed-flow curve, at LOS D, the maximum service flow rate for an ideal facility is determined to be approximately 1,750 pcphpl. Applying the percentages for design-hour volume and directional distribution produces a volume of 3,300 vph in the peak direction. By using Equation 7-3 and a heavy-vehicle adjustment factor based on Table 7-7, N, the minimum number of lanes required per direction, is 2.4. Because essentially ideal geometric conditions were assumed, three lanes per direction, or a six-lane cross section, are needed. If it is assumed that design criteria require a 12-ft median to allow for turning bays as needed, 12-ft lanes, and 10-ft shoulders, a six-lane cross section would require 104 ft of right-of-way. If the existing 90-ft right-of-way is the maximum allowable, one solution would be to reduce the lane widths to 11 ft, allow for only a 6-ft raised median and 4-ft shoulders, and provide a 5-ft offset to the right-of-way. The resulting total lateral clearance is at least 10 ft in each direction of travel. The access-point density would be unchanged. This particular design would provide freeflow speed of 50.2 mph. A six-lane cross section of this reduced design would provide an LOS D (almost LOS C) for the estimated service flow rate of 1,343 pcphpl. The anticipated average travel speed would be 50.2 mph for this six-lane cross section. Thus, a six-lane roadway with less than ideal geometry would satisfy the design requirements of LOS D operation. This design is only one of several, however, that would produce the required level of service. Furthermore, the analysis does not address safety considerations, which may be overriding. CALCULATION 4—DESIGN ANALYSIS OF AN EXISTING MULTILANE ROADWAY
1. Description—A six-lane divided roadway located in an urban setting is the subject of a rehabilitation program aimed at improving traffic operations. The 2.5-mi section located in level terrain has signalized intersections at either end and one signal installation in the middle. This last signal is being replaced by a gradeseparated roadway at the same location. The current peak-hour flow rate is 1,400 pcphpl, and the current average travel time through the section is 3.0 min. At-grade access is provided only at the signalized intersections. The current roadway has 11-ft lanes separated by a 16-ft raised median. The shoulder on each side of the roadway measures 4 ft. 2. Objective—Determine the expected travel speed of the improved roadway when the grade separation is complete. How much additional traffic can be added and maintain the improved level of service? 3. Solution—The new free-flow speed as a result of the change in travel time must be found. The existence of the grade separation is not a reason for segmenting the roadway. Figure 7-12 shows the results of the analysis. Before removal of the signal, the average travel time through the 2.5-mi section was 180 sec under free-flow conditions, or an average travel speed of 50 mph. At a flow rate of 1,400 pcphpl, LOS is D. Removing the traffic signal is estimated to reduce the average travel time by 30 to 150 sec. This corresponds to a freeflow speed of approximately 60 mph. (No increase in traffic volume is expected as a result of constructing the grade separation.)
multilane rural and suburban highways
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Figure 7-9. Illustration of solution to Calculation 2—level segment.
Updated December 1997
7-26
rural and suburban highways
Figure 7-10. Illustration of solution to Calculation 2—grade segment.
Updated December 1997
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Figure 7-11. Illustration of solution to Calculation 3.
Updated December 1997
7-28
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Figure 7-12. Illustration of solution to Calculation 4.
Updated December 1997
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7-29
Figure 7-13. Illustration of solution to Calculation 5.
Updated December 1997
7-30
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Sketching the new free-flow speed on the graph indicates that at a flow rate of 1,400 pcphpl, the expected average travel speed is 60 mph under LOS C conditions. By reading to the right to the density curve marking the boundary between LOS C and D, the maximum flow rate for LOS C at 60 mph is estimated to be 1,620 pcphpl. Thus, an additional 220 passenger cars per lane could be added and still maintain LOS C. CALCULATION 5—PLANNING ANALYSIS FOR A NEW ROADWAY
1. Description—A new corridor is to be developed on the outskirts of a metropolitan area. The highway is to be constructed in approximately 10 years. Future traffic projections indicate that the highway should be designed to carry 42,000 vehicles per day with 5 to 10 percent trucks. At the current time it is anticipated that the corridor will have ideal design conditions through rolling terrain. From similar multilane highways, it is expected that the freeflow speed on this highway will be 50 mph. 2. Objective—Determine the number of lanes needed to provide LOS C operation. 3. Solution—In the absence of more specific information on the proposed highway and forecast traffic, the planning approach may be considered. An estimate will be made of the directional design hourly volume (DDHV), which will be compared with the values for Table 7-11. The first step is to calculate the DDHV using Equation 7-7. AADT reflects a year-round average. The value for K represents
the percent of the AADT expected in the design hour. The value for D reflects the directional distribution of traffic in that hour. Historically, these values have been referred to as the K-factor and the D-factor. For suburban areas, these values have traditionally been 0.10 and 60/40, respectively. In this example, these values result in a DDHV of 2,520 vph. The table at the bottom of the worksheet in Figure 7-13 indicates that a six-lane facility with a free-flow speed of 50 mph under ideal conditions can handle 2,850 to 3,090 vph and still operate at LOS C. The calculations for this planning analysis are displayed on the worksheet in Figure 7-13. The value for K should represent local practice for the design hourly volume. It may be the ratio between the 30th, 50th, or some other hour of the year and AADT. This information is generally available to the user. The data for similar facilities in the general area may have been collected for other analyses or as a part of the modeling process for developing a traffic forecast. The value for K, which is dependent on the environment around the roadway, has been observed to increase with distance from urban areas. The value for D, the directional distribution, varies as a function of route type and distance from activity centers. Usually the highvolume direction is evaluated. Use of default values can lead to results that differ significantly from those using more specific local data. It is strongly recommended that when default values are used in applying the planning methodology, local values for defaults be determined. Furthermore, the planning method is more useful for scaling roadways on a systemwide basis than for making design decisions for a specific roadway.
VII. ACKNOWLEDGMENTS This chapter is based upon research performed for the National Cooperative Highway Research Program by JHK & Associates and the Midwest Research Institute. The principal researchers were William R. Reilly, Douglas W. Harwood, James M. Schoen, and Michael F. Holling. The chapter is a revision of the research product and was developed by members of the Subcommittee on Multilane Highways of
the Committee on Highway Capacity and Quality of Service. The members of the subcommittee are Ulrich Brannolte; Barbara Ostrom; Ronald Pfefer, Chairman; William Reilly; and Fred Rooney.
VIII. REFERENCES 1. Hool, J.N., Maghsoodloo, S., Veren, A.D., and Brown, D.D., ‘‘Analysis of Selective Enforcement Strategy Effects on Rural Alabama Traffic Speeds.’’ Transportation Research Record 910, Transportation Research Board, Washington, D.C. (1983), pp. 74–81. 2. Armour, M., ‘‘The Effect of Police Presence on Urban Driving Speeds.’’ Australian Road Research, Vol. 14, No. 3 (Sept. 1984), pp. 142–148.
Updated December 1997
3. Hauer, E., and Ahlin, F.J., ‘‘Speed Enforcement and Speed Choice.’’ Accident Analysis and Prevention, Vol. 14, No. 4 (1982), pp. 267–278. 4. Tignor, S.C., ‘‘Driver Speed Behavior on U.S. Streets and Highways.’’ Compendium of Technical Papers, Institute of Transportation Engineers (August 5–8, 1990).
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APPENDIX I FIGURES AND WORKSHEETS FOR USE IN THE ANALYSIS OF MULTILANE HIGHWAYS FIGURES Figure 7-1
Speed-flow relationships on multilane highways......................................................................................................... 7-32
Figure 7-2
Density-flow relationships on multilane highways ...................................................................................................... 7-33
Figure 7-3
Speed-flow curves with LOS criteria. *Maximum density for respective levels of service. **Maximum densities for LOS E occur at volume-to-capacity ratio of 1.0. They are 40, 41, 43, and 45 pc/mi/ln at free-flow speeds of 60, 55, 50, and 45 mph, respectively ........................................................................................................................... 7-34
WORKSHEETS Operational and Design Analysis Worksheet.......................................................................................................................................... 7-35 Planning Analysis Worksheet .................................................................................................................................................................. 7-36
Updated December 1997
Figure 7-1. Speed-flow relationships on multilane highways.
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Updated December 1997
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Figure 7-2. Density-flow relationships on multilane highways.
multilane rural and suburban highways
Updated December 1997
Figure 7-3. Speed-flow curves with LOS criteria. *Maximum density for respective levels of service. **Maximum densities for LOS E occur at volume-to-capacity ratio of 1.0. They are 40, 41, 43, and 45 pc/mi/ln at free-flow speeds of 60, 55, 50, and 45 mph, respectively.
7-34
Updated December 1997
rural and suburban highways
multilane rural and suburban highways
7-35
Updated December 1997
7-36
rural and suburban highways Planning Analysis Worksheet
Updated December 1997
multilane rural and suburban highways
7-37
ADDENDUM: ADJUSTMENT FOR DRIVER POPULATION As described under Other Adjustments (p. 7-6), the methodology in Chapter 7 for the analysis of traffic flow on multilane highways is based on traffic data collected across the United States. These data did not specifically focus on the possible variation in traffic flow for differing driver populations (i.e., commuters or frequent drivers versus infrequent drivers). Although little documented data are currently available and the effect of driver population on traffic flow is not well understood, it is generally accepted that traffic streams with different characteristics from those consisting of commuters and frequent drivers (i.e., those who drive on weekends, for recreation, and perhaps even at mid-day) use roadways less efficiently than do those who drive frequently. A limited number of studies on uninterrupted-flow roadways have reported lower capacities on weekends, particularly in recreational areas. The adjustment factor fp is used to reflect this effect. The values for fp range from 1.0 to 0.85. Typically, the analyst should select 1.0, which reflects weekday commuter traffic (i.e., familiar users), unless there is sufficient evidence or it is the analyst’s judgment
that a lesser value reflecting more recreational or weekend traffic characteristics should be applied. Where greater accuracy is needed, comparative field studies of weekday and weekend traffic flow and speeds are recommended. In the analysis of multilane highway level of service, the driver population effect is reflected as an adjustment to the hourly service flow rate, vp . Thus, to determine the service flow rate, the analyst should replace Equation 7-3 (p. 7-11) with the following equation: vp =
V (N) (PHF) (fHV) (fp)
where: vp = service flow rate (pcphpl), V = volume (number of vehicles passing a point in 1 hr), N = number of lanes, PHF = peak-hour factor, fHV = heavy-vehicle adjustment factor, and fp = driver population adustment factor.
Updated December 1997
chapter 8
TWO-LANE HIGHWAYS
CONTENTS i.
introduction .......................................................................................................................................................................... Levels of Analysis................................................................................................................................................................. Operational Characteristics.................................................................................................................................................... Ideal Conditions.....................................................................................................................................................................
ii.
methodology.......................................................................................................................................................................... 8-5 Levels of Service................................................................................................................................................................... 8-5 Operational Analysis ............................................................................................................................................................. 8-6 Use of the Peak Hour Factor........................................................................................................................................... 8-7 Analysis of General Terrain Segments............................................................................................................................ 8-7 Analysis of Specific Grades ............................................................................................................................................ 8-8 Highway System Planning .................................................................................................................................................... 8-13
iii.
procedures for application ................................................................................................................................................ Operational Analysis of General Terrain Segments............................................................................................................. Operational Analysis of Specific Grades.............................................................................................................................. Planning .................................................................................................................................................................................
8-14 8-14 8-15 8-17
iv.
design and operational treatments................................................................................................................................. Passing Sight Distance .......................................................................................................................................................... Paved Shoulders .................................................................................................................................................................... Three-Lane Highways ........................................................................................................................................................... Passing Lanes ................................................................................................................................................................... Continuous Two-Way Median Left-Turn Lanes............................................................................................................. Reversible Lane................................................................................................................................................................ Intersection Treatments .................................................................................................................................................... Climbing Lanes ................................................................................................................................................................ Turnouts............................................................................................................................................................................ Short Four-Lane Sections......................................................................................................................................................
8-17 8-18 8-18 8-18 8-18 8-20 8-20 8-20 8-20 8-20 8-21
v.
sample calculations ............................................................................................................................................................ Calculation 1—Finding Service Flow Rates for a General Terrain Segment..................................................................... Calculation 2—Finding Level of Service for a General Terrain Segment ......................................................................... Calculation 3—Finding Service Flow Rates for a Specific Grade...................................................................................... Calculation 4—Finding Level of Service and Capacity of a Specific Grade..................................................................... Calculation 5—Consideration of a Climbing Lane.............................................................................................................. Calculation 6—Planning Application 1 ................................................................................................................................ Calculation 7—Planning Application 2 ................................................................................................................................ Calculation 8—Planning Application 3 ................................................................................................................................
8-21 8-21 8-23 8-23 8-24 8-26 8-26 8-27 8-27
vi.
references .............................................................................................................................................................................. 8-27
8-2 8-2 8-2 8-4
appendix I. Figures and Worksheets for Use in Analysis of Two-Lane Highways............................................................. 8-28
8-1
8-2
rural highways
I. INTRODUCTION A two-lane highway may be defined as a two-lane roadway having one lane for use by traffic in each direction. Passing of slower vehicles requires the use of the opposing lane where sight distance and gaps in the opposing traffic stream permit. As volumes and/or geometric restrictions increase, the ability to pass decreases, resulting in the formation of platoons in the traffic stream. Motorists in these platoons are subject to delay because of the inability to pass. Two-lane highways compose the predominant mileage of most national highway systems. They are used for a variety of functions, are located in all geographic areas, and serve a wide range of traffic requirements. Consideration of operating quality must account for these disparate traffic functions. Efficient mobility is the principal function of major two-lane highways used as primary arteries connecting major traffic generators or as primary links in state and national highway networks. Such routes tend to serve long-distance commercial and recreational travelers, and may have sections of many miles through rural environments without traffic control interruptions. Consistent high-speed operations and infrequent passing delays are desirable for these facilities. Many paved, two-lane rural roads basically serve an accessibility function. They provide all-weather accessibility to an area, often for relatively low traffic volumes. The provision of cost-effective access is the dominant policy consideration. High speed, while beneficial, is not the principal concern. Delay, as indicated by the formation of platoons, and the utilization of capacity are more relevant measures of service quality. Two-lane roads also serve scenic and recreational areas where the vista and environment are to be experienced and enjoyed without traffic interruption or delay. A safe roadway is desired, but high-speed operation is neither expected nor desired. Short sections of high-volume two-lane roads sometimes serve as short connections between two major multilane roadways or urban centers. For such short links, traffic conditions tend to be better than might be expected for longer two-lane segments, and the expectations of motorists regarding service quality are generally higher than for longer sections. For these reasons, three parameters are used to describe service quality for two-lane highways: 1. Average travel speed. 2. Percent time delay. 3. Capacity utilization. Average travel speed reflects the mobility function of twolane highways, and is the length of the highway segment under consideration divided by the average travel time of all vehicles traversing the segment in both directions over some designated time interval. Percent time delay reflects both mobility and access functions, and is defined as the average percent of time that all vehicles are delayed while traveling in platoons due to the inability to pass. ‘‘Percent time delay’’ is difficult to measure directly in the field. The percent of vehicles traveling at headways less than 5 sec can be used as a surrogate measure in field studies.
The utilization of capacity reflects the access function, and is defined as the ratio of the demand flow rate to the capacity of the facility. Level-of-service criteria utilize all three of the parameters noted above, with percent time delay being the primary measure of service quality. Speed and capacity utilization are secondary measures. This chapter provides specific definitions and methodologies for the estimation of level of service for all types of two-lane highways. Subsequent sections provide a descriptive list of treatments for alleviating both spot and section design and/or operational problems that may arise because of high volume and/or geometric restrictions. A set of example calculations is provided to illustrate the use and application of procedures. A complete set of worksheets for all levels of analysis is also provided. Illustration 8-1 shows typical views of two-lane, twoway rural highways.
LEVELS OF ANALYSIS
This chapter is based on a comprehensive study of two-lane highway operation (1,2). Microscopic simulation combined with additional field data (3) and theoretical considerations were used to develop the methodology. Analysis is provided at two levels: 1. Operational analysis—This application is intended to determine the level of service for an existing two-lane highway with existing traffic and roadway conditions, or for projected future conditions; operational analysis applications are presented for general terrain segments and for specific grades. 2. System planning—This application enables planners to quickly determine the AADT volumes which can be accommodated on two-lane highways for various levels of service and terrain conditions. Design computations cannot be readily performed for two-lane highways because the number of lanes is fixed. Modifications to grade and alignment, however, could improve the operational efficiency of a two-lane facility. For other design options, procedures for the appropriate types of facilities would be consulted. Procedures of Chapter 3, ‘‘Basic Freeway Segments,’’ and Chapter 7, ‘‘Multilane Highways,’’ would often be useful in investigating design alternatives. The selection of an appropriate level of analysis is based on the objectives of the analysis, the available data base, and the accuracy requirements.
OPERATIONAL CHARACTERISTICS
Traffic operations on two-lane, two-way highways are unique. Lane-changing and passing are possible only in the face of oncoming traffic in the opposing lane. Passing demand increases rapidly as traffic volumes increase, while passing capacity in the opposing lane declines as volumes increase. Thus, unlike
two-lane highways
8-3
Illustration 8-1. Typical views of two-lane two-way highways in rural environments.
other types of uninterrupted flow facilities, on two-lane highways, normal traffic flow in one direction influences flow in the other direction. Motorists are forced to adjust their individual travel speed as volume increases and the ability to pass declines. Two traffic stream characteristics, average travel speed and percent time delay, are used as operational measures describing the quality of service provided to motorists on a two-lane highway. A relatively high running speed has become an accepted criterion for primary highway design. Mean speeds of traffic flow are frequently observed above 55 mph on primary rural highways. Research has shown that speed is fairly insensitive to volume on two-lane highways without significant grades or turning traffic (4). Consequently, average speeds of less than 50 mph are judged undesirable for primary two-lane highways in level terrain because of the high percentage of time motorists would be delayed.
‘‘Percent time delay’’ is the average percent of the total travel time that all motorists are delayed in platoons while traveling a given section of highway. Motorists are defined to be delayed when traveling behind a platoon leader at speeds less than their desired speed and at headways less than 5 sec. For field measurement purposes, percent time delay in a section is approximately the same as the percentage of all vehicles traveling in platoons at headways less than 5 sec (2,5). Percent time delay reflects the changing service quality perceived by motorists under a wide range of geometric and traffic conditions. At low traffic volumes, motorists are almost never delayed because demand for passing is low, average headways are high, and the ability to pass is high. The percent time delay for such conditions is near 0 percent. As volumes approach capacity, passing demand greatly exceeds passing capacity, major platoons of traffic exist, and motorists are delayed almost
rural highways
8-4
a. Relationship between average speed and flow on two-lane highways.
b. Relationship between percent time delay and flow on two-lane highways.
Figure 8-1. Speed-flow and percent time delay-flow relationships for two-lane rural highways (ideal conditions). 100 percent of the time. Even though speeds may be relatively high near capacity (40 mph or more), driver frustration would be excessive if these conditions routinely existed for long periods of time. The basic relationships between average travel speed, percent time delay, and flow are shown in Figure 8-1. These curves assume ideal traffic and roadway conditions. The average speed represents the average travel or space mean speed of all traffic traveling in both directions over the section of highway in question. Percent time delay is the average for all vehicles in the traffic stream. IDEAL CONDITIONS
Ideal conditions for two-lane highways are defined as no restrictive geometric, traffic, or environmental conditions. Specifically, they include: 1. Design speed greater than or equal to 60 mph. 2. Lane widths greater than or equal to 12 ft. 3. Clear shoulders wider than or equal to 6 ft. 4. No ‘‘no passing zones’’ on the highway. 5. All passenger cars in the traffic stream. 6. A 50/50 directional split of traffic. 7. No impediments to through traffic due to traffic control or turning vehicles. 8. Level terrain. The capacity of two-lane rural highways under these ideal conditions is 2,800 pcph, total, in both directions. This capacity
reflects the impact of opposing vehicles on passing opportunities, and therefore on the ability to efficiently fill gaps in the traffic stream. This phenomenom restricts capacity to a lower value than the 2,000 pcphpl which may be accommodated on multilane uninterrupted flow facilities. Directional distribution is defined to be 50/50 for ideal conditions. Most directional distribution factors observed on rural two-lane highways range from 55/45 to 70/30. On recreational routes, the directional distribution may be as high as 80/20 or more during holiday or other peak periods. Some variation in speed and percent time delay occurs by direction with changing directional distribution factors and volume levels. Minor changes in average traffic stream characteristics will also occur with directional distribution. The frequency of no passing zones along a two-lane highway is used to characterize roadway design and to define expected traffic conditions. A no passing zone is defined as any marked no passing zone or, as a surrogate, any section of road wherein the passing sight distance is 1,500 ft or less. The average percentage of no passing zones in both directions along a section is used in the procedures. The typical percentage of no passing zones found on rural two-lane highways ranges from 20 percent to 50 percent. Values approaching 100 percent can be found on sections of winding mountainous roads. No passing zones have a greater effect in mountainous terrain than on level or rolling highway segments. Heavy platoon formation along a highway section also may cause greater than expected operational problems on an adjacent downstream section having restricted passing opportunities.
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8-5
II. METHODOLOGY LEVELS OF SERVICE
Table 8-2 gives level-of-service criteria for specific grade segments. These criteria relate the average travel speed of upgrade vehicles to level of service. Operations on sustained two-lane grades are substantially different from extended segments of general terrain. The speed of upgrade vehicles is seriously impacted, as the formation of platoons behind slow-moving vehicles intensifies and passing maneuvers generally become more difficult. Further, unlike general terrain segments, where the approximate average travel speed at which capacity occurs can be identified, the capacity speed for a specific grade depends on the steepness and length of the grade and volume. Because of this, estimation of capacity is complex. Thus, Table 8-2 defines separate level-of-service criteria for specific grade segments. In addition, this chapter includes special computational procedures for sustained grades on two-lane highways. Downgrade operations are not specifically addressed by these procedures. Downgrade operations on gentle grades (less than 3 percent) are generally comparable to those on a level roadway. On more severe grades, downgrade operations are about midway between those experienced on a level roadway and those experienced on an upgrade of equivalent traffic and roadway characteristics. The principal concern on steep downgrades is the potential for ‘‘runaway’’ trucks. The highest quality of traffic service occurs when motorists are able to drive at their desired speed. Without strict enforcement, this highest quality, representative of level-of-service A, would result in average speeds approaching 60 mph on twolane highways. The passing frequency required to maintain these speeds has not reached a demanding level. Passing demand is
As noted previously, level-of-service criteria for two-lane highways address both mobility and accessibility concerns. The primary measure of service quality is percent time delay, with speed and capacity utilization used as secondary measures. Levelof-service criteria are defined for peak 15-min flow periods, and are intended for application to segments of significant length. Level-of-service criteria for general terrain segments are given in Table 8-1. For each level of service, the percent time delay is shown. Average travel speed is also shown, with values varying slightly by type of terrain. The body of the table includes maximum values of v/c ratio for the various terrain categories and levels of service A through F. The v/c ratios shown in Table 8-1 are somewhat different from those used in other chapters. For two-lane highways, the values given represent the ratio of flow rate to ‘‘ideal capacity,’’ where ideal capacity is 2,800 pcph for a level terrain segment with ideal geometrics and 0 percent no passing zones. Two-lane highways are quite complex, and capacities vary depending on terrain and the degree of passing restrictions. To simplify computational procedures, v/c ratios are given in terms of the constant ‘‘ideal capacity’’ of 2,800 pcph, total in both directions of flow. The level-of-service criteria of Table 8-1 are for extended segments of two-lane rural highways where efficient mobility is the primary objective of the facility. Where speeds have been restricted by an agency, such as through a town or village, the percentage of time delay and capacity utilization are the only meaningful indicators of level of service.
Table 8-1. Level-of-Service for General Two-Lane Highway Segments v/c ratioa level terrain percent time avgb los delay speed A B C D E F a b
≤ ≤ ≤ ≤ >
30 45 60 75 75 100
≥ ≥ ≥ ≥ ≥ <
58 55 52 50 45 45
rolling terrain
percent no passing zones 0
20
40
60
80
0.15 0.27 0.43 0.64 1.00 —
0.12 0.24 0.39 0.62 1.00 —
0.09 0.21 0.36 0.60 1.00 —
0.07 0.19 0.34 0.59 1.00 —
0.05 0.17 0.33 0.58 1.00 —
avgb 100 speed
0.04 0.16 0.32 0.57 1.00 —
≥ ≥ ≥ ≥ ≥ <
57 54 51 49 40 40
mountainous terrain
percent no passing zones 0
20
40
60
80
0.15 0.26 0.42 0.62 0.97 —
0.10 0.23 0.39 0.57 0.94 —
0.07 0.19 0.35 0.52 0.92 —
0.05 0.17 0.32 0.48 0.91 —
0.04 0.15 0.30 0.46 0.90 —
avgb 100 speed
0.03 0.13 0.28 0.43 0.90 —
Ratio of flow rate to an ideal capacity of 2,800 pcph in both directions. These speeds are provided for information only and apply to roads with design speeds of 60 mph or higher.
≥ ≥ ≥ ≥ ≥ <
56 54 49 45 35 35
percent no passing zones 0
20
40
60
80
100
0.14 0.25 0.39 0.58 0.91 —
0.09 0.20 0.33 0.50 0.87 —
0.07 0.16 0.28 0.45 0.84 —
0.04 0.13 0.23 0.40 0.82 —
0.02 0.12 0.20 0.37 0.80 —
0.01 0.10 0.16 0.33 0.78 —
rural highways
8-6
Table 8-2. Level-of-Service Criteria for Specific Grades level of service
average upgrade speed (mph)
A B C D E F
≥ 55 ≥ 50 ≥ 45 ≥ 40 ≥ 25–40a < 25–40a
a
The exact speed at which capacity occurs varies with the percentage and length of grade, traffic compositions, and volume; computational procedures are provided to find this value.
well below passing capacity, and almost no platoons of three or more vehicles are observed. Drivers would be delayed no more than 30 percent of the time by slow-moving vehicles. A maximum flow rate of 420 pcph, total in both directions, may be achieved under ideal conditions. Level-of-service B characterizes the region of traffic flow wherein speeds of 55 mph or slightly higher are expected on level terrain. Passing demand needed to maintain desired speeds becomes significant and approximately equals the passing capacity at the lower boundary of level-of-service B. Drivers are delayed up to 45 percent of the time on the average. Service flow rates of 750 pcph, total in both directions, can be achieved under ideal conditions. Above this flow rate, the number of platoons forming in the traffic stream begins to increase dramatically. Further increases in flow characterize level-of-service C, resulting in noticeable increases in platoon formation, platoon size, and frequency of passing impediment. Average speed still exceeds 52 mph on level terrain, even though unrestricted passing demand exceeds passing capacity. At higher volume levels, chaining of platoons and significant reductions in passing capacity begin to occur. While traffic flow is stable, it is becoming susceptible to congestion due to turning traffic and slow-moving vehicles. Percent time delays are up to 60 percent. A service flow rate of up to 1,200 pcph, total in both directions, can be accommodated under ideal conditions. Unstable traffic flow is approached as traffic flows enter levelof-service D. The two opposing traffic streams essentially begin to operate separately at higher volume levels, as passing becomes extremely difficult. Passing demand is very high, while passing capacity approaches zero. Mean platoon sizes of 5 to 10 vehicles are common, although speeds of 50 mph can still be maintained under ideal conditions. The fraction of no passing zones along the roadway section usually has little influence on passing. Turning vehicles and/or roadside distractions cause major shock-waves in the traffic stream. The percentage of time motorists are delayed approaches 75 percent. Maximum service flow rates of 1,800 pcph, total in both directions, can be maintained under ideal conditions. This is the highest flow rate that can be maintained for any length of time over an extended section of level terrain without a high probability of breakdown. Level-of-service E is defined as traffic flow conditions on twolane highways having a percent time delay of greater than 75 percent. Under ideal conditions, speeds will drop below 50 mph. Average travel speeds on highways with less than ideal conditions will be slower, as low as 25 mph on sustained upgrades.
Passing is virtually impossible under level-of-service E conditions, and platooning becomes intense when slower vehicles or other interruptions are encountered. The highest volume attainable under level-of-service E defines the capacity of the highway. Under ideal conditions, capacity is 2,800 pcph, total in both directions. For other conditions, capacity is lower. Note that the v/c ratios of Table 8-1 are not all 1.00 at capacity. This is because the ratios are relative to ‘‘ideal capacity’’ as discussed. Operating conditions at capacity are unstable and difficult to predict. Traffic operations are seldom observed near capacity on rural highways, primarily because of a lack of demand. Capacity of two-lane highways is affected by the directional split of traffic. As directional split moves away from the 50/50 ‘‘ideal’’ condition, total two-way capacity is reduced, as follows: Directional Split
Total Capacity (pcph)
Ratio of Capacity to Ideal Capacity
50/50 60/40 70/30 80/20 90/10 100/0
2,800 2,650 2,500 2,300 2,100 2,000
1.00 0.94 0.89 0.83 0.75 0.71
For short lengths of two-lane road, such as tunnels or bridges, opposing traffic interactions may have only a minor effect on capacity. The capacity in each direction may approximate that of a fully loaded single lane, given appropriate adjustments for the lane width and shoulder width (5). As with other highway types, level-of-service F represents heavily congested flow with traffic demand exceeding capacity. Volumes are lower than capacity, and speeds are below capacity speed. Level-of-service E is seldom attained over extended sections on level terrain as more than a transient condition; most often, perturbations in traffic flow as level E is approached cause a rapid transition to level-of-service F.
OPERATIONAL ANALYSIS
This section presents the methodology for operational analysis of general terrain segments and specific grades on two-lane highways. Separate procedures for general highway segments and grades are used, because the dynamics of traffic interaction on sustained two-lane grades differ from those on general terrain segments. Grades of less than 3 percent or shorter than 1/2 mile may be included in general terrain analysis. Grades both longer and steeper than these values should generally be treated as specific grades. Level, rolling, and mountainous terrain are as defined in Chapters 1 and 3. The length of grade is taken to be the tangent length of grade plus a portion of the vertical curves at the beginning and end of the grade. About one-fourth of the length of vertical curves at the beginning and end of a grade are included in the grade length. Where two grades (in the same direction) are joined by a vertical curve, one-half the length of the curve is included in each grade segment.
two-lane highways The objective of operational analysis is generally the determination of level of service for an existing or projected facility operating under existing or projected traffic demand. Operational analysis may also be used to determine the capacity of a twolane highway segment, or the service flow rate which can be accommodated at any given level of service. Use of the Peak Hour Factor
As for other facility types, two-lane highway analysis is based on flow rates for a peak 15-min period within the hour of interest, which is usually the peak hour. The criteria of Table 8-1 refer to equivalent hourly flow rates based on the peak 15 min of flow. These criteria are used to compute service flow rates, SF, which are compared to existing or projected flow rates to determine level of service. Thus, full-hour demand volumes must be converted to flow rates for the peak 15 min, as follows:
8-7
The decision to use flow rates or full-hour volumes in an analysis is related to whether or not peaking characteristics will cause substantial fluctuation in operating conditions within the peak hour, and whether the impact of such fluctuations will impact design and/or operational policy decisions. In general, where the peak hour factor is less than 0.85, operating conditions will vary substantially within the hour. Where the peak hour factor can be determined from local field data, this should be done. Where field data are not available, the factors tabulated in Table 8-3 may be used. These are based solely on the assumption of random flow and may be somewhat higher than those obtained from field studies. When level of service is to be determined for a given traffic volume, a value appropriate to the volume level on the subject segment is selected from the upper portion of the table. When a service flow rate is to be computed, a value is selected from the lower portion of the table, because volume is unknown. Analysis of General Terrain Segments
v = V/PHF where: v = flow rate for the peak 15 min, total for both directions of flow, in vph; V = full-hour volume total for both directions of flow, in vph; and PHF = peak hour factor. When criteria are compared to flow rates, the predicted operating characteristics are expected to prevail for the 15-min period for which the flow rate applies. For many rural conditions, the analyst may wish to examine average conditions over a peak hour. Full-hour volumes, unadjusted for the PHF, are compared to criteria directly for these cases. It should be noted, however, that prediction of an average level-of-service C during a full hour may include portions of the hour operating at level D or E, while other portions operate at A or B.
The general terrain methodology estimates average traffic operational measures along a section of highway based on average terrain, geometric, and traffic conditions. Terrain is classified as level, rolling, or mountainous, as described previously. The general terrain procedure is usually applied to highway sections of at least 2 miles in length. Highway geometric features include a general description of longitudinal section characteristics and specific roadway crosssection information. Longitudinal section characteristics are described by the average percent of the highway having no passing zones. The average for both directions is used. The percentage of roadway along which sight distance is less than 1,500 ft may be used as a surrogate for no passing zone data. Roadway crosssection data include lane width and usable shoulder width. Geometric data on design speed and specific grades are not used directly, but are reflected in the other geometric factors discussed.
Table 8-3. Peak Hour Factors for Two-Lane Highways Based on Random Flow A. Level-of-Service Determinations total 2-way hourly volume (vph)
peak hour factor (phf)
total 2-way hourly volume (vph)
peak hour factor (phf)
100 200 300 400 500 600 700 800 900
0.83 0.87 0.90 0.91 0.91 0.92 0.92 0.93 0.93
1,000 1,100 1,200 1,300 1,400 1,500 1,600 1,700 1,800 ≥ 1,900
0.93 0.94 0.94 0.94 0.94 0.95 0.95 0.95 0.95 0.96
B. Service Flow-Rate Determinations Level of Service Peak Hour Factor
A 0.91
B 0.92
C 0.94
D 0.95
E 1.00
rural highways
8-8
Traffic data needed to apply the general terrain methodology include the two-way hourly volume, a peak hour factor, and the directional distribution of traffic flow. Peak hour factors may be computed from field data, or appropriate default values may be selected from Table 8-3. Traffic data also include the proportion of trucks, recreational vehicles (RV’s), and buses in the traffic stream. When estimates of the traffic mix are not available, the following default values for these fractions may be used for primary routes: T PT = 0.14 (trucks) T PR = 0.04 (RV’s) T PD = 0.00 (buses) Recreational routes would typically have a higher proportion of recreational vehicles than shown for primary rural routes. 1. General relationship—The general relationship describing traffic operations on general terrain segments is as follows: SFi = 2,800 × (v/c)i × fd × fw × fHV
(8-1)
where: SFi = total service flow rate in both directions for prevailing roadway and traffic conditions, for level of service i, in vph; (v/c)i = ratio of flow rate to ideal capacity for level of service i, obtained from Table 8-1; fd = adjustment factor for directional distribution of traffic, obtained from Table 8-4; fw = adjustment factor for narrow lanes and restricted shoulder width, obtained from Table 8-5; fHV = adjustment factor for the presence of heavy vehicles in the traffic stream, computed as: (8-2) fHV = 1/[1 + PT (ET − 1) + PR(ER − 1) + PB(EB − 1)] where: PT = proportion of trucks in the traffic stream, expressed as a decimal; PR = proportion of RV’s in the traffic stream, expressed as a decimal; PB = proportion of buses in the traffic stream, expressed as a decimal; ET = passenger-car equivalent for trucks, obtained from Table 8-6; ER = passenger-car equivalent for RV’s, obtained from Table 8-6; and EB = passenger-car equivalent for buses, obtained from Table 8-6. Equation 8-1 takes an ideal capacity of 2,800 pcph, and adjusts it to reflect a v/c ratio appropriate for the desired level of service, directional distributions other than 50/50, lane width restrictions and narrow shoulders, and heavy vehicles in the traffic stream. 2. Adjustment for v/c ratio—The v/c ratios given in Table 8-1 reflect a complex relationship among speed, flow, delay, and geometric parameters for two-lane highways. Specifically, v/c values vary with level-of-service criteria, terrain type, and the
magnitude of passing restrictions. Note that v/c ratios at capacity are not equal to 1.00 for rolling or mountainous terrain. This is because the ratios are based on an ideal capacity of 2,800 pcph, which cannot be achieved on severe terrains. Further, as the formation of platoons is more frequent where terrain is rolling or mountainous, passing restrictions have a greater effect on capacity and service flow rate than on level terrain. 3. Adjustment for directional distribution—All of the v/c values in Table 8-1 are for a 50/50 directional distribution of traffic on a two-lane highway. For other directional distributions, the factors shown in Table 8-4 must be applied to Table 8-1 values. 4. Adjustment for narrow lanes and restricted shoulder width— Narrow lanes force motorists to drive closer to vehicles in the opposing lane than they would normally desire. Restricted or narrow shoulders have much the same effect, as drivers shy away from roadside objects or point restrictions perceived to be close enough to the roadway to pose a hazard. Motorists compensate for driving closer to opposing vehicles by slowing down and/or by leaving larger headways between vehicles in the same lane. Both reactions result in lower flow rates being sustained at any given speed. Factors reflecting this behavior are shown in Table 8-5, and are applied to v/c values taken from Table 8-1. Factors at capacity are higher than those for other levels of service, as the impact of narrow lanes and restricted shoulder widths is less deleterious when vehicles are already traveling at reduced speeds which prevail under capacity operation. 5. Adjustment for heavy vehicles in the traffic stream—The v/c ratios of Table 8-1 are based on a traffic stream consisting of only passenger cars. All vehicles having only four wheels contacting the pavement may be considered to be passenger cars. This includes light vans and pick-up trucks. ‘‘Heavy vehicles’’ are categorized as trucks, recreational vehicles, or buses, and the traffic stream is characterized by the proportion of such vehicles in the traffic mix. The adjustment factor for heavy vehicles, fHV, is computed using Eq. 8-2 and the passengercar equivalents given in Table 8-6. A wide range in the proportions of trucks and RV’s in the traffic stream are found on rural highways. Equation 8-2 will yield an adjustment factor for any given mix. In addition, there is some variation in the weight distribution between heavy (>35,000 lb) and medium-duty (≤35,000 lb) trucks. The equivalents of Table 8-6 assume a 50/50 distribution between heavy and medium-duty trucks. Two-lane highways serving unusually high proportions of heavy trucks, such as in coal, gravel, or timber operations, particularly those in mountainous terrain, would have higher values of ET than those shown in the table. The deleterious impact of heavy vehicles on two-lane highways increases markedly as terrain becomes more severe. As heavy vehicles slow on steeper grades, platoon formation becomes more frequent and severe. This effect is compounded by passing sight distance restrictions often accompanying severe terrain and leads to serious deterioration of traffic flow.
Analysis of Specific Grades
The analysis of extended specific grades on two-lane highways is more complex than for general terrain segments. The analysis procedures assume that the approach to the grade is level. On such grades, the operation of upgrade vehicles is substantially
two-lane highways
8-9
Table 8-4. Adjustment Factors for Directional Distribution on General Terrain Segments Directional Distribution
100/0
90/10
80/20
70/30
60/40
50/50
Adjustment Factor, fd
0.71
0.75
0.83
0.89
0.94
1.00
Table 8-5. Adjustment Factors for the Combined Effect of Narrow Lanes and Restricted Shoulder Width, fw 12-ft lanesb
11-ft lanesb
10-ft lanesb
9-ft lanesb
usablea shoulder width (ft)
los a–d
los e
los a–d
los e
los a–d
los e
los a–d
los e
≥6 4 2 0
1.00 0.92 0.81 0.70
1.00 0.97 0.93 0.88
0.93 0.85 0.75 0.65
0.94 0.92 0.88 0.82
0.84 0.77 0.68 0.58
0.87 0.85 0.81 0.75
0.70 0.65 0.57 0.49
0.76 0.74 0.70 0.66
a b
Where shoulder width is different on each side of the roadway, use the average shoulder width. For analysis of specific grades, use LOS E factors for all speeds less than 45 mph.
impacted, while downgrade vehicles experience far less impact. As a result, level-of-service criteria presented in Table 8-2 are based on the average upgrade travel speed. This speed is the average speed of all vehicles traveling up the grade. Where composite grades are present, the average grade is used in analysis. The average grade is the total rise, in feet, of the composite grade divided by the horizontal length of the grade, in feet, multiplied by 100 to adjust from a decimal to a percentage. The average upgrade speed at which capacity occurs varies between 25 and 40 mph, depending upon the percent grade, the percentage of no passing zones, and other factors. Because operating conditions at capacity vary for each grade, the finding of capacity is not as straightforward as service flow rate computations for levels-of-service A through D, where speed is established using the criteria of Table 8-2. Research has found that grades on two-lane highways have a more significant impact on operations than similar grades on multilane highways. Platoons forming behind slow-moving vehicles can be broken up or dissipated only by passing maneuvers using the opposing lane. On two-lane highways, the same geometric features causing platoons to form also tend to restrict passing opportunities as well. It has also been found that most passenger cars, even in the absence of heavy vehicles, are affected by extended grades, and will operate less efficiently than on level terrain. Additional operational problems due to vehicle stalls, accidents, or other incidents are not accounted for in the procedure. The effects of rain, snow, ice, and other negative environmental factors are also not considered. 1. Relationship between speed and service flow rate on specific grades—Average upgrade speeds on two-lane highways may be estimated for specific grades of a given percent and length of grade, assuming a level approach to the grade. Two-way service flow rates, SF, may be calculated for a specific level of service, or correspondingly, for any designated average upgrade speed. The need to provide a climbing lane based on AASHTO’s safety warrant is not part of the procedure, but sample calculation 5 illustrates the evaluation of a potential climbing lane.
Table 8-6. Average Passenger-Car Equivalents for Trucks, RV’s, and Buses on Two-Lane Highways Over General Terrain Segments type of terrain
vehicle type
level of service
level
rolling
mountainous
Trucks, ET
A B and C D and E
2.0 2.2 2.0
4.0 5.0 5.0
7.0 10.0 12.0
RV’s, ER
A B and C D and E
2.2 2.5 1.6
3.2 3.9 3.3
5.0 5.2 5.2
Buses, EB
A B and C D and E
1.8 2.0 1.6
3.0 3.4 2.9
5.7 6.0 6.5
source: Ref. 6
The service flow rate for any given average upgrade speed is given by the following relationship: SFi = 2,800 × (v/c)i × fd × fw × fg × fHV
(8-3)
where: SFi = service flow rate for level-of-service i, or speed i, total vph for both directions, for prevailing roadway and traffic conditions. (v/c)i = v/c ratio for level-of-service i or speed i, obtained from Table 8-7; fd = adjustment factor for directional distribution, obtained from Table 8-8; fw = adjustment factor for narrow lanes and restricted shoulder width, obtained from Table 8-5;
rural highways
8-10
fg = adjustment factor for the operational effects of grades on passenger cars, computed as described below; and fHV = adjustment factor for the presence of heavy vehicles in the upgrade traffic stream, computed as described subsequently. This relationship for specific grades is generally not applied to grades of less than 3 percent or shorter than 1/2 mile. 2. Adjustment for v/c ratio—Table 8-7 shows values of v/c ratio related to percent grade, average upgrade speed, and percent no passing zones. The values shown are the ratio of flow rate to an ideal capacity of 2,800 pcph, and assume that passenger cars are unaffected by extended grades. Another adjustment is applied to account for the impacts of grades on
passenger-car operation. This is an important point, because a v/c ratio of 1.00 in Table 8-7 DOES NOT necessarily signify capacity. The solution for capacity of an extended grade is discussed later. However, solutions for capacity or service flow rate exceeding 2,000 vph total indicate that the specific grade is not affecting operations and that the general terrain methodology should be used. Values of v/c approaching or equal to 0.00 mean that the associated average upgrade speed is difficult or impossible to achieve for the percent grade and percent no passing zones indicated. 3. Adjustment for directional distribution—On extended grades, the directional distribution can be a critical factor affecting operations. Table 8-8 contains adjustment factors for a range of directional distributions with a significant upgrade component.
Table 8-7. Value of v/c Ratioa vs. Speed, Percent Grade, and Percent No Passing Zones for Specific Grades percent grade 3
4
5
6
7
a
percent no passing zones
average upgrade speed (mph)
0
20
40
60
80
100
55 52.5 50 45 42.5 40 55 52.5 50 45 42.5 40 55 52.5 50 45 42.5 40 35 55 52.5 50 45 42.5 40 35 30 55 52.5 50 45 42.5 40 35 30
0.27 0.42 0.64 1.00 1.00 1.00 0.25 0.40 0.61 0.97 0.99 1.00 0.21 0.36 0.57 0.93 0.97 0.98 1.00 0.12 0.27 0.48 0.85 0.93 0.97 1.00 1.00 0.00 0.13 0.34 0.77 0.86 0.93 1.00 1.00
0.23 0.38 0.59 0.95 0.98 1.00 0.21 0.36 0.56 0.92 0.96 1.00 0.17 0.31 0.49 0.84 0.90 0.96 1.00 0.10 0.22 0.40 0.76 0.84 0.91 0.96 0.99 0.00 0.10 0.27 0.65 0.75 0.82 0.91 0.95
0.19 0.33 0.55 0.91 0.97 1.00 0.18 0.31 0.52 0.88 0.95 1.00 0.14 0.27 0.45 0.79 0.87 0.95 1.00 0.08 0.18 0.35 0.68 0.78 0.87 0.95 0.99 0.00 0.08 0.22 0.55 0.67 0.75 0.87 0.92
0.17 0.31 0.52 0.88 0.96 1.00 0.16 0.29 0.49 0.85 0.94 1.00 0.12 0.24 0.41 0.75 0.85 0.94 1.00 0.06 0.16 0.31 0.63 0.74 0.83 0.93 0.98 0.00 0.07 0.18 0.46 0.60 0.69 0.82 0.90
0.14 0.29 0.49 0.86 0.95 1.00 0.13 0.27 0.47 0.83 0.93 1.00 0.10 0.22 0.39 0.72 0.83 0.93 1.00 0.05 0.14 0.28 0.59 0.70 0.81 0.91 0.98 0.00 0.05 0.15 0.40 0.54 0.64 0.79 0.88
0.12 0.27 0.47 0.84 0.94 1.00 0.11 0.25 0.45 0.81 0.92 1.00 0.08 0.20 0.37 0.70 0.82 0.92 1.00 0.04 0.13 0.26 0.55 0.67 0.78 0.90 0.98 0.00 0.04 0.12 0.35 0.48 0.59 0.76 0.86
Ratio of flow rate to ideal capacity of 2,800 pcph, assuming passenger-car operation is unaffected by grade. NOTE: Interpolate for intermediate values of ‘‘Percent No Passing Zone’’; round ‘‘Percent Grade’’ to the next higher integer value.
two-lane highways Table 8-8. Adjustment Factor for Directional Distribution on Specific Grades, fd percent of traffic on upgrade
adjustment factor
100 90 80 70 60 50 40 ≤ 30
0.58 0.64 0.70 0.78 0.87 1.00 1.20 1.50
(8-4)
fg = adjustment factor for the operation of passenger cars on grades; PP = proportion of passenger cars in the upgrade traffic stream, expressed as a decimal; IP = impedance factor for passenger cars, computed as: (8-5)
E = base passenger-car equivalent for a given percent grade, length of grade, and speed, selected from Table 8-9; and Eo = base passenger-car equivalent for 0 percent grade and a given speed, selected from Table 8-9. The passenger-car equivalents of Table 8-9 are used for both the passenger-car and heavy vehicle adjustment factors. The passenger-car factor adjusts from the base v/c ratios, which assume no operational impact of grades on cars, to prevailing conditions of grade. The heavy vehicle adjustment factor is based on passenger-car equivalents related to passenger cars operating on the grade specified. 6. Adjustment for heavy vehicles in the traffic stream—The adjustment factor for heavy vehicles is computed as follows: fHV = 1/[1 + PHV (EHV − 1)]
(8-7)
PT/HV = proportion of trucks among heavy vehicles, i.e., the proportion of trucks in the traffic stream divided by the total proportion of heavy vehicles in the traffic stream; and E = base passenger-car equivalent for a given percent grade, length of grade, and speed, selected from Table 8-9.
where:
IP = 0.02 (E − Eo)
PHV = total proportion of heavy vehicles (trucks + RV’s + buses) in the upgrade traffic stream; EHV = passenger-car equivalent for specific mix of heavy vehicles present in the upgrade traffic stream, computed as: EHV = 1 + (0.25 + PT/HV) (E − 1)
4. Adjustment for narrow lanes and/or restricted shoulder width—The impact of narrow lanes and/or restricted shoulder widths on grades is the same as for general terrain segments. The appropriate factor is selected from Table 8-5, presented previously. 5. Adjustment for passenger cars on grades—The v/c ratios of Table 8-7 assume that passenger cars will maintain their speed on grades if unimpeded. Recent studies (1,2) have indicated that passenger-car operation is affected by grades, even where heavy vehicles are not present in the traffic stream. The factor fg adjusts the v/c ratios of Table 8-7 to account for this effect. The factor is computed as: fg = 1/[1 + (PPIP)]
8-11
(8-6)
where: fHV = adjustment factor for the presence of heavy vehicles in the upgrade traffic stream;
The passenger-car equivalents presented in Table 8-9 represent an average mix of trucks, recreational vehicles, and buses in the traffic stream. This average mix is for 14 percent trucks, 4 percent RV’s, and no buses. The values of EHV computed by this procedure yield equivalent volumes which travel at the same average overall speed as the actual mixed traffic stream under stable flow conditions. Any tendency of vehicles to stall or perform sluggishly at high volume levels and power requirements is not accounted for in these procedures. The existence of heavy vehicles on two-lane highway grades is a particularly difficult problem, because an increase in formation of platoons is caused at the same time as passing restrictions usually also increase. Thus, the decision of whether to provide a climbing lane for heavy vehicles is often a critical one for extended grades on two-lane highways. A common criterion sometimes used in the design of grades is to include a climbing lane where the operating speed of trucks falls 10 mph or more (11). Figures 8-2 and 8-3 show speed reduction curves for a 200-lb/hp truck and a 300-lb/hp truck. The former is considered indicative of a representative truck for the average mix of trucks occurring on two-lane highways. The latter is representative of a ‘‘heavy’’ truck, such as heavily loaded farm vehicles, coal carriers, gravel carriers, or log carriers. The choice of which type of truck should be used is based on safety considerations. Speed reduction is related to the steepness and length of the grade in Figures 8-2 and 8-3. For a more detailed depiction of the operating characteristics of trucks on extended upgrades, the truck performance curves included in Appendix I of Chapter 3 may be consulted. In addition to the 10-mph speed reduction criterion, a climbing lane might be considered wherever a level-of-service analysis indicates a serious deterioration in operating quality on an extended grade when compared to the adjacent approach segment of the same highway. Heavy vehicles in the traffic stream on extended grades also cause delay to other vehicles. Delay can be evaluated as the difference in travel time between what vehicles could achieve if unimpeded by heavy vehicles and the travel time actually experienced in the mixed traffic stream. Sample calculations illustrate the computation of this delay. 7. Capacity of specific grade segments—Sections 1 through 6 above describe the computation of service flow rates on specific two-lane highway grades. For levels-of-service A through D, this is a simple process. The speed relating to the desired LOS
rural highways
8-12
Table 8-9. Passenger-Car Equivalents for Specific Grades of Two-Lane Rural Highways, E and EO
grade (%)
length of grade (mi)
55.0
52.5
50.0
45.0
40.0
30.0
0
All
2.1
1.8
1.6
1.4
1.3
1.3
3
1
⁄4 ⁄2 3 ⁄4 1 1 1⁄ 2 2 3 4
2.9 3.7 4.8 6.5 11.2 19.8 71.0
2.3 2.9 3.6 4.6 6.6 9.3 21.0 48.0
2.0 2.4 2.9 3.5 5.1 6.7 10.8 20.5
1.7 2.0 2.3 2.6 3.4 4.6 7.3 11.3
1.6 1.8 2.0 2.3 2.9 3.7 5.6 7.7
1.5 1.7 1.9 2.1 2.5 2.9 3.8 4.9
1
⁄4 ⁄2 3 ⁄4 1 1 1⁄ 2 2 3 4
3.2 4.4 6.3 9.6 19.5 43.0
2.5 3.4 4.4 6.3 10.3 16.1 48.0
a
a
2.2 2.8 3.5 4.5 7.4 10.8 20.0 51.0
1.8 2.2 2.7 3.2 4.7 6.9 12.5 22.8
1.7 2.0 2.3 2.7 3.8 5.3 9.0 13.8
1.6 1.9 2.1 2.4 3.1 3.8 5.5 7.4
1
⁄4 ⁄2 3 ⁄4 1 1 1⁄ 2 2 3 4
3.6 5.4 8.3 14.1 34.0 91.0
2.8 3.9 5.7 8.4 16.0 28.3
a
a
2.3 3.2 4.3 5.9 10.8 17.4 37.0
a
a
a
2.0 2.5 3.1 4.0 6.3 10.2 22.0 55.0
1.8 2.2 2.7 3.3 4.9 7.5 14.6 25.0
1.7 2.0 2.4 2.8 3.8 4.8 7.8 11.5
1
⁄4 ⁄2 3 ⁄4 1 1 1⁄ 2 2 3 4
4.0 6.5 11.0 20.4 60.0
3.1 4.8 7.2 11.7 25.2 50.0
2.5 3.7 5.2 7.8 16.0 28.2 70.0
2.1 2.8 3.7 4.9 8.5 15.3 38.0 90.0
1.9 2.4 3.1 4.0 6.4 10.7 23.9 45.0
1.8 2.2 2.7 3.3 4.7 6.3 11.3 18.1
1
2.2 3.2 4.3 6.1 11.5 22.8 66.0
2.0 2.7 3.6 4.8 8.4 15.4 38.5
a
a
1.9 2.4 3.0 3.8 5.8 8.2 16.1 28.0
1
4
1
5
1
6
1
7
⁄4 ⁄2 3 ⁄4 1 1 1⁄ 2 2 3 4 1
average upgrade speed (mph)
a
a
a a
a
a
a
a
4.5 7.9 14.5 31.4
3.4 5.7 9.1 16.0 39.5 88.0
2.7 4.2 6.3 10.0 23.5 46.0
a
a
a
a
a
a
a a
a
Speed not attainable on grade specified. NOTE: Round ‘‘Percent Grade’’ to next higher integer value.
is selected from Table 8-2, and appropriate adjustment factors are selected for use in Eq. 8-3. The service flow rate at capacity, i.e., SFE, is not as easily determined, because the speed at which it occurs varies depending on the percent and length of the grade in question. For the normal range of grades, i.e., 3 to 7 percent up to 4 miles long, capacity may occur at speeds ranging from 25 to 40 mph. The speed at which capacity occurs is related to the flow rate at capacity by the following equation: Sc = 25 + 3.75(vc /1000)2
(8-8)
where: Sc = speed at which capacity occurs, in mph; and vc = flow rate at capacity, in mixed vph. For convenience, the equation predicts upgrade speeds based on total two-way flow rates. The equation is valid for speed up to 40 mph. If the service flow rates computed for various speeds using Eq. 8-3 and the capacity speed vs. capacity flow rate relationship of Eq. 8-8 are plotted, the two curves will intersect. The inter-
two-lane highways
8-13
Figure 8-2. Speed reduction curve for a 200-lb/hp truck.
Figure 8-3. Speed reduction curve for a 300-lb/hp truck.
section defines both the speed at capacity and the flow rate at capacity for the grade in question. This procedure for determining capacity is illustrated in the sample calculations.
The AADT’s presented in Table 8-10 illustrate a wide range of conditions, and were computed from service flow rates as follows:
AADTi = SFi × PHF/K
HIGHWAY SYSTEM PLANNING
The planning procedure enables highway operating agencies to perform very general planning and policy studies of a rural twolane highway system. Traffic, geometric, and terrain data would be only generally classified, with traffic demand expressed in terms of an average annual daily traffic (AADT), perhaps of some future forecast year. Table 8-10 presents estimated maximum AADT’s for two-lane highways as related to: 1. Level of service. 2. Type of terrain. 3. Design hour factor, K. The levels of service refer to operating conditions within the peak 15-min period of the day. In constructing Table 8-10, the default values of the peak hour factor (PHF) shown in Table 8-3 were assumed. For each level of service, the related percent time delay criteria were applied across all three types of terrain. The planning criteria also assume a typical traffic mix of 14 percent trucks, 4 percent RV’s, and no buses. A 60/40 directional split is used, along with percent no passing zone values of 20 percent, 40 percent, and 60 percent for level, rolling, and mountainous terrain, respectively. Ideal geometrics of 12-ft lanes, 6-ft shoulders, and 60-mph design speed were used.
(8-9)
where: AADTi = the maximum AADT for level-of-service i, based on the assumed conditions described above, in vpd; SFi = maximum service flow rate for level-of-service i, computed from Eq. 8-3, based on the assumed conditions described above, in vph; PHF = peak hour factor, selected from Table 8-3 for the indicated level of service; and K = design hour factor, i.e., the proportion of AADT expected to occur in the design hour. The K-factor is normally expressed in design problems as DHV = AADT × K, where the DHV is the total two-way design hour volume, and K is estimated from the ratio of the 30th HV to the AADT from a similar site. The 30th HV is the 30th highest hourly volume during the year and is often used as a design volume for rural highways. Since the DHV should be less than SFi for the selected level of service, the actual AADT for a road should be less than the maximum value shown in Table 8-10. Traffic conditions occurring during the highest hourly volume of the year (1st HV) would usually be no worse than one level of service less than that existing for the 30th HV for most rural highways.
rural highways
8-14
Table 8-10. Maximum AADT’s vs. Level of Service and Type of Terrain for Two-Lane Rural Highways level of service k-factor
a
b
c
d
e
7,900 7,200 6,600 6,100 5,700 5,300
13,500 12,200 11,200 10,400 9,600 9,000
22,900 20,800 19,000 17,600 16,300 15,200
8,000 7,200 6,600 6,100 5,700 5,300
14,800 13,500 12,300 11,400 10,600 9,900
3,700 3,400 3,100 2,900 2,700 2,500
8,100 7,300 6,700 6,200 5,800 5,400
Level Terrain 0.10 0.11 0.12 0.13 0.14 0.15
2,400 2,200 2,000 1,900 1,700 1,600
4,800 4,400 4,000 3,700 3,400 3,200
Rolling Terrain 0.10 0.11 0.12 0.13 0.14 0.15
1,100 1,000 900 900 800 700
2,800 2,500 2,300 2,100 2,000 1,800
5,200 4,700 4,400 4,000 3,700 3,500
Mountainous Terrain 0.10 0.11 0.12 0.13 0.14 0.15
500 400 400 400 300 300
1,300 1,200 1,100 1,000 900 900
2,400 2,200 2,000 1,800 1,700 1,600
NOTE: All values rounded to the nearest 100 vpd. Assumed conditions include 60/40 directional split, 14 percent trucks, 4 percent RV’s, no buses, and PHF values from Table 8-3. For level terrain, 20 percent no passing zones were assumed; for rolling terrain, 40 percent no passing zones; for mountainous terrain, 60 percent no passing zones.
III. PROCEDURES FOR APPLICATION The methodology described in the previous section is generally applied in either the operational analysis or planning mode. Design computations, as used in this manual, focus on the determination of the number of lanes required for a given facility. Such computations have little significance for two-lane highways, where the number of lanes is fixed. Such design features as horizontal and vertical alignment, however, have a significant impact on operations. Operational analyses can be performed for alternative designs to document this impact. Where computations indicate that a two-lane highway is not adequate for existing or projected demands, various multilane options may be considered and analyzed using other chapters of this manual. A separate section of this chapter deals with operational and design measures for two-lane highways, short of reconstructing the entire highway as a multilane facility. This material should be consulted where a two-lane facility presently has or is expected to experience operational difficulties.
OPERATIONAL ANALYSIS OF GENERAL TERRAIN SEGMENTS
The objective in operational analysis is to determine the level of service for a given segment or segments of roadway for a known existing set of conditions, or for a future set of conditions
which are hypothesized and/or forecast. The general approach will be to compute service flow rates for each level of service and compare these values with the existing flow rate on the facility. This is done using Eq. 8-1: SFi = 2,800 × (v/c) i × fd × fw × fHV where all terms are as previously defined. A service flow rate for each LOS is computed because the heavy vehicle factor varies with LOS, and a direct solution of the equation for v/c ratio would be iterative. Users preferring to solve for v/c may do so, but must iterate until the assumed LOS used in computing the heavy vehicle factor is the same as that indicated by the v/c ratio found. In general, the following computational steps are used. Computations may be conveniently performed on the worksheet illustrated in Figure 8-4. 1. Summarize all input data on traffic and roadway conditions, including: T Existing or forecast peak hour volume, in vph. T Peak hour factor, PHF, from local data or default value selected from Table 8-3. T Traffic composition (% trucks, % RV’s, % buses).
two-lane highways
8-15
Figure 8-4. Worksheet for operational analysis of general terrain segments.
T Directional distribution of traffic. T Terrain type. T Lane and usable shoulder widths, in ft. T Design speed, in mph. 2. Select appropriate values of the following factors for each LOS from the tables indicated: T The v/c ratio from Table 8-1. T The directional distribution factor, fd, from Table 8-4. T The lane width and shoulder width factor, fw, from Table 8-5. T Passenger-car equivalents, ET, ER, and EB, for trucks, RV’s, and buses, from Table 8-6. 3. Compute the heavy vehicle factor, fHV, for each LOS from: fHV = 1/[1 + PT (ET − 1) + PR(ER − 1) + PB(EB − 1)]
alleviation measures presented in the next section should be considered, as well as the expansion of the facility to four or more lanes. Expansion to a multilane facility should be examined using the methodology presented in Chapter 7. OPERATIONAL ANALYSIS OF SPECIFIC GRADES
The operational analysis of specific grades is similar to the procedure for general terrain segments. The level of service for the upgrade direction is sought, and is found by comparing an actual two-way flow rate to the service flow rates for the various levels of service. As noted in the ‘‘Methodology’’ section, however, the determination of capacity for specific grades requires the plotting of a service flow rate-speed curve, and a curve representing the relationship of speed at capacity to flow rate at capacity. The worksheet shown in Figure 8-5 is used to simplify the following computational steps.
4. Compute the service flow rate, SF, for each LOS from: SFi = 2,800 × (v/c)i × fd × fw × fHV 5. Convert the existing or forecast volume to an equivalent flow rate, as follows: v = V/PHF. 6. Compare the actual flow rate of step 5 with the service flow rate of step 4 to determine the level of service. Where the level of service is found to be inadequate, the
1. Summarize all required input data on traffic and roadway conditions, including: T Existing or forecast peak hour volume, in vph. T Peak hour factor, PHF, from local data or default value from Table 8-3. T Traffic composition (% trucks, % RV’s, % buses, % passenger cars). T Directional distribution of traffic.
Figure 8-5(a). Worksheet for operational analysis of specific grades on two-lane highways (page 1).
Figure 8-5(b). Worksheet for operational analysis of specific grades on two-lane highways (page 2).
8-16
rural highways
two-lane highways T T T T T
Percent grade. Percent no passing zones. Length of grade, in miles. Lane and usable shoulder width, in ft. Design speed, in mph.
2. Select values of the following factors from the indicated tables for the following average speeds: 55 mph (LOS A), 52.5 mph, 50 mph (LOS B), 45 mph (LOS C), 40 mph (LOS D), and 30 mph. This range of speeds will allow the plotting of a service flow rate vs. speed curve to find capacity and the speed at capacity. The v/c ratio from Table 8-7. The directional distribution factor, fd, from Table 8-8. The lane and shoulder width factor, fw, from Table 8-5. The passenger-car equivalent, E, for the percent and length of grade, from Table 8-9. T The passenger-car equivalent, Eo, for a 0 percent grade, from Table 8-9.
T T T T
3. Compute the grade factor, fg, as follows: fg = 1/[1 + PpIp]
8-17
6. Plot the service flow rates vs. speeds resulting from the computations of steps 2–5 on the grid included in the worksheet of Figure 8-5. Note that the curve for speed at capacity vs. flow rate at capacity is already drawn on this grid. 7. Find the speed at capacity and the service flow rate at capacity from the intersection of the two curves on the plot of step 6. 8. Summarize the service flow rates for each level of service on the worksheet as indicated. 9. Convert the actual or forecast volume to a flow rate, as follows: v = V/PHF. 10. Compare the actual flow rate of step 9 with the service flow rates of step 8 to determine the level of service. As with general terrain segments, a two-lane highway grade displaying unacceptable operating conditions would be considered for improvement. If heavy vehicles on the upgrade are the principal difficulty, the addition of a truck climbing lane should be considered. If operational problems are more broad-based, any of the alleviation techniques discussed in the next section could be considered, as well as expansion of the facility to four or more lanes. Again, the multilane option would be examined using procedures in Chapter 7.
Ip = 0.02(E − Eo) PLANNING
where all values are as previously defined. 4. Compute the heavy vehicle factor, fHV, for each of the speeds noted in step 2 as follows: fHV = 1/[1 + PHV (EHV − 1)] EHV = 1 + (0.25 + PT/HV)(E − 1) PT/HV = PT /[PT + PR + PB] where all values are as previously defined. 5. Compute the service flow rate, SF, for each of the speeds noted in step 2 as follows: SFi = 2,800 × (v/c)i × fd × fw × fg × fHV
The highway system planning technique described in the ‘‘Methodology’’ section is easily applied. Table 8-10 may be entered with a known or forecast AADT to determine expected level of service during the peak 15 min of flow, or with a known LOS to find the maximum allowable AADT. No computations are needed to use this table, although users are cautioned that any conditions varying widely from those noted in the footnotes to Table 8-10 will indicate the need to conduct an operational analysis for the facility in question. Users may also find Table 8-10 useful in making preliminary estimates of LOS in general terrain segment analysis.
IV. DESIGN AND OPERATIONAL TREATMENTS Addressing those operational problems that may exist on rural two-lane highways requires an understanding of the nature of twolane highway systems. Only about 30 percent of all travel in the United States occurs on rural two-lane roads, even though this network comprises 80 percent of all paved rural highways. For the most part, two-lane highways carry light traffic and experience few operational problems. Highway agencies are typically more concerned with pavement maintenance and roadside safety issues on such highways. Some two-lane highways, however, periodically experience
severe operational and safety problems due to a variety of traffic, geometric, and environmental causes. Special treatments for such highways may be needed before capacity levels are approached. In some areas, the two-lane rural arterial system carries a disproportionately large share of rural traffic, including significant components involved in interstate commerce. Many of these highways are located near major urban areas and are experiencing rapid growth in traffic. Heavy turning movements to roadside developments can block through traffic and increase delay.
8-18
rural highways
As much as 60 percent of all two-lane highway mileage is located in terrain classified as rolling or mountainous. This, coupled with occasionally high opposing volumes, is not favorable to either passing or turning maneuvers. When these and other rural highways experience increased recreational travel, major operational problems may arise. Large numbers of recreational and other heavy vehicles in the traffic stream increase the demand for passing, while at the same time making such maneuvers more difficult. Two-lane highways serving as major routes to recreational areas may operate at or near capacity on weekends in peak seasons. When any of the foregoing situations exist, the frequent result is a reduced level of service, increased platooning, increased delay, an increase in questionable passing maneuvers, and generally frustrated drivers. Nevertheless, many such situations do not justify the reconstruction of the two-lane highway to a full multilane facility. In these cases, one or more of the special design and/or operational treatments discussed in this section may be useful. A wide range of design and operational solutions are needed to address the variety of problems encountered on two-lane highways. The operational and/or safety problems on a particular section may be so severe as to call for an expansion of the facility to four or more lanes. However, limited reconstruction funds, difficult terrain, and other problems may not always permit full reconstruction of a two-lane facility as a multilane highway. Less costly and less environmentally disruptive solutions may be required. Highways experiencing less severe operational and/or safety problems, together with those experiencing site-specific reductions in level of service, may be candidates for treatment with one or more of the following alleviation techniques: 1. Realignment to improve passing sight distance. 2. Use of paved shoulders. 3. Three-lane roadways with two lanes designated for travel in one direction (passing prohibited or permitted in opposing direction). 4. Three-lane road sections with continuous two-way median left-turn lanes. 5. Three-lane roadway with reversible center lane. 6. Special intersection treatments. 7. Truck or heavy vehicle climbing lanes. 8. Turnouts. 9. Short four-lane segments. Selection of the appropriate treatment requires identification of the probable causes of the operational and safety problems existing, and the determination of cost-effectiveness of the design alternatives for a given set of highway geometric, traffic, and system constraints. The following discussions address the use of alleviation measures on two-lane highways. They are intended to provide the user with general information, and should not be construed as firm guidelines or criteria.
PASSING SIGHT DISTANCE
The opportunity to pass, given a constant volume, is a function of the availability of passing sight distance. Provision of passing sight distance is an important component in basic two-lane
highway design and, as illustrated by Tables 8-1 and 8-7, has a critical impact on capacity and service flow rate. Where long queues are likely to form because of severe passing restrictions, every effort should be made to continuously and completely disperse the platoon once significant passing sight distance is regained. In these passing sections, short segments with passing sight distance restrictions should be avoided where possible. Inclusion of periodic passing lanes for each direction should be considered where the distance between segments with passing sight distance available is long and queuing extensive.
PAVED SHOULDERS
A roadway that is constructed with structurally adequate paved shoulders can be used to assist in dispersal and breakup of platoons. Slower moving vehicles may temporarily use the shoulder to permit faster vehicles to pass, returning to the travel lane when passing maneuvers have been completed. In Texas and Canada, where some agencies construct wide shoulders for a total roadway width of 40 to 44 ft, a high percentage of the driving population uses the shoulder in this manner—particularly in western Canada where long distance recreational travel is heavy during the summer. Illustration 8-2 presents a typical use of paved shoulders as described previously. Five states allow the use of shoulders for slow-moving vehicles at all times. An additional ten states permit such use under specified conditions.
THREE-LANE HIGHWAYS
Three-lane roadways are a rational intermediate solution to fourlane expansions for two-lane highways experiencing operational problems. Because of funding and terrain constraints, three-lane roadways may be considered for spot and segment improvements. There are numerous methods for using the third travel lane on such segments. In the 1940’s and 1950’s, the third (center) lane was used for passing by vehicles in either direction—the first vehicle to occupy the center lane had the right-of-way. This condition was found to be hazardous, particularly in hilly terrain. This use of three-lane highways in the United States has been generally discontinued. Other three-lane highway treatments are being safely and efficiently applied, including the use of passing lanes, turning lanes, and climbing lanes.
Passing Lanes
This three-lane roadway design assigns the third (center) lane to one direction of travel for a short distance (approximately 1 mile), then alternates the assignment of the passing lane to the other direction. This cyclic process may be continued along an entire highway section, or may be combined in an urban fringe area with two-way left-turn lanes and/or specific intersection turning treatments. In a rural setting, intermittently spaced passing lane sections have been successfully used to break up platoons and reduce delay. Two lanes are provided for unimpeded passing in one direction for 1 to 2 miles followed by a transition to two lanes
two-lane highways
8-19
Illustration 8-2. Slow-moving vehicle uses the shoulder of a two-lane rural highway, permitting faster vehicles to pass.
of similar design for the opposing flow. Advance signing advises motorists of the next upcoming passing lane to reduce driver anxiety and frustration. Two operational markings are practiced: passing in the single-lane direction may be permitted if passing sight distance is available, or passing in the single-lane direction
may be prohibited. Figure 8-6 depicts these markings, and various methods of providing for the transition when the direction of the passing lane is changed. Permissive passing for the onelane direction is not used by some agencies when the AADT exceeds about 3,000 vpd.
Figure 8-6. Use of third lane for passing lanes.
rural highways
8-20
Table 8-11. Spacing of Passing Lanes on Two-Lane Highways Two-Way Peak Hourly Volume (vph)
400
300
200
Distance to Next Passing Lane (miles)
5
6.5
9
Detailed analysis of intersections may be performed using the procedures of Chapter 9, ‘‘Signalized Intersections,’’ and Chapter 10, ‘‘Unsignalized Intersections.’’
Climbing Lanes
An analytic study of passing lane requirements was conducted in Ontario, Canada (7). This study recommended that passing lanes should consistently be from 1.0 to 1.25 miles long. This length was found to be adequate to disperse most platoons, to provide for additional transition zones, and yet not be too long to change drivers’ expectations about the true nature of the highway. Table 8-11 gives the recommended spacing between passing lanes in a given direction which resulted from the study. Continuous Two-Way Median Left-Turn Lanes
On two-lane highways having sizable left-turn traffic, a single travel lane in each direction often becomes subject to long delays as vehicles await opportunities to complete left turns. By providing a continuous refuge area for left-turning traffic, the two-way leftturn lane can help to maintain through traffic capacity, with the added benefit of separating opposing flows. The ability to pass, however, is eliminated. Two-way left-turn lanes are not usually used where speeds are less than 25 mph or more than 50 mph, and are most often used in urban fringe areas or on a major route passing through a small town or village. Reversible Lane
This is another use of the third (center) lane of a three-lane highway which is most applicable where travel demands are of a tidal nature—that is, extreme directional splits occur. The center lane is reversed by time of day to match the peak flow. The center lane is controlled by overhead signs or traffic signals indicating the direction of travel assigned at the time. Passing is not permitted in this application in the direction of the single lane. The reversible lane technique is most applicable to routes joining residential areas and high-employment centers, and for many recreational routes. Intersection Treatments
Conventional analysis of two-lane highways assumes uninterrupted flow, which is normally representative of rural conditions. With increasing development occurring in some rural areas, and in suburban fringe areas, the demand for high-volume access and egress can grow. Major intersections along two-lane highways become more common and important to the overall quality of flow on main routes. Adequate protected turning lanes for both left and right turns are useful in minimizing disruption to through traffic. Bypass lanes for through traffic may be considered where a protected left-turn lane is not feasible, particularly where paved shoulders are provided and/or where Tintersections are involved.
Traditional climbing lanes also form three-lane cross sections when used in conjunction with two-lane highways. They are generally applied as a spot improvement, most often on steep, sustained grades which cause heavy vehicles, particularly heavy trucks, to travel at slow speeds. This reduces capacity, creates platoons, and increases delay. Additionally, safety problems may arise when the reduction in speed of heavy trucks exceeds 10 mph along the grade. Estimated operating speed characteristics of trucks are illustrated in Figures I.3-1, I.3-2, and I.3-3 in Appendix I of Chapter 3. Resulting lengths of grade producing 10-mph speed reductions are plotted in Figures 8-2 and 8-3, presented earlier in this chapter. AASHTO presently warrants a climbing lane wherever the speed of a 300-lb/hp truck is reduced by 10 mph or more and the volume and percentage of heavy trucks justify the added cost. One set of criteria that might be applied to reflect the economic considerations is: 1. Upgrade traffic flow rate exceeds 200 vph. 2. Upgrade truck flow rate exceeds 20 vph. 3. One of the following conditions exists: T Level-of-service E or F exists on the grade. T A reduction of two or more levels of service is experienced when moving from the approach segment to the grade. T A 10-mph or greater speed reduction is expected for a typical heavy truck. These general guides for the consideration of climbing lanes on grades would apply only to climbing lanes on two-lane highways and should not be used in conjunction with consideration of climbing lanes on multilane highways.
Turnouts
The use of turnouts for improving the level of service on twolane, two-way highways is more prevalent in the rolling and mountainous terrain of the western United States. Turnouts are short segments of a third lane added to one side of the highway or the other which permit slow vehicles at the head of platoons to pull off the main roadway, allowing faster vehicles to pass. Turnouts are used satisfactorily on both upgrades and downgrades, as well as on level terrain, to improve traffic flow. Impeding motorists are legally required to use turnouts where provided under certain prescribed conditions, which vary by state. A recent study of operational characteristics revealed that few drivers actually stop at turnouts (8). Several additional conclusions drawn from this study included: 1. Turnouts are safe when properly used. 2. A series of turnouts at regular intervals can provide considerable delay reduction.
two-lane highways 3. Turnouts are not a substitute for a passing or climbing lane of adequate length. 4. About 10 percent of all platoon leaders use properly designated turnouts. 5. Large trucks tend to avoid turnouts. Turnouts are a short but functional treatment of irritating causes of operational delay. A western state recommends that the length of turnouts vary with approach speed according to the criteria of Table 8-12 (9). Approach speeds of potential turnout-users vary with prevailing traffic and roadway conditions, and differ between upgrades and downgrades. Turnout lengths of more than 500 ft are only used on downgrades exceeding 3 percent where high approach speeds are expected to exist. Lengths greater than 600 ft are never designed, as drivers may mistakenly attempt to use them as passing lanes.
SHORT FOUR-LANE SECTIONS
Short sections of four-lane cross section may be constructed along a primarily two-lane highway to break up platoons, to provide the desired frequency of safe passing zones, and to eliminate interference from low-speed vehicles. Such sections are particularly advantageous in rolling terrain, or where the alignment is winding or the profile includes critical grades from
8-21
Table 8-12. Length of Turnouts on Two-Lane Highways Approach Speed (mph) Minimum Length of Turnout (ft)
25
30
40
50
55
60
200
200
250
375
450
535
both directions. The decision to use a short four-lane segment, as compared to using a three-lane option, may be based on longrange planning objectives for the facility, availability of rights-ofway, existing cross section, topography, and on the desire to reduce platooning and passing problems. The transition from a two-lane to a four-lane roadway should be designed to provide sufficient sight distance for passing. For the length of four-lane segments, AASHTO suggests that they be sufficiently long to permit several vehicles in line behind a slow-moving vehicle to pass before reaching the normal section of two-lane highway. Four-lane sections of 1.0 to 1.5 miles should be sufficiently long to dissipate most queues formed, depending on volume and terrain conditions. Further, it is noted that sections of four-lane highway, particularly divided sections, longer than 2 miles may cause drivers to lose their sense of awareness that the road is basically a two-lane facility.
V. SAMPLE CALCULATIONS CALCULATION 1—FINDING SERVICE FLOW RATES FOR A GENERAL TERRAIN SEGMENT
1. Description—A segment of rural two-lane highway is expected to have the following characteristics: a. Roadway characteristics—70-mph design speed; 12-ft lanes; 10-ft paved shoulders; level terrain; 0 percent no passing zones; length = 5 miles. b. Traffic characteristics—70/30 directional split; 10 percent trucks; 5 percent recreational vehicles; 1 percent buses; 84 percent passenger cars. What is the capacity of the section? What is the maximum flow rate which can be accommodated at level-of-service C? 2. Solution—The solution to this problem is found by computing the service flow rates for levels-of-service C and E (capacity), using Eq. 8.1: SFi = 2,800 × (v/c)i × fd × fw × fHV where fHV = 1/[1 + PT (ET − 1) + PR(ER − 1) + PB(EB − 1)] The following values are selected for use in these computations:
(v/c)C = 0.43 (Table 8-1, level terrain 0 percent no passing zones, LOS C); (v/c)E = 1.00 (Table 8-1, level terrain, 0 percent no passing zones, LOS E); fd = 0.89 (Table 8-4, 70/30 split); fw = 1.00 (Table 8-5, 12-ft lanes, >6-ft shoulders); ET = 2.2 for LOS C, 2.0 for LOS E (Table 8-6, level terrain); ER = 2.5 for LOS C, 1.6 for LOS E (Table 8-6, level terrain); EB = 2.0 for LOS C, 1.6 for LOS E (Table 8-6, level terrain); PT = 0.10 (Given); PR = 0.05 (Given); and PB = 0.01 (Given).
Then: fHV(LOS C) = 1/[1 + 0.10(2.2 − 1) + 0.05(2.5 − 1) + 0.01(2.0 − 1)] = 0.83 fHV(LOS E) = 1/[1 + 0.10(2.0 − 1) + 0.05(1.6 − 1) + 0.01(1.6 − 1)] = 0.88
Figure 8-7. Worksheet summarizing solution to Calculation 1.
Figure 8-8. Worksheet summarizing solution to Calculation 2.
8-22
rural highways
two-lane highways
8-23
PT = 0.05 (Given); and PR = 0.10 (Given).
and: SFC = 2,800 × 0.43 × 0.89 × 1.00 × 0.83 = 889 vph SFE = 2,800 × 1.00 × 0.89 × 1.00 × 0.88 = 2,193 vph Thus, the highway will have an expected capacity of 2,193 vph, total in both directions, and can accommodate a flow rate of up to 889 vph at level-of-service C. The worksheet for general terrain sections may be used to perform these computations, as shown in Figure 8-7.
Then: fHV (LOS A) = 1/[1 + 0.05(7 − 1) + 0.10(5.0 − 1)] = 0.588 (LOS B, C) = 1/[1 + 0.05(10 − 1) + 0.10 (5.2 − 1)] = 0.535 (LOS D, E) = 1/[1 + 0.05(12 − 1) + 0.10(5.2 − 1)] = 0.508 and: SFA = 2,800 × 0.02 × 0.94 × 0.75 × 0.588 = 23 vph
CALCULATION 2—FINDING LEVEL OF SERVICE FOR A GENERAL TERRAIN SEGMENT
1. Description—A two-lane rural highway carries a peak hour volume of 180 vph and has the following characteristics: a. Roadway characteristics—60-mph design speed; 11-ft lanes; 2-ft shoulders; mountainous terrain; 80 percent no passing zones; length = 10 miles. b. Traffic characteristics—60/40 directional split; 5 percent trucks; 10 percent recreational vehicles; no buses; 85 percent passenger cars.
At what level of service will the highway operate during peak periods? 2. Solution—The solution is found by comparing the actual flow rate to service flow rates computed for each LOS. The actual flow rate is found as: v = V/PHF where: V = 180 vph (Given) PHF = 0.87 (Default value, Table 8-3, 200 vph)
SFB = 2,800 × 0.12 × 0.94 × 0.75 × 0.535 = 127 vph SFC = 2,800 × 0.20 × 0.94 × 0.75 × 0.535 = 211 vph SFD = 2,800 × 0.37 × 0.94 × 0.75 × 0.508 = 371 vph SFE = 2,800 × 0.80 × 0.94 × 0.88 × 0.508 = 941 vph If the actual flow rate of 207 vph (which represents the flow rate during the peak 15 min of flow) is compared to these values, it is seen that it is higher than the service flow rate for LOS B (127 vph), but is less than the service flow rate for LOS C (211 vph). Therefore, the level of service for the highway is C for the conditions described. This problem illustrates several points. On severe terrain, such as the situation for this problem, ‘‘good’’ operating conditions can be sustained only at low flow rates. The capacity of the roadway is also severely limited, reaching only 941 vph, which is approximately one-third of the ideal capacity of 2,800 vph. Note that the v/c ratio used in the computation of capacity is only 0.80. This is because all v/c ratios in the two-lane methodology are referenced to the ideal capacity of 2,800 vph, which cannot be achieved in severe terrain with passing sight distance restrictions. This solution may be summarized or done on the general terrain section worksheet, as shown in Figure 8-8.
CALCULATION 3—FINDING SERVICE FLOW RATES FOR A SPECIFIC GRADE
and: v = 180/0.87 = 207 vph Service flow rates are computed from Eq. 8-1: SFi = 2,800 × (v/c)i × fd × fw × fHV fHV = 1/[1 + PT (ET − 1) + PR(ER − 1) + PB(EB − 1)] where: v/c = 0.02 for LOS A, 0.12 for LOS B, 0.20 for LOS C, 0.37 for LOS D, 0.80 for LOS E (Table 8-1, mountainous terrain, 80 percent no passing zones); fd = 0.94 (Table 8-4, 60/40 split); fw = 0.75 for LOS A through D, 0.88 for LOS E (Table 8-5, 11-ft lanes, 2-ft shoulders); ET = 7 for LOS A, 10 for LOS B, C, 12 for LOS D, E, (Table 8-6, mountainous terrain); ER = 5.0 for LOS A, 5.2 for LOS B-E (Table 8-6, mountainous terrain);
1. Description—A rural two-lane highway in mountainous terrain has a 6 percent grade of 2 miles. Other relevant characteristics include: a. Roadway characteristics—12-ft lanes; 8-ft shoulders; 60 percent no passing zones. b. Traffic characteristics—70/30 directional split; 12 percent trucks; 7 percent recreational vehicles; 1 percent buses, 80 percent passenger cars; PHF = 0.85.
What is the maximum volume which can be accommodated on the grade at a speed of 40 mph (LOS D, Table 8-2)? 2. Solution—Service flow rate on specific grades is computed using Eq. 8-3, as follows: SFi = 2,800 × (v/c)i × fd × fw × fg × fHV
rural highways
8-24 where: fg = 1/[1 + Pp Ip] from Eq. 8-4 Ip = 0.02 (E − Eo) from Eq. 8-5 and:
At what level of service does the grade operate? What upgrade speed can be expected during the peak 15 min of flow? What is the capacity of the grade? If the approach speed to the grade is 55 mph, what delay is incurred by vehicles climbing the grade? 2. Solution—The finding of capacity for a specific grade requires plotting of the service flow rate vs. speed curve which results from Eq. 8-3: SFi = 2,800 × (v/c)i × fd × fw × fg × fHV
fHV = 1/[1 + PHV(EHV − 1)] from Eq. 8-6 EHV = 1 + (0.25 + PT/HV)(E − 1) from Eq. 8-7
where:
The following values are used in these computations:
fg = 1/[1 + Pp Ip]
(v/c)D = 0.83 (Table 8-7, 40 mph, 6 percent grade, 60 percent no passing zones); fd = 0.78 (Table 8-8, 70/30 split, 70 percent upgrade); fw = 1.00 (Table 8-5, 12-ft lanes, >6-ft shoulders); E = 10.7 (Table 8-9, 40 mph, 6 percent for 2-mile grade); Eo = 1.3 (Table 8-9, 40 mph, 0 percent grade); PHV = PT + PR + PB = 0.12 + 0.07 + 0.01 = 0.20; and PT/HV = PT /PHV = 0.12/0.20 = 0.60.
Ip = 0.02 (E − Eo)
Then, computing factors fg and fHV: Ip = 0.02 (10.7 − 1.3) = 0.188 fg = 1/[1 + (0.80 × 0.188)] = 0.87 EHV = 1 + (0.25 + 0.60) (10.7 − 1) = 9.25 fHV = 1/[1 + 0.20(9.25 − 1)] = 0.38 The service flow rate for the peak 15 min is now computed using Eq. 8-3: SFD = 2,800 × 0.83 × 0.78 × 1.00 × 0.87 × 0.38 = 599 vph Since the question asks for a maximum volume, rather than a flow rate, the service flow rate is converted to a full hour volume as follows: V = SF × PHF = 599 × 0.85 = 509 vph Thus, the maximum full-hour volume which can be accommodated at 40 mph, or LOS D, on the grade described is 509 vph. The maximum flow rate is 599 vph.
CALCULATION 4—FINDING LEVEL OF SERVICE AND CAPACITY OF A SPECIFIC GRADE
1. Description—A rural two-lane highway in mountainous terrain has a grade of 7 percent, 2 miles long. It currently carries a peak hour volume of 500 vph. Other relevant characteristics include: a. Roadway characteristics—60-mph design speed; 11-ft lanes; 4-ft shoulders; 80 percent no passing zones. b. Traffic characteristics—80/20 directional split; 4 percent trucks; 10 percent recreational vehicles; 2 percent buses; 84 percent passenger cars; PHF = 0.85.
and: fHV = 1/[1 + PHV(EHV − 1)] EHV = 1 + (0.25 + PT/HV) (E − 1) Capacity is found at the point where this curve intersects the speed at capacity vs. flow rate at capacity curve on the specific grade worksheet. The upgrade speed is found by entering this curve with the actual flow rate. To plot the curve, the procedure recommends computing service flow rate points for the following speeds: 55 mph (LOS A), 52.5 mph, 50 mph (LOS B), 45 mph (LOS C), 40 mph (LOS D), and 30 mph. These points would be plotted on the specific grade worksheet of Figure 8-5, and a smooth curve constructed. Once capacity is determined, the service flow rates for every LOS will be known, and the actual LOS can be determined by comparing the actual flow rate to the computed values. The following values are used in these computations: v/c = 0.00 for 55 mph 0.05 for 52.5 mph 0.15 for 50 mph 0.40 for 45 mph 0.64 for 40 mph 0.88 for 30 mph (Table 8-7, 7 percent grade, 80 percent no passing zones); fd = 0.70 (Table 8-8, 80/20 split); fw = 0.85 for 55–45 mph 0.92 for 45–30 mph (Table 8-5, 11-ft lanes, 4-ft shoulders); E = 88.0 for 52.5 mph 46.0 for 50 mph 22.8 for 45 mph 15.4 for 40 mph 8.2 for 30 mph (Table 8-9, 7 percent grade, 2 miles, no value given for 55 mph); 1.6 for 50 mph Eo = 1.8 for 52.5 mph 1.4 for 45 mph 1.3 for 40 mph, 30 mph (Table 8-9, 0 percent grade); Pp = 0.84 (Given); PHV = PT + PR + PB = 0.04 + 0.10 + 0.02 = 0.16; and PT/HV = PT /PHV = 0.04/0.16 = 0.25. Values of fg may now be computed as follows: Ip(52.5) = 0.02(88.0 − 1.8) = 1.724 (50.0) = 0.02(46.0 − 1.6) = 0.888
two-lane highways (45.0) (40.0) (30.0) fg(52.5) (50.0) (45.0) (40.0) (30.0)
= = = = = = = =
Note that the low or zero service flow rates for 55.0 and 52.5 mph indicate that these average upgrade speeds are virtually impossible to maintain on the upgrade described in this problem. These computations are summarized on the specific grade worksheet shown in Figure 8-9. The curve defined by these points is also plotted on the worksheet. The intersection of the plotted curve with the speed at capacity vs. flow rate at capacity curve indicates that capacity is 950 vph, total in both directions, which occurs at an average upgrade speed of 28.0 mph. To find the existing level of service, the volume of 500 vph is converted to a flow rate for the peak 15-min period:
0.02(22.8 − 1.4) = 0.428 0.02(15.4 − 1.3) = 0.282 0.02(8.2 − 1.3) = 0.138 1/[1 + 0.84(1.724)] = 0.41 1/[1 + 0.84(0.888)] = 0.57 1/[1 + 0.84(0.428)] = 0.74 1/[1 + 0.84(0.282)] = 0.81 1/[1 + 0.84(0.138)] = 0.90
Values of fHV are also computed: EHV(52.5) (50.0) (45.0) (40.0) (30.0) fHV(52.5) (50.0) (45.0) (40.0) (30.0)
= = = = = = = = = =
1 + (0.25 + 0.25)(88.0 − 1) = 44.5 1 + (0.25 + 0.25)(46.0 − 1) = 23.5 1 + (0.25 + 0.25)(22.8 − 1) = 11.9 1 + (0.25 + 0.25)(15.4 − 1) = 8.2 1 + (0.25 + 0.25)(8.2 − 1) = 4.6 1/[1 + 0.16(44.5 − 1)] = 0.13 1/[1 + 0.16(23.6 − 1)] = 0.22 1/[1 + 0.16(11.9 − 1)] = 0.36 1/[1 + 0.16(8.2 − 1)] = 0.46 1/[1 + 0.16(4.6 − 1)] = 0.63
Having computed all relevant factors, the total two-way service flow rates for the designated speeds may be computed: speed 2,800 × v/c × 55.0 52.5 50.0 45.0 40.0 30.0
2,800 2,800 2,800 2,800 2,800 2,800
0.00 0.05 0.15 0.40 0.64 0.88
fd 0.70 0.70 0.70 0.70 0.70 0.70
×
fw 0.85 0.85 0.85 0.85 0.92 0.92
×
fg
× fHV =
— 0.41 0.57 0.74 0.81 0.90
— 0.13 0.22 0.36 0.46 0.63
8-25
SF 0 4 31 178 430 900
vph vph vph vph vph vph
v = V/PHF = 500/0.85 = 588 vph The plotted curve is entered on the worksheet with 588 vph, and the upgrade speed is found to be 37 mph. Because this speed is less than 40 mph, the minimum value for LOS D (Table 8-2), but greater than the speed at capacity (28 mph), the level of service is E. This can also be determined by comparing the actual flow rate of 588 vph with the service flow rate for LOS D (40 mph) of 430 vph and capacity (950 vph). The last part of this problem asks to find the delay incurred by vehicles traveling up the grade. ‘‘Delay’’ is defined as the difference in travel time experienced by vehicles traversing the upgrade at the existing speed and the travel time which would be experienced if they were able to maintain their approach speed on the grade. Thus: Travel time at 55.0 mph = (2 miles/55 mph) × 3600 sec/hour = 130.9 sec/veh Travel time at 37.0 mph = (2 miles/37 mph) × 3600 sec/hour = 194.6 sec/veh Delay = 194.6 − 130.9 = 63.7 sec/veh
Figure 8-9. Worksheet for Calculation 4 (pages 1 and 2).
rural highways
8-26 CALCULATION 5—CONSIDERATION OF A CLIMBING LANE
1. Description—A rural two-lane highway has a 4 percent upgrade of 11⁄2 miles, and has the following other characteristics: a. Roadway characteristics—level terrain approach; 12-ft lanes; 8-ft shoulders; 40 percent no passing zones. b. Traffic characteristics—DHV = 400 vph; 15 percent trucks; 5 percent recreational vehicles; 1 percent buses; 79 percent passenger cars; 60/40 directional split; PHF = 0.85.
Is the addition of a climbing lane justified at this location? 2. Solution—It is assumed that a climbing lane on a two-lane highway is generally justified when the following conditions are met: 1. Upgrade flow rate is greater than 200 vph. 2. Upgrade truck flow rate is greater than 20 vph. 3. One of the following occurs: a. The grade operates at LOS E or F. b. The typical heavy truck reduces its speed by more than 10 mph on the grade. c. The LOS on the grade is two or more levels poorer than on the approach to the grade.
PT/HV = 0.15/0.21 = 0.71. Using these values to compute the service flow rate at levelof-service D: Ip = 0.02(3.8 − 1.3) = 0.05 fg = 1/[1 + (0.79 × 0.05)] = 0.96 EHV = 1 + (0.25 + 0.71)(3.8 − 1) = 3.69 fHV = 1/[1 + 0.21(3.69 − 1)] = 0.64 SFD = 2,800 × 1.00 × 0.87 × 1.00 × 0.96 × 0.64 = 1,497 vph The actual flow rate is the DHV divided by the PHF, or 400/ 0.85 = 471 vph. As this is clearly less than the service flow rate for LOS D, the existing LOS is not E, and this condition is not met. The next condition to investigate is whether a 10-mph speed reduction of heavy trucks would exist on the grade described. Based on the assumption that the typical truck on this grade has a weight/horsepower ratio of 200 lb/hp, Figure 8-2 is used to estimate the speed reduction experienced as shown below:
Each of these conditions should be checked to justify the construction of the climbing lane: Upgrade flow rate = 400 × 0.60/0.85 = 282 vph > 200 vph OK Upgrade trucks = 400 × 0.15 × 0.60/0.85 = 42 vph > 20 vph OK To justify a climbing lane, only one of the conditions specified in item 3 must be demonstrated. The LOS will be E or worse if the actual flow rate exceeds the service flow rate for LOS D. This value is computed using Eq. 8-3: SFD = 2,800 × (v/c)D × fd × fw × fg × fHV where: fg = 1/[1 + Pp Ip] Ip = 0.02 (E − Eo) and: fHV = 1/[1 + PHV(EHV − 1)]
It can be seen that the speed reduction will be well in excess of 20 mph, which is greater than 10 mph, fulfilling the last required condition for justifying a climbing lane. Note that because only one of the conditions in item 3 needs to be satisfied, it is not necessary to investigate the third condition. It can be concluded that a climbing lane is justified on the basis of the stated criteria.
EHV = 1 + (0.25 + PT/HV)(E − 1) CALCULATION 6—PLANNING APPLICATION 1
The following values are used: (v/c)D = 1.00 (Table 8-7, 4 percent grade, 40 mph, 40 percent no passing zones); fd = 0.87 (Table 8-8, 60/40 directional split); fw = 1.00 (Table 8-5); E = 3.8 (Table 8-9, 4 percent, 11⁄2-mile grade, 40 mph); Eo = 1.3 (Table 8-9, 0 percent grade, 40 mph); PHV = 0.15 + 0.05 + 0.01 = 0.21; and
1. Description—A rural two-lane highway in mountainous terrain is located in an area where the design hour factor, K, is 0.14. What is the maximum AADT which can be accommodated without the LOS falling below D during the peak 15-min flow period? 2. Solution—The solution is simply found by entering Table 8-10 with mountainous terrain, LOS D, and a K-factor of 0.14. The maximum permissible AADT is found to be 2,700 vpd.
two-lane highways CALCULATION 7—PLANNING APPLICATION 2
1. Description—A rural two-lane highway is located in rolling terrain in an area where the design hour factor, K, is 0.12. Its current AADT is 5,000 vpd. What is the likely LOS during the peak 15 min of flow? 2. Solution—Again, the solution is straightforward using Table 8-10. The maximum AADT’s for the various levels of service are found for rolling terrain and a K-factor of 0.12. The 5,000 AADT is seen to fall between the maximum values for LOS C (4,400 vpd) and LOS D (6,600 vpd). The LOS is therefore expected to be D during the peak 15 min of flow.
8-27
percent per year. The responsible highway agency’s policy is to expand two-lane highways to four lanes before the level of service becomes E during peak periods. In how many years will expansion of the facility have to be completed under this policy? If it will take 7 years to construct a four-lane highway, how long will it be before the construction project should begin? 2. Solution—The policy requires that expansion of the highway be completed before the AADT exceeds the maximum allowable value for LOS D. From Table 8-10, the maximum AADT for LOS D, for level terrain and a K-factor of 0.12, is 11,200 vpd. The question now becomes: How many years will it take an AADT of 6,600 vpd to grow to 11,200 vpd at a rate of 5 percent per year? Therefore: 11,200 = 6,600(1 + 0.05)n
CALCULATION 8—PLANNING APPLICATION 3
1. Description—A two-lane highway carrying an AADT of 6,600 vpd is located in level terrain in an area where the design hour factor, K, is 0.12. The area has a traffic growth rate of 5
n = 10.9 years Construction should begin in 10.9 − 7 years, or in 3.9 years.
VI. REFERENCES 1. Messer, C.J., ‘‘Two-Lane, Two-Way Rural Highway Level of Service and Capacity Procedures.’’ Project report, NCHRP Project 3-28A, Texas Transportation Institute, College Station, Tex. (Feb. 1983). 2. Messer, C.J., ‘‘Two-Lane, Two-Way Rural Highway Capacity.’’ Final report, NCHRP Project 3-28A, Texas Transportation Institute, College Station, Tex. (Feb. 1983). 3. Krummins, I., ‘‘Capacity and Level of Service of Two-Lane Rural Highways in Alberta.’’ Thesis, University of Calgary, Calgary, Alberta, Canada (Sept. 1981). 4. Yagar, S., ‘‘Capacity and Level of Service for 2-Lane Rural Highways.’’ Report to the Ontario Ministry of Transportation and Communications, Downsview, Ontario, Canada (1980). 5. Traffic Capacity of Major Routes. Organization for Economic Development, Paris (Jan. 1983). 6. Werner, A., and Morrall, J.F., ‘‘Passenger Car Equivalen-
7.
8.
9. 10.
11.
cies of Trucks, Buses, and Recreational Vehicles for TwoLane Rural Highways.’’ Transportation Research Record 615 (1976). Development of Passing Lane Criteria. Ontario Ministry of Transportation and Communications, Downsview, Canada (1975). Rooney, F., Turnouts: Traffic Operational Report No. 2. Office of Traffic, California Department of Transportation, Sacramento, Calif. (1976). Theoretical Analysis: Slow Moving Vehicle Turnouts. Oregon Department of Transportation (1978). St. John, A.D. and Kobett, D.R., ‘‘Grade Effects on Traffic Flow Stability and Capacity.’’ NCHRP Report 185 (1978) 110 pp. A Policy on Geometric Design of Highways and Streets. American Association of State Highway and Transportation Officials, Washington, D.C. (1984).
rural highways
8-28
APPENDIX I FIGURES AND WORKSHEETS FOR USE IN ANALYSIS OF TWO-LANE HIGHWAYS FIGURES Figure 8-1. Figure 8-2. Figure 8-3.
PAGE Speed-flow and percent time delay-flow relationships for two-lane rural highways (ideal conditions) ................... 8-28 Speed reduction curve for a 200-lb/hp truck................................................................................................................ 8-29 Speed reduction curve for a 300-lb/hp truck................................................................................................................ 8-29
WORKSHEETS Worksheet for General Terrain Segments............................................................................................................................................... 8-30 Worksheet for Specific Grades (Page 1)................................................................................................................................................. 8-31 Worksheet for Specific Grades (Page 2)................................................................................................................................................. 8-32
Figure 8-1. Speed-flow and percent time delay-flow relationships for two-lane rural highways (ideal conditions).
two-lane highways 8-29
Figure 8-2. Speed reduction curve for a 200-lb/hp truck.
Figure 8-3. Speed reduction curve for a 300-lb/hp truck.
8-30
rural highways
two-lane highways
8-31
8-32
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two-lane highways
8-33
chapter 9
SIGNALIZED INTERSECTIONS
CONTENTS i.
introduction .......................................................................................................................................................................... Traffic Signals ....................................................................................................................................................................... Green Time, Effective Green Time, and Lost Times in Signal Cycles .............................................................................. Capacity and Level of Service.............................................................................................................................................. Capacity of Signalized Intersections ............................................................................................................................... Level of Service for Signalized Intersections ................................................................................................................. Relating Capacity and Level of Service.......................................................................................................................... Computational Alternatives for Delay and Level of Service ......................................................................................... Levels of Analysis............................................................................................................................................................ Suitability of Operational Configurations .......................................................................................................................
9-2 9-2 9-4 9-5 9-5 9-6 9-7 9-7 9-8 9-8
ii.
methodology.......................................................................................................................................................................... Operational Analysis ............................................................................................................................................................. Input Module .................................................................................................................................................................... Volume Adjustment Module............................................................................................................................................ Saturation Flow Rate Module.......................................................................................................................................... Capacity Analysis Module............................................................................................................................................... LOS Module..................................................................................................................................................................... Interpretation of Results................................................................................................................................................... Planning Analysis .................................................................................................................................................................. Overview of Planning Method ........................................................................................................................................ Field Data Requirements.................................................................................................................................................. Default Values.................................................................................................................................................................. Synthesis of Signal Operation ......................................................................................................................................... Other Analyses .................................................................................................................................................................
9-8 9-8 9-9 9-12 9-14 9-22 9-27 9-30 9-31 9-32 9-32 9-33 9-33 9-34
iii.
procedures for application ................................................................................................................................................ Operational Analysis ............................................................................................................................................................. Input Module .................................................................................................................................................................... Volume Adjustment Module............................................................................................................................................ Saturation Flow Rate Module.......................................................................................................................................... Capacity Analysis Module............................................................................................................................................... LOS Module..................................................................................................................................................................... Supplemental Uniform Delay Worksheet........................................................................................................................ Planning Analysis .................................................................................................................................................................. Worksheet Operations ...................................................................................................................................................... Computational Requirements........................................................................................................................................... Lane Volume Worksheet ................................................................................................................................................. Signal Operations Worksheet .......................................................................................................................................... Limitations of Planning Method...................................................................................................................................... Procedures for Other Analyses .............................................................................................................................................
9-34 9-34 9-34 9-38 9-38 9-43 9-46 9-48 9-50 9-50 9-50 9-50 9-56 9-57 9-58
iv.
sample calculations ............................................................................................................................................................ Calculation 1: Operational Analysis of Existing Pretimed, Two-Phase Signal .................................................................. Calculation 2: Operational Analysis of Three-Phase, Pretimed Signal............................................................................... Calculation 3: Operational Analysis of Multiphase Actuated Signal.................................................................................. Calculation 4: Planning Analysis of Intersection with Multilane Approaches ................................................................... Calculation 5: Planning Analysis of Intersection with Single-Lane Approaches ............................................................... Calculation 6: Determining v/c and Service Flow Rates—An Alternative Use of Operational Analysis Procedure .......
9-60 9-60 9-69 9-78 9-84 9-86 9-88
9-1
Updated December 1997
urban streets
9-2 v.
references .............................................................................................................................................................................. 9-96 appendix i. Intersection Geometrics—Suggestions for Estimating Design Elements .......................................................... 9-97 appendix ii. Suggestions for Establishing Signal Design in Analysis .................................................................................. 9-98 appendix iii. Measurement of Intersection Control Delay in the Field ................................................................................ 9-117 appendix iv. Direct Measurement of Prevailing Saturation Flow Rates .............................................................................. 9-121 appendix v. Worksheets for Use in Analysis ........................................................................................................................ 9-124 appendix vi. Extension of Signal Delay Models To Incorporate Effect of Initial Queue ................................................... 9-139
I. INTRODUCTION This chapter contains procedures for the analysis of signalized intersection capacity and level of service. The signalized intersection is one of the most complex locations in a traffic system. Signalized intersection analysis must consider a wide variety of prevailing conditions including the amount and distribution of traffic movements, traffic composition, geometric characteristics, and the details of intersection signalization. The methodology of this chapter focuses on the determination of level of service for known or projected prevailing conditions but presents computational alternatives for determining other variables using an assumed or desired level of service. In other chapters of this manual, the capacity of a highway is related primarily to the geometric characteristics of the facility as well as to the composition of the traffic stream on the facility. Geometrics is a fixed, or nonvarying, characteristic of a facility. Thus, allowing for some variation in traffic composition over time, the capacity of a facility is generally a stable value that can be significantly improved only by initiating geometric improvements. At the signalized intersection, an additional element is introduced into the concept of capacity: time allocation. A traffic signal essentially allocates time among conflicting traffic movements that seek use of the same physical space. The way in which time is allocated has a significant impact on the operation and the capacity of the intersection and its approaches. The methodology presented here addresses the capacity and level of service of intersection approaches and the level of service of the intersection as a whole. Capacity is evaluated in terms of the ratio of demand flow rate (volume) to capacity (v/c ratio), whereas level of service is evaluated on the basis of average control delay per vehicle (in seconds per vehicle). The capacity of the intersection as a whole is not addressed, because both the design and the signalization of intersections focus on the accommodation of major movements in the intersection and on its approaches. Capacity is therefore only meaningful as applied to these major movements and approaches.
TRAFFIC SIGNALS
Modern traffic signals allocate time in a variety of ways, from the simplest two-phase pretimed mode to the most complex multiphase actuated mode. The basic terminology of traffic signals is described and the various types of signal operation and their impact Updated December 1997
on capacity are outlined briefly. The following terms are commonly used to describe traffic signal operation: Cycle—any complete sequence of signal indications; Cycle length—the total time for the signal to complete one cycle, stated in seconds and given the symbol C; Interval—a period of time during which all signal indications remain constant; Phase—the part of a cycle allocated to any combination of traffic movements receiving the right-of-way simultaneously during one or more intervals; Change-and-clearance interval—the yellow plus all-red intervals that occur between phases to provide for clearance of the intersection before conflicting movements are released, stated in seconds and given the symbol Y; Green time—the time within a given phase during which the green indication is shown, stated in seconds and given the symbol G; Lost time—time during which the intersection is not effectively used by any movement, which occurs during the change-and-clearance intervals (when the intersection is cleared) and at the beginning of each phase as the first few vehicles in a standing queue experience start-up delays, given the symbol L; Effective green time—the time that is effectively available to a movement, generally taken to be the green time plus the changeand-clearance interval minus the lost time for the designated movement, stated in seconds and given the symbol gi; Effective green ratio—the ratio of effective green time to the cycle length, given the symbol, gi /C; Effective red time—the time during which a given movement or set of movements is effectively not permitted to occur, the cycle length minus the effective green time, stated in seconds and given the symbol ri. Traffic engineering textbooks describe three types of traffic signal controllers: 1. Pretimed controllers: A preset sequence of phases is displayed in repetitive order. Each phase has a fixed green time and a change-and-clearance interval that are repeated in each cycle to produce a constant cycle length. 2. Fully actuated controllers: The timing on all of the approaches to an intersection is influenced by vehicle detectors. Each phase is subject to a minimum and a maximum green time, and
signalized intersections some phases may be skipped if no demand is detected. The cycle length for fully actuated control will vary from cycle to cycle. 3. Semiactuated controllers: Some approaches (typically on the minor street) have detectors, and some do not. The earliest form of semiactuated control was designed to confine the green indication to the major street in the absence of a minor-street actuation. Once actuated, the minor-street green is displayed for a period just long enough to accommodate the traffic demand. Although these equipment-based definitions have persisted in traffic engineering terminology, the evolution of traffic control technology has complicated their function from the analyst’s perspective. For purposes of capacity and level of service (LOS) analysis, it is no longer sufficient to consider the controller type as a global descriptor of the intersection operation. Instead, an expanded set of these definitions must be applied individually to each lane group. Each traffic movement may be served by a phase that is either actuated or nonactuated. Nonactuated phases may be coordinated with neighboring signals on the same route, or they may function in an isolated mode without any influence from other signals. Nonactuated phases generally operate with fixed minimum green times, which may be extended by reassigning unused green time from actuated phases with low demand, if such phases exist. Actuated phases, on the other hand, may be used for intersections at which other phases are coordinated, but they may not, for the purposes of this chapter, be coordinated themselves. Actuated phases are subject to being shortened on cycles with low demand. On cycles with no demand, they may be skipped entirely, or they may be displayed for their minimum duration. With systems in which the nonactuated phases are coordinated, the actuated phases are also subject to early termination (force-off) to accommodate the progression design for the system. The capacity analysis procedures in this chapter are based on known or projected signalization plans. Two alternative procedures are provided to assist the analyst in establishing signalization plans. The first is the planning method, which produces estimates of the cycle length and green times that could be considered to constitute a ‘‘reasonable and effective’’ signal timing plan. The planning method requires minimal field data and relies instead on default values for the required traffic and control parameters. Although intended primarily for planning purposes, this method may be used to design initial timing plans for pretimed signals. Timing plans produced by the planning method will not generally be optimal with respect to intersection performance, and they may not even be implementable because certain practical considerations such as minimum phase times are ignored. Their main purpose will be to support the analysis of capacity and level of service at signalized intersections using the methodology in this chapter. A more detailed procedure is provided in Appendix II for estimating the timing plan at both pretimed and traffic-actuated signals. The pretimed procedure provides the basis for the design of signal timing plans that equalize the degree of saturation on the critical approaches for each phase of the signal sequence. This procedure does not provide for optimum operation. The planning method builds on this procedure by adding some assumptions and approximations to produce a complete worksheet for timing plan estimation. Controllers with traffic-actuated phases will respond to detector inputs to generate different timing plans on each cycle of operation. Therefore the traffic-actuated procedure contained in Appendix II
9-3
is not intended to design timing plans but to estimate the average value of the cycle length and phase times that will result from a specified combination of traffic conditions and controller settings. This procedure may be applied to controllers with coordinated phases in addition to those that operate in an isolated mode. It is necessary to know the details of the actuated controller settings for each phase because these settings will have a significant impact on the resulting timing plan. Although this procedure fairly represents the traffic signal timing that can be expected at an intersection with actuated control given the stated variables, it does not represent the minimum delay cycle or optimum operation. These two signal timing estimation procedures provide a useful computational resource. However, local policies or methods should also be consulted when traffic signal operation is determined. The timing plan estimation methodology in this chapter is provided to assist in capacity analysis and should not be construed to suggest nationally accepted standards, criteria, or guidelines for traffic signal operation. It is not only the allocation of green time that has a significant impact on capacity and operations at a signalized intersection but also the manner in which turning movements are accommodated within the phase sequence. Signal phasing can provide for protected, permitted, or not opposed turning movements. A permitted turning movement is made through a conflicting pedestrian flow or opposing-vehicle flow. Thus, a left-turn movement that is made at the same time as the opposing through movement is considered to be permitted, as is a right-turn movement made at the same time as pedestrian crossings in a conflicting crosswalk. Protected turns are those made without these conflicts, such as turns made during an exclusive left-turn phase or a right-turn phase during which conflicting pedestrian movements are prohibited. Permitted turns experience the friction of selecting and passing through gaps in a conflicting vehicle or pedestrian flow. Thus, a single permitted turn often consumes more of the available green time than a single protected turn. Either permitted or protected turning phases may be more efficient in a given situation, depending on the turning and opposing volumes, intersection geometry, and other factors. Turning movements that are not opposed do not receive a dedicated left-turn phase (i.e., a green arrow), but because of the nature of the intersection, they are never in conflict with through traffic. This condition occurs on one-way streets, at T-intersections, and with signal phasing plans that provide complete separation between all movements in opposite directions (i.e., split-phase operation). Such movements must be treated differently in some cases because they may be accommodated in shared lanes without impeding the through traffic. It is important to distinguish between left turns that are not opposed at any time and those that may be unopposed during some part of the signal cycle and opposed during another part. Left turns that are opposed during any part of the sequence will impede through traffic in shared lanes. The preceding discussion emphasizes this primary concept: the capacity of an intersection is highly dependent on the signalization present. Given the range of potential signal control schemes, intersection capacity is far more variable than that on other types of facilities, where capacity is mainly dependent upon the physical geometry of the roadway. In effect, signalization, which can be changed frequently and quickly, allows considerable latitude in the management of the physical capacity of the intersection space Updated December 1997
urban streets
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Figure 9-1. Relationship among actual green, lost-time elements, extension of effective green, and effective green.
and geometry. Thus, the concept of intersection capacity is somewhat different from that discussed in previous chapters. GREEN TIME, EFFECTIVE GREEN TIME, AND LOST TIMES IN SIGNAL CYCLES
For any given lane group at a signalized intersection, only three signal indications are seen: green, yellow, and red. The red indication usually includes a short period during which all indications are red, referred to as an ‘‘all-red’’ interval, which with the yellow indication forms the change-and-clearance interval between two green phases. For analysis purposes, it is convenient to divide the signal cycle for a given lane group into two simplified components: effective green and effective red. Effective green time for a given lane group is the time that may be used by vehicles in the subject lane group at the saturation flow rate. Effective red is defined as the cycle length minus the effective green. It is important that the relationship between the actual green, yellow, and red times shown on signal faces and the effective green and red times be well understood. Each time a movement is started and stopped, two ‘‘lost times’’ are experienced. At the beginning of movement, the first several vehicles in the queue experience start-up losses that result in their movement at less than the saturation flow rate (Figure 9-1). At the end of a movement, there is a portion of the change-and-clearance interval (yellow and all-red) that is not used for vehicular movement. The following definitions apply to these variables: Gi = actual green time allotted to lane group i, sec; Yi = sum of actual yellow change time plus all-red clearance time allotted to lane group i, sec; Ri = actual red time exclusive of the all-red clearance time allotted to lane group i, sec; gi = effective green time for lane group i, sec; ri = effective red time for lane group i, sec; l1 = start-up lost time, sec; l2 = clearance lost time, sec; e = extension of effective green (the amount of change-andclearance time usable as effective green), sec; and tL = total lost time for the lane group (the sum of l1 and l2), sec. Research has shown that start-up lost time (l1) is normally about 2 sec. It has also shown that the extension of effective green (e) is normally about 2 sec (sometimes longer under congested conditions). The remainder of the change-and-clearance time is the clearance lost time (l2). It is analytically convenient to combine Updated December 1997
the two lost times and apply both at the beginning of a particular traffic movement, particularly for protected-plus-permitted phasing analysis. Thus the following relationships exist for typical conditions, and the relationship among actual green, lost time, extension of effective green, and effective green is illustrated in Figure 9-1. l1 = 2 (typical) l2 = Y i − e where e = 2 (typical; e may be higher in congested conditions); tL = l1 + l2 = l1 + Yi − e = 2 + Yi − 2 = Yi (typical; tL may be less in congested conditions). As shown, the total lost time for the movement is deducted from the beginning of the actual green phase. Thus, a small portion of Gi becomes part of the effective red, ri. This portion is equal to the lost time for the movement, tL. Because all of the lost time for the movement is deducted at the beginning of the green, effective green can be assumed to run through the end of the yellow-plusall-red change-and-clearance interval, Yi. Thus, for any given movement: gi = Gi + Yi − tL
(9-1)
ri = Ri + tL
(9-2)
The simplified concept of applying all of the lost time at the beginning of a movement makes it easier to analyze more complex signalizations involving protected-plus-permitted left-turn treatments. As a general rule, a lost time tL is applied each time a movement starts. Thus, where a given movement starts in a protected phase and continues through a permitted phase (or vice versa), only one lost time is deducted. No lost time is assumed to occur at the boundary between the permitted and protected phases for continuing movements. Figure 9-2 diagrams a more complex phasing involving a protected-plus-permitted left-turn movement, a classic lead-lag phasing scheme in which left turns are protected in Phase 1a [eastbound (EB)] and Phase 1c [westbound (WB)] and permitted during the common Phase 1b. The question of how many lost times are included in such a phase sequence is an important one. Using the general rule that the entire lost time for a movement is applied at the time the movement begins, the following may be determined: T In Phase 1a, the EB through and left-turn movements begin. Thus, a lost time tL is applied to both movements.
signalized intersections
9-5
Figure 9-2. Protected-plus-permitted signal phasing.
T In Phase 1b, the EB through and left-turn movements continue. No lost times are assigned to the continuing movements in this phase. The WB through and left-turn movements begin in this phase, however, and a lost time tL must be applied to these movements. T In Phase 1c, only the WB through and left turns continue. Because these movements did not start in this phase, no lost time is applied here. Further, because no movements begin in Phase 1c, no lost time is applied to any movement in Phase 1c. T In Phase 2, northbound (NB) and southbound (SB) movements begin, and a lost time tL must be applied. The total lost time in the signal cycle, L, is also important. This is the total lost time involved in the critical path through the signal cycle. The determination of the critical path and the finding of L are discussed later in this chapter.
The v/c ratio is a measure of capacity sufficiency, that is, whether or not the physical geometry and signal design provide sufficient capacity for the subject movement or movements. Delay is a measure of quality of service to the road user. Both must be analyzed to fully understand the anticipated operational characteristics of the intersection, and neither can be substituted for the other. As a practical matter, however, it must be recognized that an intersection cannot operate beyond its capacity indefinitely without experiencing excessive delay. For planning purposes, it may be more appropriate to consider the provision of adequate future capacity as related to geometric design features. Delay may be less of a concern, because it may be improved significantly through coordination of signals and improved signal design. In the analysis of existing problem locations, delay may be a more significant consideration when improved controls are considered. Both of these important concepts are discussed in more detail in the sections that follow.
CAPACITY AND LEVEL OF SERVICE
The concepts of capacity and level of service are central to the analysis of intersections, as they are for all types of facilities. In intersection analysis, however, the two concepts are not as strongly correlated as they are for other facility types. In previous chapters, the same analysis results yielded a determination of both the capacity and the level of service of the facility. For signalized intersections, the two are analyzed separately and are not related in a simple way to each other. It is critical to note at the outset, however, that both capacity and level of service must be fully considered to evaluate the overall operation of a signalized intersection. A separate capacity is computed for each lane group approaching an intersection. A lane group is defined as one or more lanes that accommodate traffic and have a common stop line and capacity shared by all vehicles. Capacity analysis results in the computation of volume-to-capacity (v/c) ratios for each lane group. The v/c ratio is the actual or projected rate of flow on a designated lane group during a 15-min interval divided by the capacity of the lane group. Although the capacity of the entire intersection is not defined, a composite v/c ratio for the sum of the critical lane groups within the intersection is computed as an indication of the overall intersection sufficiency. Level of service is based on the average control delay per vehicle for various movements within the intersection. Although v/c affects delay, there are other parameters that more strongly affect it, such as the quality of progression, length of green phases, cycle lengths, and others. Thus, for any given v/c ratio, a range of delay values may result, and vice versa. For this reason, both the capacity and level of service of the intersection must be carefully examined.
Capacity of Signalized Intersections
Capacity at intersections is defined for each lane group. The lane group capacity is the maximum rate of flow for the subject lane group that may pass through the intersection under prevailing traffic, roadway, and signalization conditions. The rate of flow is generally measured or projected for a 15-min period, and capacity is stated in vehicles per hour (vph). Traffic conditions include volumes on each approach, the distribution of vehicles by movement (left, through, right), the vehicle type distribution within each movement, the location of and use of bus stops within the intersection area, pedestrian crossing flows, and parking movements near the intersection area. Roadway conditions include the basic geometrics of the intersection, including the number and width of lanes, grades, and lane use allocations (including parking lanes). Signalization conditions include a full definition of the signal phasing, timing, and type of control, and an evaluation of signal progression for each lane group. The capacity of designated lane groups within an approach is evaluated and determined using the procedures in this chapter. This may be done to isolate lanes serving a particular movement or movements, such as an exclusive right- or left-turn lane. Lanes so designated for separate analysis were defined earlier as lane groups. The procedure in this chapter contains guidelines for when and how separate lane groups should be designated on an approach. Capacity at signalized intersections is based on the concept of saturation flow and saturation flow rate, defined as the maximum Updated December 1997
urban streets
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rate of flow that can pass through a given lane group under prevailing traffic and roadway conditions, assuming that the lane group has 100 percent of real time available as effective green time. Saturation flow rate is given the symbol s and is expressed in units of vehicles per hour of effective green time (vphg) for a given lane group. The flow ratio for a given lane group is defined as the ratio of the actual or projected demand flow rate for the lane group (vi) to the saturation flow rate (si). The flow ratio is given the symbol (v/s)i (for lane group i). The capacity of a given lane group may be stated as ci = si (gi /C)
(9-3)
where ci = capacity of lane group i, vph; si = saturation flow rate for lane group i, vphg; and gi /C = effective green ratio for lane group i. The ratio of flow rate to capacity (v/c), often called the volumeto-capacity ratio, is given the symbol X in intersection analysis. This new symbol is introduced in this chapter to emphasize the strong relationship of capacity to signalization conditions and for consistency with the literature, which also refers to this variable as the degree of saturation. For a given lane group i: Xi = (v/c)i = vi /(sigi /C) = viC/(sigi)
(9-4)
where Xi = (v/c)i = ratio for lane group i; vi = actual or projected demand flow rate for lane group i, vph; si = saturation flow rate for lane group i, vphg; gi = effective green time for lane group i, sec; and C = cycle length, sec.
where Xc = critical v/c ratio for the intersection; ∑(v/s)ci = summation of flow ratios for all critical lane groups, i; C = cycle length, sec; and L = total lost time per cycle, computed as the sum of the lost time tL for all critical lane groups, i. Equation 9-5 is useful in evaluating the overall intersection with respect to the geometrics and total cycle length provided and also in estimating signal timings when they are unknown or not specified by local policies or procedures. It gives the v/c ratio for all critical movements, assuming that green time has been allocated in proportion to the v/s values. It is therefore possible to have a critical v/c ratio of less than 1.0 and still have individual movements oversaturated within the signal cycle. A critical v/c ratio less than 1.0, however, does indicate that all movements in the intersection can be accommodated within the defined cycle length and phase sequence by proportionally allocating green time. In essence, the total available green time in the phase sequence is adequate to handle all movements if allocated solely on the basis of v/s. The Xc value can, however, be misleading when used as an indicator of the overall sufficiency of the intersection geometrics, as is often required in planning applications. The problem is that low flow rates dictate the need for short cycle lengths to minimize delay. Inspection of Equation 9-5 suggests that shorter cycle lengths produce a higher Xc, for a specified level of traffic demand. Furthermore, many signal timing methods, including the planning method described later in this chapter, are based on a fixed target value of Xc. This tends to make Xc independent of the demand volumes. A broader indicator of the overall sufficiency of the intersection is therefore obtained by substituting the maximum cycle length acceptable to the agency responsible for the signal operation in place of the actual cycle length in Equation 9-5: Xcm =
Sustainable values of Xi range from 1.0 when the flow rate equals capacity to zero when the flow rate is zero. Values above 1.0 indicate an excess of demand over capacity. The capacity of the full intersection is not a significant concept and is not specifically defined here. Rarely do all movements at an intersection become saturated at the same time of day. It is the ability of individual movements to move through the intersection with some efficiency that is the critical concern. Another capacity concept of utility in the analysis of signalized intersections, however, is the critical v/c ratio Xc, which is the v/c ratio for the intersection as a whole, considering only the lane groups that have the highest flow ratio (v/s) for a given signal phase. For example, in a two-phase signal, opposing lane groups move during the same green time. Generally, one of these two lane groups will require more green time than the other (i.e., it will have a higher flow ratio). This would be the ‘‘critical’’ lane group for the subject signal phase. Each signal phase will have a critical lane group that determines the green-time requirements for the phase. When signal phases overlap, the identification of these critical lane groups becomes somewhat complex; this situation is discussed in Section II, Methodology. The critical v/c ratio for the intersection is defined in terms of critical lane groups or approaches: Xc = Updated December 1997
o (v/s)
ci
[C/(C − L)]
(9-5)
o (v/s)
ci
[Cmax/(Cmax − L)]
(9-6)
where Xcm = critical v/c ratio based on the maximum acceptable cycle length, and Cmax = maximum acceptable cycle length, sec. For planning purposes, Xcm offers a more appropriate indicator of the proportion of the actual capacity of the intersection that is being used by the specified traffic volumes. In the balance of this chapter, Xc will be used to represent the critical v/c ratio for operational analyses and Xcm will be used for planning analysis. The analysis of capacity in this chapter focuses on the computation of saturation flow rates, capacities, and v/c ratios for various lane groups of the intersection. Procedures for these computations are described in greater detail in Sections II, Methodology, and III, Procedures for Application.
Level of Service for Signalized Intersections
Level of service for signalized intersections is defined in terms of delay, which is a measure of driver discomfort, frustration, fuel consumption, and lost travel time. The delay experienced by a motorist is made up of a number of factors that relate to control, geometrics, traffic, and incidents. Total delay is the difference
signalized intersections Table 9-1. Level-of-Service Criteria for Signalized Intersections level of service A B C D E F
control delay per vehicle (sec) ≤10 >10 >20 >35 >55 >80
and and and and
≤20 ≤35 ≤55 ≤80
between the travel time actually experienced and the reference travel time that would result during ideal conditions: in the absence of traffic control, in the absence of geometric delay, in the absence of any incidents, and when there are no other vehicles on the road. In Chapters 9, 10, and 11, only the portion of total delay attributed to the control facility is quantified. This delay is called control delay. Control delay includes initial deceleration delay, queue move-up time, stopped delay, and final acceleration delay. In contrast, in previous versions of this chapter of the HCM (1994 and earlier), delay included only stopped delay. In this chapter, control delay may also be referred to as signal delay. Specifically, LOS criteria for traffic signals are stated in terms of the average control delay per vehicle, typically for a 15-min analysis period. The criteria are given in Table 9-1. Delay may be measured in the field or estimated using procedures presented later in this chapter. Delay is a complex measure and is dependent on a number of variables, including the quality of progression, the cycle length, the green ratio, and the v/c ratio for the lane group in question. LOS A describes operations with very low control delay, up to 10 sec per vehicle. This level of service occurs when progression is extremely favorable and most vehicles arrive during the green phase. Most vehicles do not stop at all. Short cycle lengths may also contribute to low delay. LOS B describes operations with control delay greater than 10 and up to 20 sec per vehicle. This level generally occurs with good progression, short cycle lengths, or both. More vehicles stop than with LOS A, causing higher levels of average delay. LOS C describes operations with control delay greater than 20 and up to 35 sec per vehicle. These higher delays may result from fair progression, longer cycle lengths, or both. Individual cycle failures may begin to appear at this level. The number of vehicles stopping is significant at this level, though many still pass through the intersection without stopping. LOS D describes operations with control delay greater than 35 and up to 55 sec per vehicle. At level D, the influence of congestion becomes more noticeable. Longer delays may result from some combination of unfavorable progression, long cycle lengths, or high v/c ratios. Many vehicles stop, and the proportion of vehicles not stopping declines. Individual cycle failures are noticeable. LOS E describes operations with control delay greater than 55 and up to 80 sec per vehicle. This level is considered by many agencies to be the limit of acceptable delay. These high delay values generally indicate poor progression, long cycle lengths, and high v/c ratios. Individual cycle failures are frequent occurrences. LOS F describes operations with control delay in excess of 80 sec per vehicle. This level, considered to be unacceptable to most drivers, often occurs with oversaturation, that is, when arrival flow rates exceed the capacity of the intersection. It may also occur at
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high v/c ratios below 1.0 with many individual cycle failures. Poor progression and long cycle lengths may also be major contributing factors to such delay levels. Relating Capacity and Level of Service
Because delay is a complex measure, its relationship to capacity is also complex. The levels of service in Table 9-1 were established on the basis of the acceptability of various amounts of delay to drivers. Although local standards may vary, LOS C may be regarded as a desirable design objective. It is important to note that this concept is not related to capacity in a simple one-to-one fashion. In previous chapters, the lower bound of LOS E was defined to be capacity; that is, the v/c ratio is by definition 1.0. This is not the case for the procedures in this chapter. It is possible, for example, to have delays in the range of LOS F (unacceptable) while the v/c ratio is below 1.0, perhaps as low as 0.75 to 0.85. Very long delays can occur at such v/c ratios when some combination of the following conditions exists: (a) the cycle length is long, (b) the lane group in question is disadvantaged by the signal timing (has a long red time), and (c) the signal progression for the subject movements is poor. The reverse is also possible: a saturated lane group (i.e., v/c ratio greater than 1.0) may have short delays if (a) the cycle length is short or (b) the signal progression is favorable for the subject lane group, or both. Thus, the designation LOS F does not automatically imply that the intersection, approach, or lane group is over capacity, nor does a level of service better than E automatically imply that unused capacity is available. The procedures and methods in this chapter require the analysis of both capacity and LOS conditions to fully evaluate the operation of a signalized intersection. It is imperative that the analyst recognize the unique relationship of these two concepts as they apply to signalized intersections. Computational Alternatives for Delay and Level of Service
This chapter defines the level of service at a signalized intersection in terms of average control delay per vehicle. It also establishes threshold delay values for the various levels of service and presents a detailed computational methodology for estimating delay. The methodology prescribed here represents a broad accumulation of professional knowledge, experience, and research. As such, it offers a consistent and impartial means of assessing the level of service at signalized intersections under a full range of operating conditions. It must be recognized, however, that delay is a quantity that may be directly measured in the field. The results of the computations described in this chapter cannot be expected to supersede the results of properly executed field studies that measure delay. Furthermore, the literature contains a variety of models that offer delay estimation techniques based on complex software algorithms, some of which require additional field data. Some of these models are designed to deal explicitly with unusual situations of geometrics, signal operation, driver behavior, and so forth. It is not, therefore, possible to argue the superiority of the macroscopic model contained in this chapter over all of the more microscopic methods under all conditions, as described in Chapter 1. Updated December 1997
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urban streets
Although worksheets are provided for all the calculations, the use of computerized versions of these procedures is a universal practice. The primary purpose of the worksheets is to explain the computational methodology in a clear and understandable manner. Productivity considerations dictate the need for automation, and fortunately there is an excellent choice of software products that implement the methodology of this chapter. It is not the purpose of this manual to endorse, compare, or even mention these products; however, their importance to the analysis of signalized intersection capacity and level of service cannot be ignored, nor can the professional responsibility of the analyst for the final results. The software must be viewed as a supplement to this manual to be used with a thorough understanding of the procedures, and not simply as a time-saving alternative. For example, the interpretation of the level of precision available from computations performed by software should be compatible with the accuracy of the input data. To simplify the description of the computational process, certain parameters may be assumed to apply globally to all movements. This is common practice in signalized intersection analysis and is reflected in all the worksheets and sample calculations. It is not, however, the intent in this chapter to preclude the use of movement-specific values when such information is available and a higher level of precision is required.
analysis into the level of operational analysis. The accuracy of the computed level of service will depend on the degree of effort applied to the development of the data items that are represented by default values (e.g., lane widths, truck proportions) and on the quality of the approximated signal timing plan. Thus, planning and operational analyses may be viewed as two applications that represent the extremes of a continuous range of possibilities. The operational analysis methodology considers the full details of each of four components: demand flow rates at the intersection, signalization of the intersection, geometric design or characteristics of the intersection, and the delay or level of service that results from these. The methodology is capable of treating any of these four components as an unknown to be determined knowing the details of the other three. Thus the method can be used to
Levels of Analysis
Although the methodology is capable of computations in all four modes, the specific procedures and worksheets are designed for the first of these, that is, a solution for level of service. In developing alternative signal and geometric designs, it is often necessary to consider changes simultaneously in both. Rarely can signalization be considered in isolation from geometric design and vice versa. Thus, the most frequent type of analysis would consider such alternatives on a trial-and-error basis and would not attempt to hold one constant and solve for the other. Sample calculations, however, illustrate alternative uses of the methodology.
Two levels of analysis are presented. The primary methodology used is the operational analysis. At this level, detailed information on all prevailing traffic, roadway, and signalization characteristics must be provided. The method provides for a full analysis of capacity and level of service and can be used to evaluate alternative traffic demands, geometric designs, or signal plans, or all three. A second method is provided for planning analysis. At this level, only capacity is addressed because it is not necessary, nor is it practical, to perform detailed calculations of delay given the accuracy of the data that are generally available for planning purposes. Basic information on intersection geometrics, lane utilization, and movement-specific traffic volumes is required, along with the manner in which each of the left turns is accommodated (protected, permitted, etc.) and the presence or absence of parking on each approach. The planning method generates two important products: (a) a projection of the status of the intersection with respect to its capacity and (b) an approximation of a signal timing plan. Combining this approximation with appropriate values for other parameters used in the operational analysis, it is possible to extend the planning
1. Solve for level of service, knowing details of intersection flows, signalization, and geometrics; 2. Solve for allowable service flow rates for selected levels of service, knowing the details of signalization and geometrics; 3. Solve for signal timing (for an assumed phase plan), knowing the desired level of service and the details of flows and geometrics; and 4. Solve for basic geometrics (number or allocation of lanes), knowing the desired level of service and the details of flows and signalization.
Suitability of Operational Configurations
The methodology presented in this chapter covers a wide range of operational configurations, including combinations of phase plans, lane utilization, and left-turn treatment alternatives. It is important to note that some of these configurations may be considered unacceptable from a traffic safety point of view by some operating agencies. The safety aspect of signalized intersections cannot be ignored, and the provision in this chapter of an analysis methodology for a specific operational configuration does not imply an endorsement of its suitability for application at all locations.
II. METHODOLOGY OPERATIONAL ANALYSIS
Operational analysis results in the determination of capacity and level of service for each lane group as well as the level of service for the intersection as a whole. It requires that detailed information be provided concerning geometric, traffic, and signalization conditions at the intersection. These may be known for existing cases Updated December 1997
or projected for future situations. Because the operational analysis of signalized intersections is complex, it is divided into five distinct modules, as follows: 1. Input Module: All required information upon which subsequent computations are based is defined. The module includes all necessary data on intersection geometry, traffic volumes and
signalized intersections
9-9
Figure 9-3. Operational analysis procedure.
conditions, and signalization. It is used to provide a convenient summary for the remainder of the analysis. 2. Volume Adjustment Module: Demand volumes should be provided in terms of the average flow rates (vph) for the 15-min analysis period, in which case peak-hour factor values of 1.0 should be used. Demand volumes may also be stated in terms of average hourly volumes (vph), in which case the Volume Adjustment Module uses the peak-hour factors provided to convert these to flow rates for the 15-min analysis period. In special cases, analysis periods other than 15 min may be used, in which case average flow rates (vph) should be provided for the analysis period and peak-hour factors of 1.0 should be used. The definition of lane groups for analysis also takes place in this module. 3. Saturation Flow Rate Module: The saturation flow rate is computed for each of the lane groups established for analysis. The flow rate is based on the adjustment of an ‘‘ideal’’ saturation flow rate to reflect a variety of prevailing conditions. 4. Capacity Analysis Module: Volumes and saturation flow rates are manipulated to compute the capacity and v/c ratios for each lane group and the critical v/c ratio for the intersection. 5. LOS Module: Delay is estimated for each lane group established for analysis. Delay measures are aggregated for approaches and for the intersection as a whole, and levels of service are determined. Figure 9-3 is a diagram of the modules and the analysis procedure. Each module is discussed in detail in the sections that follow.
The methodology in this chapter provides formulas and lookup tables for all factors that are to be used. In all cases, the tables provide entries for the extreme limits that are allowed by the method; in no case should the tabulated values be extrapolated beyond these limits except when extrapolation is explicitly recommended (e.g., for lane width factors). Interpolation between tabulated values is suggested to avoid the discontinuities that can occur without interpolation, but the recommended practice in all cases is to use the formulas that are provided to completely avoid the issues of both interpolation and extrapolation. All the examples presented later in this chapter are based on the formulas.
Input Module
Figure 9-4 provides a summary of the input information required to conduct an operational analysis. This information forms the basis for selecting computational values and procedures in the modules that follow. The data needed are detailed and varied, and fall into four main categories; geometric conditions, traffic conditions, signalization conditions, and default values. Geometric Conditions
Intersection geometry is generally presented in diagrammatic form and must include all of the relevant information, including approach grades, the number and width of lanes, and parking conUpdated December 1997
9-10
urban streets ple-period analysis using the procedures in Appendix VI should be performed using each of these subperiods individually. The length of the subperiods would normally be, but not be limited to, 15 min each. Vehicle type distribution is quantified as the percent of heavy vehicles (%HV) in each movement, where heavy vehicles are defined as those with more than four wheels touching the pavement. The number of local buses on each approach should also be identified, including only those buses making stops to pick up or discharge passengers at the intersection (on either the approach or departure side). Buses not making such stops are considered to be heavy vehicles. Pedestrian flows are needed, because these will interfere with permitted right turns. The pedestrian flow for a given vehicular approach is the flow in the crosswalk interfering with right turns from the approach. Thus, for a westbound approach, the pedestrian flow in the north crosswalk would be used; for an eastbound approach, the south-crosswalk flow; for a northbound approach, the east-crosswalk flow; and for a southbound approach, the westcrosswalk flow. One of the most critical traffic characteristics that must be quantified to complete an operational analysis of a signalized intersection is the quality of the progression. The parameter that best describes this characteristic is the arrival type (AT) for each lane group. This parameter is a general categorization that represents the quality of progression in an approximate manner. Six arrival types are defined for the dominant arrival flow as follows:
Figure 9-4. Input data needs for each analysis lane group.
ditions. The existence of exclusive left- or right-turn lanes should be noted, along with the storage lengths of such lanes. When the specifics of geometry are to be designed, these features must be assumed for the analysis to continue. State or local policies and guidelines should be used in establishing the trial design. When these are not readily available, Appendix I of this chapter contains suggestions for geometric design that may be useful in preparing a preliminary design for analysis. Traffic Conditions
Traffic volumes for the intersection must be specified for each movement on each approach. These volumes are the flow rates in vehicles per hour for the 15-min analysis period, which is the normal analysis period length (T = 0.25). If the 15-min data are not known, they may be estimated using hourly volumes and peakhour factors. In situations where v/c is greater than about 0.9, control delay is significantly affected by the length of the analysis period. In these cases, if the 15-min flow rate remains relatively constant for more than 15 min, the length of time the flow is constant should be used as the analysis period, T, in hours. If v/c exceeds 1.0 during the analysis period, the length of the analysis period should be extended to cover the period of oversaturation in the same fashion, as long as the average flow during that period is relatively constant. If the resulting analysis period is longer than 15 min and different flow rates can be identified during equal-length subperiods within the longer analysis period, a multiUpdated December 1997
Arrival Type I: Dense platoon, containing over 80 percent of the lane group volume, arriving at the start of the red phase. This AT is representative of network links that may experience very poor progression quality as a result of conditions such as overall network signal optimization. Arrival Type 2: Moderately dense platoon arriving in the middle of the red phase or dispersed platoon, containing 40 to 80 percent of the lane group volume, arriving throughout the red phase. This AT is representative of unfavorable progression on two-way arterials. Arrival Type 3: Random arrivals in which the main platoon contains less than 40 percent of the lane group volume. This AT is representative of operations at isolated and noninterconnected signalized intersections characterized by highly dispersed platoons. It may also be used to represent coordinated operation in which the benefits of progression are minimal. Arrival Type 4: Moderately dense platoon arriving in the middle of the green phase or dispersed platoon, containing 40 to 80 percent of the lane group volume, arriving throughout the green phase. This AT is representative of favorable progression quality on a two-way arterial. Arrival Type 5: Dense to moderately dense platoon, containing over 80 percent of the lane group volume, arriving at the start of the green phase. This AT is representative of highly favorable progression quality, which may occur on routes with low to moderate side-street entries and which receive high-priority treatment in the signal timing plan design. Arrival Type 6: This arrival type is reserved for exceptional progression quality on routes with near-ideal progression characteristics. It is representative of very dense platoons progressing over a number of closely spaced intersections with minimal or negligible side-street entries. The arrival type is best observed in the field but could be approximated by examining time-space diagrams for the arterial or street
signalized intersections Table 9-2. Relationship Between Arrival Type and Platoon Ratio (Rp) arrival type 1 2 3 4 5 6
range of platoon ratio (Rp) ≤0.50 >0.50 >0.85 >1.15 >1.50 >2.00
and and and and
≤0.85 ≤1.15 ≤1.50 ≤2.00
default value (Rp) 0.333 0.667 1.000 1.333 1.667 2.000
progression quality Very poor Unfavorable Random arrivals Favorable Highly favorable Exceptional
in question. The arrival type should be determined as accurately as possible because it will have a significant impact on delay estimates and LOS determination. Although there are no definitive parameters to precisely quantify arrival type, the following ratio is a useful value: Rp = P(C/gi)
(9-7)
where Rp = platoon ratio; P = proportion of all vehicles in movement arriving during the green phase; C = cycle length; and gi = effective green time for the movement or lane group. P may be estimated or observed in the field, whereas gi and C are computed from the signal timing. Note that when P is estimated, its value may not exceed 1.0. The approximate ranges of Rp are related to arrival type as shown in Table 9-2, and default values are suggested for use in subsequent computations. Another traffic condition of interest is the activity in parking lanes adjacent to analysis lane groups. Parking activity is measured in terms of the number of parking maneuvers per hour within 250 ft upstream of the stop line (Nm). Each vehicle entering or leaving a parking place is considered to be a parking maneuver. Signalization Conditions
Complete information regarding signalization is needed. This includes a phase diagram illustrating the phase plan, cycle length, green times, and change-and-clearance intervals. Actuated lane groups must be identified, including the existence of pushbutton pedestrian-actuated phases. If pedestrian timing requirements exist, the minimum green time for the phase should be indicated and must be provided for in the signal timing. The minimum green time for a phase may be estimated as Gp = 7.0 + (W/4.0) − Yi
(9-8)
where Gp = minimum green time, sec; W = distance from the curb to the center of the farthest travel lane on the street being crossed or to the nearest pedestrian refuge island if the pedestrian crossing is to be made over two signal cycles, ft; and Yi = change-and-clearance interval (yellow + all-red time), sec. It is assumed that the 15th-percentile walking speed of pedestrians crossing a street is 4.0 fps in this computation. This is lower
9-11
than the average pedestrian walking speed of 4.5 fps cited in Chapter 13, Pedestrians. The lower value is intended to accommodate crossing pedestrians who walk at speeds slower than the average. Where local policy uses different criteria for estimating minimum pedestrian crossing requirements, these criteria should be used in lieu of Equation 9-8. When signal phases are actuated, the cycle length and green times will vary from cycle to cycle in response to demand. To establish values for analysis, the operation of the signal should be observed in the field during the same period that volumes are observed. Average values of cycle length and green time may then be used. When signalization is to be established as part of the analysis, state or local policies and procedures should be applied where appropriate in designing the signalization for analysis. Appendix II and the planning method presented later in this chapter contain suggestions for the design of a trial signalization that may also be useful. These should not be construed to be standards or criteria for signal design. It should be noted that a trial signalization cannot be designed until the Volume Adjustment and Saturation Flow Rate modules have been completed. In some cases, the computations will be iterative, because left-turn adjustments for permitted turns used in the Saturation Flow Rate Module depend on signal timing. Appendix II also contains suggestions for estimating the timing of an actuated signal if field observations are unavailable. It should be noted that an operational analysis requires the specification of a signal timing plan for the intersection under study. The planning level analysis presented later in this chapter offers a method for establishing a ‘‘reasonable and effective’’ signal timing plan. The planning procedure is based on the methodology presented in Appendix II to determine an appropriate cycle length and green time allocation for pretimed control. This procedure is recommended only for the estimation of level of service and not for the design of an implementable signal timing plan. The signal timing design process is more complicated and involves, for example, iterative checks for minimum green time violations. When one or more phases are traffic actuated, the timing plan will differ on each cycle. The traffic-actuated procedure presented in Appendix II may be used to estimate the average cycle lengths and phase times under these conditions, provided that the controller settings are available. The design of an implementable timing plan is a complex and iterative process that may be carried out with the assistance of computer software. Although the methodology presented here is oriented toward the estimation of delay at traffic signals, it was suggested in Section I of this chapter that the computations could be applied iteratively to develop a signal timing plan. Some of the available signal timing software products employ the methodology of this chapter at least in part. There are, however, several aspects of signal timing design that are beyond the scope of this manual. One such aspect is the choice of the timing strategy itself. At intersections with traffic-actuated phases, the signal timing plan is determined on each cycle by the instantaneous traffic demand and the controller settings. When all of the phases are pretimed, a timing plan design must be developed. Timing plan design and estimation are covered in detail in Appendix II. Default Values
Occasionally, some of the field data noted in Figure 9-4 will not be available. When critical variables are missing, it may be Updated December 1997
urban streets
9-12
Table 9-3. Default Values for Use in Operational and Planning Analyses characteristic
default value
Traffic Ideal saturation flow rate Conflicting pedestrian volume (assume none unless field data indicate otherwise) Percent heavy vehicles Grade (percent) Number of stopping buses Parking conditions Parking maneuvers Arrival type Lane groups with through movements Lane groups without through movements Peak-hour factor Lane utilization adjustment factor
1,900 pcphgpl None: 0 peds/hr Low: 50 peds/hr Moderate: 200 peds/hr High: 400 peds/hr 2 0 0/hr No parking 20/hr where parking exists 3 if isolated 4 if coordinateda 3 0.90 See Table 9-4
a b
Two major analytic steps are performed in the Volume Adjustment Module: (a) movement volumes are adjusted to flow rates for a 15-min period of analysis, if necessary, and (b) lane groups for analysis are established. Adjustment of Movement Volumes To Reflect Peak Flow Rates
As with other chapters and procedures in this manual, the initial computational process is to convert any demands stated as hourly volumes to flow rates for the 15-min analysis period within the hour. This is done by dividing the movement volumes by an appropriate peak-hour factor (PHF), which may be defined for the intersection as a whole, for each approach, or for each movement. vp = V/PHF
(9-9)
where vp = flow rate during 15-min analysis period, vph; V = hourly volume, vph; and PHF = peak-hour factor.
Facility and Traffic Signal Signal type Cycle length range Start-up lost time Extension of effective green time Yellow plus all-red change-andclearance interval Unit extension Area type Lane width
Volume Adjustment Module
Pretimed 60–120 sec 2.0 sec 2.0 sec 4.0 sec/phase (for planning) 3.0 secb Non-CBD 12 ft
Better arrival types are often possible with favorable progression design. Unit extensions may vary significantly based on local conditions.
Because not all intersection movements may peak at the same time, it is valuable to observe 15-min flows directly and select critical periods for analysis. The conversion of hourly volumes to peak flow rates using the PHF assumes that all movements peak during the same 15-min period, and it is therefore a conservative approach. It is particularly conservative if different PHF values are assumed for each movement. It should be noted also that statistically valid surveys of the PHF for individual movements are difficult to obtain during a single peak hour. Determination of Lane Groups for Analysis
Table 9-4. Default Lane Utilization Adjustment Factors percent of traffic in lane utilization lane group no. of lanes most heavily adjustment movements in lane group traveled lane factor (f LU) Through or shared Exclusive left turn Exclusive right turn
5
1 2 3a
100.0 52.5 36.7
1.00 0.95 0.91
52
100.0 51.5
1.00 0.97
52
100.0 56.5
1.00 0.88
1
a
1 a
a If lane group has more lanes than number shown in this table, it is recommended that surveys be made or the smallest fLU shown for that type of lane group be used.
necessary to conduct a planning analysis. However, default values may be used for some of the variables without seriously compromising computations. Caution should be used when such values are applied, and it must be recognized that results become more approximate as more default values are used. Tables 9-3 and 9-4 summarize default values for use when field data are not available. Use of many of these defaults generates no adjustments to the base, ideal conditions, but this is not true for every default, as in the case of percent heavy vehicles, peak-hour factor, and lane utilization adjustment factor. Updated December 1997
The operational analysis procedure is disaggregate; that is, it is designed to consider individual intersection approaches and individual lane groups (as defined in Section I) within approaches. It is therefore necessary to determine appropriate lane groups for analysis. Segmenting the intersection into lane groups is generally a relatively obvious process that considers both the geometry of the intersection and the distribution of traffic movements. In general, the smallest number of lane groups is used that adequately describes the operation of the intersection. The following guidelines may be applied: 1. An exclusive left-turn lane or lanes should normally be designated as a separate lane group unless there is also a shared leftthrough lane present, in which case the proper lane grouping will depend on the distribution of traffic volume between the movements. The same is true of an exclusive right-turn lane. 2. On approaches with exclusive left-turn or right-turn lanes, or both, all other lanes on the approach would generally be included in a single lane group. 3. When an approach with more than one lane includes a lane that may be used by both left-turning vehicles and through vehicles, it is necessary to determine whether conditions permit equilibrium conditions to exist or whether there are so many left turns that the lane essentially acts as an exclusive left-turn lane, which is referred to as a de facto left-turn lane. De facto left-turn lanes cannot be identified effectively until the proportion of left turns in the shared lane has been computed. A
signalized intersections
9-13
Figure 9-5. Typical lane groups for analysis.
procedure for estimating this quantity will be presented later. If the computed proportion of left turns in the shared lane equals or exceeds 1.0 (i.e., 100 percent), the shared lane must be considered a de facto left-turn lane. When two or more lanes are included in a lane group for analysis purposes, all subsequent computations treat these lanes as a single entity. Figure 9-5 shows some common lane group schemes for analysis. The operation of a shared left-turn and through lane with permitted left-turn phasing is quite complex. Left-turning vehicles execute their turning maneuvers through gaps in the opposing traffic stream. The first gap, however, does not appear until the queue of opposing vehicles clears the intersection. If a left-turner arrives during the interval in which the opposing queue is clearing, it effectively blocks the lane for both through and turning vehicles until the first gap appears. Thereafter, left-turning vehicles may move through gaps in the opposing traffic stream until the green phase terminates, at which time as many as two left-turning vehicles may be able to execute turns during the change interval. Any lane blockages or congestion in the shared lane will influence lane distribution as vehicles move to adjacent lanes to avoid turbulence and delays. Another factor also influences lane distribution. If a through vehicle arrives at the intersection at the time that a gap appears in the opposing traffic stream, no left-turning vehicle will be able to use the gap. A large number of through vehicles in the shared lane may
block so many of the available gaps as to leave insufficient capacity for left-turning vehicles. The interaction of all these mechanisms results in vehicles’ establishing an equilibrium through their selection of lanes. The procedures in this chapter attempt to address this equilibrium state and allow approaches containing shared left-turn and through lanes to be analyzed as a single lane group. Adjustment for Right Turn on Red (RTOR)
When RTOR is permitted, the right-turn volume may be reduced by the volume of right-turning vehicles moving on the red phase. This is generally done on the basis of hourly volumes before converting to flow rates. The number of vehicles able to turn right on a red phase is a function of several complex factors: T T T T T T T
Approach lane allocation (shared or exclusive right-turn lane), Demand for right-turn movements, Sight distance at the intersection approach, Degree of saturation of the conflicting through movement, Arrival patterns over the signal cycle, Left-turn signal phasing on the conflicting street, and Conflicts with pedestrians.
For an existing intersection, it is appropriate to consider the right turns on red that actually occur. For both the shared lane and the exclusive right-turn lane conditions, the number of right turns Updated December 1997
urban streets
9-14
Table 9-5. Adjustment Factor for Average Lane Width (fw)
Table 9-6. Adjustment Factor for Heavy Vehicles (fHV)
average lane width, W (ft)
percent heavy vehicles, %hv
heavy vehicle factor, fHV
0 2 4 6 8 10 15 20 25 30 35 40 45 50 75 100
1.000 0.980 0.962 0.943 0.926 0.909 0.870 0.833 0.800 0.769 0.741 0.714 0.690 0.667 0.571 0.500
lane width factor, fw
8 9 10 11 12 13 14 15 16 Note: fw = 1 +
0.867 0.900 0.933 0.967 1.000 1.033 1.067 1.100 1.133 W − 12 for W ≥ 8 (if W > 16, a two-lane analysis may be 30
considered).
on red may be subtracted from the right-turn volume before the analysis of lane group capacity or level of service. At an existing intersection, the number of right turns on red should be determined by field observations. If the analysis is dealing with future conditions or if the RTOR volume is not known from field data, it is necessary to estimate the number of vehicles that will turn right on the red. This is a very difficult quantity to estimate because of the complexity of the process and variations in driver behavior. In the absence of field data, it is preferable for most purposes to utilize the rightturn volumes directly without a reduction for the number of right turns on red except when an exclusive right-turn lane movement is ‘‘shadowed’’ by a protected left-turn phase from the cross street. For example, the westbound left turn will shadow the northbound right turn. In this case the shadowing left-turn volume per lane may be removed from the total right-turn volume as right turns on red. Free-flowing right turns that are not under signal control should be removed from the analysis. Saturation Flow Rate Module
In the Saturation Flow Rate Module, a saturation flow rate for each lane group is computed. The saturation flow rate is the flow in vehicles per hour that could be accommodated by the lane group assuming that the green phase was always available to the lane group, that is, that the green ratio (g/C) was 1.0. Computations begin with the selection of an ‘‘ideal’’ saturation flow rate, usually 1,900 passenger cars per hour of green time per lane (pcphgpl), and this value is adjusted for a variety of prevailing conditions that are not ideal. All the adjustment factors are given in Tables 9-4 through 9-12. s = so N fw fHV fg f p fbb fa fLU fRT fLT
(9-10)
where s = saturation flow rate for the subject lane group, expressed as a total for all lanes in the lane group under prevailing conditions, vphg; so = ideal saturation flow rate per lane, usually 1,900 pcphgpl; N = number of lanes in the lane group; fw = adjustment factor for lane width (12-ft lanes are standard), given in Table 9-5; fHV = adjustment factor for heavy vehicles in the traffic stream, given in Table 9-6; fg = adjustment factor for approach grade, given in Table 9-7; Updated December 1997
100 for 0 ≤ %HV ≤ 100, where ET = 2.0 100 + %HV (ET − 1) passenger cars per heavy vehicle. Note: fHV =
Table 9-7. Adjustment Factor for Approach Grade (fg) grade, %g type
percent
grade factor, fg
Downhill
−6 or less −4 −2 0 +2 +4 +6 +8 +10 or more
1.030 1.020 1.010 1.000 0.990 0.980 0.970 0.960 0.950
Level Uphill
Note: fg = 1 −
%G for − 6 ≤ %G ≤ +10. 200
fp = adjustment factor for the existence of a parking lane adjacent to the lane group and the parking activity in that lane, given in Table 9-8; fbb = adjustment factor for the blocking effect of local buses that stop within the intersection area, given in Table 9-9; fa = adjustment factor for area type, given in Table 9-10; fLU = adjustment factor for lane utilization, computed as described in the following sections; fRT = adjustment factor for right turns in the lane group, given in Table 9-11; and fLT = adjustment factor for left turns in the lane group, given in Table 9-12 or computed as described in the following sections. Measured values of the prevailing saturation flow rate will produce more accurate results than the estimation procedure described here and can be used directly without further adjustment. Appendix IV gives a procedure for measuring the prevailing saturation flow rate directly. Adjustment Factors
The use of adjustment factors is similar to that in previous chapters. Each factor accounts for the impact of one or several prevailing conditions that are different from the ideal conditions for which the ideal saturation flow rate applies.
signalized intersections
9-15
Table 9-8. Adjustment Factor for Parking (fp) no. of lanes in lane group, N
no. parking
0
10
20
30
40a
1 2 3a
1.000 1.000 1.000
0.900 0.950 0.967
0.850 0.925 0.950
0.800 0.900 0.933
0.750 0.875 0.917
0.700 0.850 0.900
Note: fp =
no. of parking maneuvers per hour, Nm
N − 0.1 − 18Nm/3600 for 0 ≤ Nm ≤ 180, fp ≥ 0.05. N
a
Use formula for more than 3 lanes or more than 40 maneuvers per hour.
Table 9-9. Adjustment Factor for Bus Blockage (fbb) no. of lanes in lane group, N
0
10
20
30
40a
1 2 3a
1.000 1.000 1.000
0.960 0.980 0.987
0.920 0.960 0.973
0.880 0.940 0.960
0.840 0.920 0.947
Note: fbb =
no. of buses stopping per hour, NB
N − 14.4NB/3600 for 0 ≤ NB ≤ 250, fbb ≥ 0.05. N
a
Use formula for more than 3 lanes or more than 40 buses stopping per hour.
Table 9-10. Adjustment Factor for Area Type (fa) type of area
area type factor, fa
CBD or similar All other areas
0.90 1.00
Table 9-11a. Adjustment Factor for Right Turns ( fRT): Formulas Cases 1–6: Exclusive/Shared Lanes and Protected/Permitted Phasing fRT = 1.0 − PRT [0.15 + (PEDS/2100) (1 − PRTA)] 0.0 ≤ PRT ≤ 1.0 Proportion of RT in lane group = 1.00 for excl. RT lane (Cases 1–3); 1700, use 1700). fRT ≥ 0.05 Case 7: Single-Lane Approach (all traffic on approach in a single lane, as defined in Figure 9-5) fRT = 0.90 − PRT [0.135 + (PEDS/2100)] 0 ≤ PRT ≤ 1.0 0 ≤ PEDS ≤ 1700 fRT = 1.00 if PRT = 0.0 fRT ≥ 0.05
Proportion of RT in lane group. Volume (peds/hr) of peds conflicting with RT (use 0 if RT is completely protected).
range of variable values case 1 2 3 4 5 6 7
Excl. RT lane; prot. RT phase Excl. RT lane; perm. RT phase Excl. RT lane; prot. + perm. RT phase Shared RT lane; prot. RT phase Shared RT lane; perm. RT phase Shared RT lane; prot. + perm. RT phase Single-lane approach
PRT
PRTA
peds
simplified formula
1.0 1.0 1.0 0–1.0 0–1.0 0–1.0 0–1.0
1.0 0.0 0–1.0 1.0 0.0 0–1.0 —
0 0–1700 0–1700 0 0–1700 0–1700 0–1700
0.85 0.85 − (PEDS/2100) 0.85 − (PEDS/2100) (1 − PRTA) 1.0 − PRT [0.15] 1.0 − PRT [0.15 + (PEDS/2100)] 1.0 − PRT [0.15 + (PEDS/2100)(1 − PRTA)] 0.9 − PRT [0.135 + (PEDS/2100)]
Updated December 1997
urban streets
9-16
Table 9-11b. Adjustment Factor for Right Turns: Factors proportion of rt’s in lane group, PRT cases 1, 2, 3
cases 4, 5, 6 case
PRTA
2 and 5
0
.20
.40 3 and 6
.60
.80
1 and 4
1.00
7
—
Updated December 1997
0
.2
.4
.6
.8
1.0
0 50 (Low) 100 200 (Mod.) 400 (High) 800 1200 ≥1700
1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
.970 .965 .960 .951 .932 .894 .856 .808
.940 .930 .921 .902 .864 .788 .711 .616
.910 .896 .881 .853 .796 .681 .567 .424
.880 .861 .842 .804 .728 .575 .423 .232
.850 .826 .802 .755 .660 .469 .279 .050
0 50 100 200 400 800 1200 ≥1700 0 50 100 200 400 800 1200 ≥1700 0 50 100 200 400 800 1200 ≥1700 0 50 100 200 400 800 1200 ≥1700
1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
.970 .966 .962 .955 .940 .909 .879 .840 .970 .967 .964 .959 .947 .924 .901 .873 .970 .968 .966 .962 .955 .940 .924 .905 .970 .969 .968 .966 .962 .955 .947 .938
.940 .932 .925 .910 .879 .818 .757 .681 .940 .934 .929 .917 .894 .849 .803 .746 .940 .936 .932 .925 .910 .879 .849 .810 .940 .938 .936 .932 .925 .910 .894 .875
.910 .899 .887 .864 .819 .727 .636 .521 .910 .901 .893 .876 .841 .773 .704 .619 .910 .904 .899 .887 .864 .819 .773 .716 .910 .907 .904 .899 .887 .864 .841 .813
.880 .865 .850 .819 .758 .636 .514 .362 .880 .869 .857 .834 .789 .697 .606 .491 .880 .872 .865 .850 .819 .758 .697 .621 .880 .876 .872 .865 .850 .819 .789 .750
.850 .831 .812 .774 .698 .545 .393 .202 .850 .836 .821 .793 .736 .621 .507 .364 .850 .840 .831 .812 .774 .698 .621 .526 .850 .845 .840 .831 .812 .774 .736 .688
1.00
.970
.940
.910
.880
.850
1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
.873 .868 .863 .854 .835 .797 .759 .711
.846 .836 .827 .808 .770 .694 .617 .522
.819 .805 .790 .762 .705 .590 .476 .333
.792 .773 .754 .716 .640 .487 .335 .144
.765 .741 .717 .670 .575 .384 .194 .050
peds
(Low) (Mod.) (High)
(Low) (Mod.) (High)
(Low) (Mod.) (High)
(Low) (Mod.) (High)
0 0 50 (Low) 100 200 (Mod.) 400 (High) 800 1200 ≥1700
signalized intersections
9-17
Table 9-12. Adjustment Factor for Left Turns (fLT) case
type of lane group
left-turn factor, fLT
1
Exclusive LT Lane; Protected Phasing
0.95
2
Exclusive LT Lane; Permitted Phasing
Special procedure; see worksheet in Fig. 9-17 or 9-18
3
Exclusive LT Lane; Protected-Plus-Permitted Phasing
4
Shared LT Lane; Protected Phasing
Apply Case 1 to protected phase Apply Case 2 to permitted phase fLT = 1.0/(1.0 + 0.05 PLT) Proportion of Left Turns, PLT Factor
5
Shared LT Lane; Permitted Phasing
6
Shared LT Lane; Protected-Plus-Permitted Phasing
0.00
0.20
0.40
0.60
0.80
1.00
1.00
0.99
0.98
0.97
0.96
0.95
Special procedure; see worksheet in Fig. 9-17 or 9-18 fLT = (1,400 − vo′)/[(1,400 − vo′) + (235 + 0.435 vo′)PLT] vo′ ≤ 1,220 vph fLT = 1/[1 + 4.525 PLT] vo′ > 1,220 vph where vo′ = vo /fLUo Opposing Volume vo′
0.00
0.20
0.40
0.60
0.80
1.00
0 200 400 600 800 1,000 1,200 ≥1,220
1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
0.97 0.95 0.92 0.88 0.83 0.74 0.55 0.52
0.94 0.90 0.85 0.79 0.71 0.58 0.38 0.36
0.91 0.86 0.80 0.72 0.62 0.48 0.29 0.27
0.88 0.82 0.75 0.66 0.55 0.41 0.24 0.22
0.86 0.78 0.70 0.61 0.49 0.36 0.20 0.18
Lane Width Adjustment Factor. The lane width adjustment factor, fw, accounts for the deleterious impact of narrow lanes on saturation flow rate and allows for an increased flow on wide lanes. Twelve-foot lanes are the standard. The lane width factor may be calculated with caution for lane widths greater than 16 ft, or an analysis using two narrow lanes may be conducted. Note that use of two lanes will always result in a higher saturation flow rate than a single wide lane, but in either case the analysis should reflect the way in which the width is actually used or expected to be used. In no case should the lane width factor be calculated for lane widths less than 8 ft.
Proportion of Left Turns, PLT
per hour in parking areas directly adjacent to the lane group and within 250 ft upstream from the stop line. If more than 180 maneuvers per hour exist, a practical limit of 180 should be used. If the parking is adjacent to an exclusive-turn-lane group, the factor only applies to that lane group. On a one-way street, parking on the left side will affect the leftmost lane group. If parking is on both sides of a single-lane group, as in a one-way street with no exclusive-turn lanes, the number of maneuvers used is the total for both sides of the lane group. Note that parking conditions with zero maneuvers are not the same as no parking.
Heavy Vehicle and Grade Adjustment Factors. The effects of heavy vehicles and grades are treated by separate factors, fHV and fg, respectively. Their separate treatment recognizes that passenger cars are affected by approach grades, as are heavy vehicles. The heavy vehicle factor accounts for the additional space occupied by these vehicles and for the differential in the operating capabilities of heavy vehicles with respect to passenger cars. The passenger car equivalent (ET) used for each heavy vehicle is 2.0 passenger car units (pcu) and is reflected in the formula. The grade factor accounts for the effect of grades on the operation of all vehicles.
Bus Blockage Adjustment Factor. The bus blockage adjustment factor, fbb, accounts for the impacts of local transit buses that stop to discharge or pick up passengers at a near-side or far-side bus stop within 250 ft of the stop line (upstream or downstream). This factor should only be used when stopping buses block traffic flow in the subject lane group. If more than 250 buses per hour exist, a practical limit of 250 should be used. When local transit buses are believed to be a major factor in intersection performance, Chapter 12, Transit Capacity, may be consulted for a more precise method of quantifying this effect. The factor used here assumes an average blockage time of 14.4 sec during a green indication.
Parking Adjustment Factor. The parking adjustment factor, fp, accounts for the frictional effect of a parking lane on flow in an adjacent lane group, as well as for the occasional blocking of an adjacent lane by vehicles moving into and out of parking spaces. Each maneuver (either in or out) is assumed to block traffic in the lane next to the parking maneuver for an average of 18 sec. The number of parking maneuvers used is the number of maneuvers
Area Type Adjustment Factor. The area type adjustment factor, fa, accounts for the relative inefficiency of business area intersections in comparison with those in other locations, primarily because of the complexity and general congestion in the business environment. Application of the area type adjustment factor reduction is typically appropriate in areas that exhibit many central business district Updated December 1997
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(CBD) characteristics. These characteristics include narrow street rights-of-way; narrow sidewalks; frequent parking maneuvers; vehicle blockages; abundant taxi or bus activity, or both; small-radius turns; limited use of exclusive-turn lanes; high pedestrian activity; dense population; mid-block curb cuts; and so forth. Use of this factor should be determined on a case-by-case basis. This factor is not limited to designated CBD areas, nor will this factor need to be used for all CBD areas. Instead, it should be used in areas where the geometric design and the traffic or pedestrian flows, or both, are such that the vehicle headways are significantly increased to the point where the capacity of the intersection is affected. Lane Utilization Adjustment Factor. The lane utilization adjustment factor accounts for the unequal distribution of traffic on each lane in a lane group when more than one lane exists and provides an adjustment to the saturation flow rate to reflect the rate at which vehicles are discharged from a lane group when variations in lane use exist. The adjustment factor is calculated on the basis of the flow in the lane with the highest volume, as follows: fLU = vg /(vg1N)
(9-11)
where fLU = lane utilization adjustment factor; vg = unadjusted demand flow rate for the lane group, vph; vg1 = unadjusted demand flow rate on the single lane in the lane group with the highest volume; and N = number of lanes in the lane group. The saturation flow rate is normally adjusted for lane utilization to account for the effect of unbalanced lane usage on lane group delay. This adjustment can be used to account for the variation in traffic flow on the individual lanes in a lane group caused by changes in upstream or downstream roadway characteristics such as the number of lanes available or flow characteristics such as the prepositioning of traffic within a lane group due to heavy turning movements within a short distance from an intersection. Actual lane volume distributions observed in the field, if known, should be used in the computation of the lane utilization adjustment factor. A lane utilization factor of 1.0 may be used when uniform traffic distribution can be assumed across all lanes in the lane group or when a lane group is composed of a single lane. When average conditions exist or traffic distribution on a lane group is not known, the default values summarized in Table 9-4 may be used. Right-Turn Adjustment Factor. Turning factors depend on a number of parameters. The most important characteristic is the manner in which turns are accommodated in the intersection. Turns may operate out of exclusive or shared lanes, with protected or permitted signal phasing, or with some combination of these conditions. The impact of turns on saturation flow rates is very much dependent on the mode of turning operations. The right-turn adjustment factor, fRT, depends on a number of variables, including 1. Whether the right turn is made from an exclusive or shared lane; 2. Type of signal phasing (protected, permitted, or protected plus permitted)—a protected right-turn phase has no conflicting pedestrian movements and a permitted phase has conflicting pedestrian movements; 3. Volume of pedestrians using the conflicting crosswalk; 4. Proportion of right-turning vehicles in the shared lane; and 5. Proportion of right turns using the protected portion of a protected-plus-permitted phase. Updated December 1997
Item 5 should be determined by field observation, but a gross estimate can be made from the signal timing by assuming that the proportion of right-turning vehicles using the protected phase is approximately equal to the proportion of the turning phase that is protected. If PRTA = 1.0—that is, the right turn is completely protected from conflicting pedestrians—a pedestrian volume of zero should be used. The right-turn factor is 1.0 if the lane group does not include any right turns. When RTOR is permitted, the right-turn volume may be reduced as described in the discussion of the Volume Adjustment Module. Left-Turn Adjustment Factor. The left-turn adjustment factor, fLT, is based on variables similar to those for the right-turn adjustment factor, including 1. Whether left turns are made from exclusive or shared lanes, 2. Type of phasing (protected, permitted, or protected plus permitted), 3. Proportion of left-turning vehicles using a shared lane group, and 4. Opposing flow rate when permitted left turns are made. The left-turn adjustment factor is 1.0 if the lane group does not include any left turns. When a left turn is not opposed at any time by through vehicles but encounters conflicting pedestrian movements, the left turn should be treated using the adjustment procedure for right turns. If no conflicting pedestrian movements are present, a normal protected left-turn adjustment should be performed. Basically, turn factors account for the fact that these movements cannot be made at the same saturation flow rates as through movements. They consume more of the available green time and consequently more of the lane group’s available capacity. The turn adjustment factors in Tables 9-11 and 9-12 reflect seven different conditions under which turns may be made, as follows: Case Case Case Case Case Case Case
1: 2: 3: 4: 5: 6: 7:
Exclusive lane with protected phasing, Exclusive lane with permitted phasing, Exclusive lane with protected-plus-permitted phasing, Shared lane with protected phasing, Shared lane with permitted phasing, Shared lane with protected-plus-permitted phasing, Single-lane approaches (right-turn factors only).
Special Procedure: Left-Turn Adjustment Factor for Permitted Phasing
When permitted left turns exist, either from shared lanes or from exclusive lanes, their impact on intersection operations is quite complicated. The procedure outlined in this section is applied to Cases 2, 3, and 5 above. Basic Case: Permitted Left Turns. The basic case for which this model was developed is one in which there are simple permitted left turns from either exclusive or shared lanes. This case does not consider the complications of protected-plus-permitted phasing nor cases in which an opposing leading phase may exist. These complications are discussed later. Consider Figure 9-6, which shows a permitted left turn being made from a shared lane group. When the green is initiated, the opposing queue begins to move. While the opposing queue clears, left turns from the subject direction are effectively blocked. The portion of effective green blocked by the clearance of an opposing
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Basic Model for Multilane Approaches and Exclusive-Permitted Left-Turn Lanes. On the basis of this conception of permitted leftturn operations, the left-turn adjustment factor for the lane from which permitted left turns are made can be stated as fm =
1 g 2(1.0) + 3 gf
4
1 2 31 + P (E
g q − gf g (0.0) + u g g
1
L
L1
− 1)
4 (9-13)
fm =
1 g 2 + 1 g 2 31 + P (E gf
gu
1
L
Figure 9-6. Permitted left turn. (Source: W. McShane and R. P. Roess, Traffic Engineering, Prentice-Hall, Englewood Cliffs, N.J.,1990, Fig. 21-8, p. 434.) queue of vehicles is designated gq. During this time, the shared lane from which subject left turns are made is blocked when a leftturning vehicle arrives. Until the first left-turning vehicle arrives, however, the shared lane is unaffected by left-turners. The portion of effective green until the arrival of the first left-turning vehicle is designated gf. Once the opposing queue of vehicles clears, subject left-turning vehicles filter through an unsaturated opposing flow at a rate affected by the magnitude of the opposing flow. The portion of the effective green during which left turns filter through the opposing flow is designated gu. This portioning of the effective green phase for permitted left turns creates up to three distinct periods for which the impact of left turns on a shared or exclusive left-turn lane must be considered: T gf: Until the arrival of the first left-turning vehicle, a shared lane is unaffected by left turns. During this period of time, the effective left-turn adjustment factor is logically 1.0, because no left turns are present. By definition, gf = 0.0 sec for exclusivepermitted left-turn lanes, because it is assumed that a queue of left-turners is present at the beginning of the phase. T gq − gf: If the first left-turning vehicle arrives before the opposing queue clears, it waits until the opposing queue clears, blocking the shared lane, and then seeks a gap in the unsaturated opposing flow that follows. During this period of time, there is effectively no movement in the shared lane, and the left-turn adjustment factor (fLT) applied to the shared lane is logically 0.0. When the first left-turning vehicle arrives after the opposing queue clears, this period of time does not exist; that is, gq − gf has a practical minimum value of zero. The value of gq has a practical range of 0.0 to g. T gu: After the opposing queue clears, left-turning vehicles select gaps through the unsaturated opposing flow. This occurs at a reduced rate because of the interference of opposing vehicles and the effect this has on other vehicles in the shared lane from which left turns are made. During this period, Figure 9-7 assigns EL1 through-car equivalents for each left-turning vehicle. From this, an adjustment factor can be computed for this period: 1/[1.0 + PL (ELl − 1)]
(9-12)
where PL is the proportion of left-turning vehicles in the shared lane. For exclusive-permitted left-turn lanes, PL = 1.0.
L1
− 1)
4
(9-13a)
Note that there is no term in this formulation to account for ‘‘sneakers,’’ that is, vehicles completing left turns during the effective-red portion of the change-and-clearance interval. This is because in saturation flow rate measurements, vehicles are counted when they enter the intersection, not when they leave it. However, there is a practical minimum number of left turns that will be made on any phase, defined by sneakers. To account for this, a practical minimum value must be imposed on fm. One sneaker per cycle may be assumed as a minimum. The probability that a second sneaker will be in position at the end of the green phase will be equal to the proportion of left turns in the shared lane, PL. The estimated number of sneakers per cycle may therefore be computed as (1 + PL). Assuming an approximate average headway of 2 sec per vehicle in an exclusive lane on a protected phase, the practical minimum value of fm may be estimated as 2(1 + PL)/g. For multilane groups, the impact of left turns on a shared lane must be extended to include their impact on the entire lane group. One might simply assume that the factor for the shared lane is fm and that the factor for each other lane in the group is 1.0. This assumes, however, that left turns affect only the lane from which they are made. This is an incorrect assumption, because vehicles maneuver from lane to lane to avoid leftturn congestion. Regression studies suggest that the following relationship is more realistic: fLT = [fm + 0.91(N − 1)]/N
(9-14)
where fLT = left-turn adjustment factor applied to a total lane group from which left turns are made, and fm = left-turn adjustment factor applied only to the lane from which left turns are made. When a single (or double) exclusive-permitted left-turn lane is involved, fLT = fm. To implement this model, it is necessary to estimate the subportions of the effective green phase, gf, gq, and gu. Regression relationships have been developed to permit this, as follows: 1. Compute gf: (9-15) gf = G exp (−0.882LTC 0.717) − tL (shared-permitted left-turn lanes) gf = 0.0 (exclusive-permitted left-turn lanes) 0 ≤ gf ≤ g where G = actual green time for the permitted phase, sec; LTC = left turns per cycle, vpc, computed as vLTC/3600; vLT = adjusted left-turn flow rate, vph; C = cycle length, sec; and tL = lost time for subject left-turn lane group, sec. Updated December 1997
urban streets
9-20
a
Use formula for more than 1,200 effective opposing flow; vo must be greater than zero. EL1 = sTH/sLT (exclusive) EL1 = sTH/sLT − 1 (shared) sLT = [vo′ exp (−vo′tc / 3,600]/[(1 − exp (−vo′tf / 3,600)] where EL1 = through-car equivalent for permitted left turns; sTH = saturation flow of through traffic, vphgpl = 1900 vphgpl; sLT = filter saturation flow of permitted left turns, vphgpl; tc = critical gap, sec = 4.5 sec; and tf = follow-up headway, sec = 2.5 sec (exclusive), 4.5 sec (shared).
Figure 9-7. Through-car equivalents, EL1, for permitted left turns (1).
2. Compute gq: volc qro − tL gq = 0.5 − [volc (1 − qro)/go]
(9-16)
volc (1 − qro)/go ≤ 0.49 0.0 ≤ gq ≤ g where volc = adjusted opposing flow rate per lane per cycle, computed as voC/(3600No fLUo), vplpc; vo = adjusted opposing flow rate, vph; fLUo = lane utilization adjustment factor for opposing flow No = number of opposing lanes; qro = opposing queue ratio, that is, the proportion of opposing flow rate originating in opposing queues, computed as 1 − Rpo(go /C), qro ≥ 0; Rpo = platoon ratio for the opposing flow, obtained from Table 9-2 on the basis of opposing arrival type; go = effective green for the opposing flow, sec; and tL = lost time for opposing lane group. 3. Compute gu: gu = g − g q
when gq ≥ gf
gu = g − g f
when gq < gf
where g = effective green time for subject permitted left turn, sec. Note: When gq < gf, that is, when the first left-turning vehicle does not arrive until after the opposing queue clears, an effective adjustment factor of 1.0 is applied throughout gf and a factor based upon EL1 thereafter. 4. Select the appropriate value of EL1 from Figure 9-7 on the basis of the opposing flow rate, vo, and the lane utilization adjustment factor of the opposing flow, fLUo. For the purposes of determining vo, opposing right and left turns from exclusive lanes are not included in vo. 5. Compute PL (proportion of left turns in shared lane):
3
PL = PLT 1 +
Updated December 1997
1
(N − 1) g gu gf + + 4.24 EL1
24
(9-17)
where PLT = proportion of left turns in the lane group, and N = number of lanes in the lane group. Note: When an exclusive-permitted left-turn lane is involved, PL = PLT = 1.0. 6. Compute fm using Equation 9-13. 7. Compute fLT using Equation 9-14. Basic Model for Single-Lane Approaches Opposed by SingleLane Approaches. The case of a single-lane approach opposed by another single-lane approach has a number of unique features that must be reflected in the model. The most critical of these is the effect of opposing left turns. An opposing left-turning vehicle in effect creates a gap in the opposing flow through which a subject left turn may be made. This can occur during the clearance of the opposing queue as well as during the unsaturated portion of the green phase. Thus, the assumption in the multilane model that there is no flow during the period gq − gf (where gq > gf) is not applicable to opposing single-lane approaches, on which there is flow during this period at a reduced rate reflecting the blocking effect of leftturning vehicles as they await an opposing left turn. Left-turning vehicles during the period gq − gf are assigned a ‘‘through-car equivalent’’ value, EL2, based upon simple queueing analysis, which can be converted to an adjustment factor for application during this period of the green. Since vehicles do not have the flexibility to choose lanes on a single-lane approach, regression relationships for predicting gf and gq are also different from those for the multilane case. Further, for a single-lane approach, fLT = fm, and PL = PLT. As in the multilane case, the opposing single-lane model has no term to account for sneakers but has a practical minimum value of fLT = 2(1 + PLT)/g. The basic model for opposing single-lane approaches is therefore gf g 1 (1.0) + diff fLT = fm = g g 1 + PLT (EL2 − 1) g 1 + u (9-18) g 1 + PLT (EL1 − 1)
12 1 23
1 23
4
4
signalized intersections
1 g 2 + 1 g 2 31 + P gf
gdiff
4 1 2 31 + P
LT
1 gu + (EL2 − 1) g
4
1 (EL1 − 1) (9-18a) where gdiff = max (gq − gf, 0). Note that when no opposing left turns are present, the value of gdiff is to be set to zero. To implement this model, it is again necessary to estimate the subportions of the effective green phase, gf, gq, and gu, as follows: fLT =
LT
1. Compute gf : gf = G exp (−0.860LTC 0.629) − tL, 0 ≤ gf ≤ g
(9-19)
where G = actual green time for the permitted phase, sec; LTC = left turns per cycle, vpc, computed as vLTC/3600; vLT = adjusted left-turn flow rate, vph; C = cycle length, sec; and tL = lost time for subject left-turn lane group, sec.
9-21
Special Cases for Permitted Left Turns. Two special cases for fully permitted left turns must be addressed: a single-lane approach opposed by a multilane approach, and vice versa. When the subject lane in these cases is the single-lane approach, it is opposed by a multilane opposing flow. Even if the opposing approach is a single through lane and an exclusive left-turn lane, opposing left turns will not open gaps in the opposing flow. Thus, the special structure of the single-lane model does not apply. The multilane model is applied, except that fLT = fm. The value of gf, however, should be computed using the single-lane equation, gf = G exp(−0.860LTC 0.629) − tL. When the multilane approach is considered, the reverse is true. The opposing flow is in a single lane, and opposing left turns could conceivably open gaps for subject left-turners. The singlelane model may be applied, with several notable revisions: T gf should be computed using the multilane equation: gf = G exp(−0.882LTC 0.717) − tL
2. Compute gq : gq = 4.943vo/c0.762 qro1.061 − tL, 0.0 ≤ gq ≤ g
(9-20)
where volc = adjusted opposing flow rate per lane per cycle, computed as voC/(3600fLUo) vplpc; vo = adjusted opposing flow rate, vph; fLUo = lane utilization adjustment factor for opposing flow qro = opposing queue ratio, that is, the proportion of opposing flow rate originating in opposing queues, computed as 1 − Rpo(go /C), qro ≥ 0; Rpo = platoon ratio for the opposing flow, obtained from Table 9-2 on the basis of opposing arrival type; and go = effective green for the opposing flow, sec. tL = lost time for opposing lane group 3. Compute gu: g u = g − gq
when gq ≥ gf
g u = g − gf
when gq < gf
where g = effective green time for subject permitted left turn, sec. Note: When gq < gf, that is, when the first left-turning vehicle does not arrive until after the opposing queue clears, an effective adjustment factor of 1.0 is applied throughout gf and a factor based upon EL1 thereafter. 4. Select the appropriate value of EL1 from Figure 9-7 on the basis of the opposing flow rate, vo, and the lane utilization adjustment factor of the opposing flow, fLUo. 5. Compute EL2: EL2 = (1 − PnTHo)/PLTo,
EL2 ≥ 1.0
(9-21)
where PLTo = proportion of left turns in opposing single-lane approach; PTHo = proportion of through and right-turning vehicles in opposing single-lane approach, computed as 1 − PLTo; and n = maximum number of opposing vehicles that could arrive during gq − gf, computed as (gq − gf)/2. Note that n is subject to a minimum value of zero. 6. Compute fLT using Equation 9-18.
T PL must be estimated and substituted for PLT in the singlelane model. PL may be estimated from PLT using the multilane equation:
31
PL = PLT 1 +
1
(N − 1) g g gf + u + 4.24 EL1
2
24
(9-17)
T fLT does not equal fm. Thus, the conversion must be made using the multilane equation, except when the subject approach is a dual left-turn lane. fLT = [fm + 0.91 (N − 1)]/N Worksheets that may be used to assist in implementing the special models for permitted left-turn movements are presented in Section III of this chapter. These worksheets do not account for the modifications that must be made to analyze single-lane approaches opposed by multilane approaches, and vice versa. More Complex Phasing with Permitted Left Turns. The models and worksheets presented in the previous section apply directly to situations in which left turns are made only on permitted phases (without protection) and in which no protected phases or opposing leading green phases exist. The models may, however, be applied to these more complex cases with some modifications. In general, protected-plus-permitted phases for exclusive lanes are analyzed by separating the portions of the phase into two lane groups for the sake of analysis. Each portion of the phase is then handled as it would be normally if the other were not present. The protected portion of the phase is treated as a protected phase, and a left-turn adjustment factor appropriate to a protected phase is selected. The permitted portion of the phase is treated as a permitted phase, and the special procedures outlined here are used to estimate a left-turn adjustment factor (with modifications as defined in this section). By doing this, separate saturation flow rates may be computed for each portion of the phase. A method for estimating delays in such cases is described later in this chapter. This method does not require that the demand volume for the protected-pluspermitted movement be divided between the two portions of the phase. However, the computation of the critical v/c ratio, Xc, does require this apportionment. The following is a reasonable Updated December 1997
9-22
urban streets
and conservative approach to apportioning the volumes for purposes of computing Xc: T The first portion of the phase, whether protected or permitted, is assumed to be fully utilized, that is, to have a v/c of 1.0, unless total demand is insufficient to use the capacity of that portion of the phase. T Any remaining demand not handled by the first portion of the phase is assigned to the second portion of the phase, whether protected or permitted. This approach assumes that when the movement is initiated, a queue is available that uses available capacity in the initial portion of the phase. In cases of a failed cycle, the unserved queue will exist after the end of the second portion of the phase, with those vehicles queued and ready to use the initial portion of the phase on the next cycle. In this sense, the initial portion of the movement can never operate at a v/c of more than 1.0. In the analysis of the permitted portion of such phases, as well as those with opposing leading protected left-turn phases, the basic models described previously may be applied. The difficulty is in selecting values of G, g, gf, gq, and gu for use in these models. The equation for gf is indexed to the beginning of effective green in the subject direction, and gq is indexed to the beginning of the effective green for the opposing flow. When leading or lagging phasing or protected-plus-permitted phasing exists, these equations must be modified to account for shifts in the initiation and overlap of various green times. Some common examples are shown in Figure 9-8. The following notation is used: G, g, gf, and gq are computed as shown in the models and worksheets. These values are modified as shown and replaced on the worksheets with G*, g*, gf*, and gq* for the permitted portion of protected-plus-permitted phasing. This extended notation is required to cover the general case of complex left-turn phasing. In most practical cases, it will not be necessary to use all the superscripted terms. The standard case is shown in Figure 9-8(a) as a starting point. Case 2 is a leading green phase. The equations shown are valid for either exclusive-lane or shared-lane operation, except that gf is zero by definition for the exclusive-lane case. For exclusive-lane operation, the leading green, G1, is followed by G/Y1, a period during which the left-turn change-and-clearance interval is displayed, and the through movement continues with a green indication. G2 has a green indication for both the through and left-turn movements, followed by a full change-and-clearance interval for all north-south movements, Y2. The effective green time for the permitted phase, g*, is equal to G2 + Y2 for the NB direction and G2 + Y2 − tL for the SB direction. Note that there is no lost time for NB movements, since both were initiated in the leading phase, and the lost time is assessed there. Thus, the NB and SB effective green times that must be used are not equal. For the NB phase, gf is computed using the total green time for NB left-turn movement, G1 + G/Y1 + G2. The computed value, however, begins with the leading-phase effective green, as shown. The value that needs to be applied to the permitted phase, however, is that portion of gf that overlaps g*, which results in gf* = gf − G1 − G/Y1 + tL. This computation would be done for a shared lane, and the result, gf*, would have to be a value between 0 and g*. For an exclusive-lane case, gf and gf* are by definition zero. For the SB phase, gf as normally computed is the same as gf*, and no adjustment is necessary. Updated December 1997
For the NB phase, gq is referenced to the beginning of the opposing (SB) effective green. Again, the value needed is the portion of the NB g* blocked by the clearance of the opposing queue. Because the NB effective green (g*) does not account for lost time, gq* = gq + tL. For the SB phase, the usual computation of gq is indexed to the start of the opposing (NB) flow, which begins in the leading phase. For analysis of the permitted phase, however, only the portion that blocks the SB permitted effective green is of interest. Thus, gq* = gq − G1 − G/Y1. The foregoing discussion is illustrative. The relationship between the normal calculations of g, G, gf, and gq and their adjusted counterparts, g*, G*, gf*, and gq*, is best illustrated by Figure 98, which may be used in conjunction with the standard worksheets to arrive at the appropriate left-turn adjustment factor for the permitted portion of a protected-plus-permitted phase plan. Obviously, ‘‘north’’ and ‘‘south’’ can be reversed or replaced by ‘‘east’’ and ‘‘west’’ without any change in the equation shown. Capacity Analysis Module
In the Capacity Analysis Module, computational results of previous modules are manipulated to compute key capacity variables, including 1. 2. 3. 4.
Flow ratio for each lane group. Capacity of each lane group. Volume-to-capacity ratio of each lane group, and Critical v/c ratio for the overall intersection.
Flow ratios are computed by dividing the adjusted demand flow, v, computed in the Volume Adjustment Module by the adjusted saturation flow rate, s, computed in the Saturation Flow Rate Module. The capacity of each lane group is computed from Equation 9-3: ci = si(gi /C) If the signal timing is not known, a timing plan will have to be estimated or assumed to make these computations. Appendix II contains suggestions for making these estimates, but state or local policies and guidelines should also be consulted whenever possible. The planning method described later also offers a procedure for the synthesis of timing plans based on the concepts presented in Appendix II. The v/c ratio for each lane group is computed directly by dividing the adjusted flows by the capacities computed above, as in Equation 9-4: Xi = vi /ci The final capacity parameter of interest is the critical v/c ratio, Xc, for the intersection. It is computed from Equation 9-5 as follows: Xc = ∑(v/s)ci C/(C − L) This ratio indicates the proportion of available capacity that could be utilized by vehicles in critical lane groups. If this ratio exceeds 1.0, one or more of the critical lane groups will be oversaturated. A ratio over 1.0 is an indication that the intersection design, cycle length, or phase plan is inadequate, or all three are inadequate, for the given demand. A ratio of less than 1.0 indicates that the design, cycle length, and phase plan are adequate to handle all critical flows without having demand exceed capacity, assum-
signalized intersections
9-23
Figure 9-8. Green time adjustments for protected-plus-permitted phasing: (a) standard case and Case 2, (b) Cases 3 and 4, and (c) Case 5. (Continued on next page.)
ing that green times are proportionally assigned. When phase splits are not proportional to the v/s ratios, some movement demands may exceed movement capacities even where the critical v/c ratio is less than 1.0. The computation of the critical v/c ratio, Xc, requires that critical lane groups be identified. During each signal phase, one or more lane groups are given the green. One lane group will have the most intense demand and will be the one that determines the amount of green time needed. This lane group would be the critical lane group for the phase in question. The critical lane group for each signal phase in effect controls the required signal timing, or, given the signal timing, the critical lane group is the one most constrained by it. The normalized measure of demand intensity on any lane group is given by the v/s ratio for the lane group. When there are no overlapping phases in the signal design, such as in a simple twophase signal, the determination of critical lane groups is straightfor-
ward: in each discrete phase, the lane group with the highest v/s ratio is critical. Thus, when phases do not overlap, 1. There is one critical lane group for each signal phase, 2. In each phase, the critical lane group is the one with the highest v/s ratio among the lane groups moving in that phase, and 3. The critical lane group v/s ratios are summed for use in computing Xc. Overlapping phases are more difficult to analyze, because various lane groups may move in several phases of the signal, and some left-turn movements may operate on a protected-and-permitted basis in various portions of the cycle. In such cases, it is necessary to find the critical path through the signal cycle. The path having the highest sum of v/s ratios is the critical path. When phases overlap, the critical path must conform to the following rules: Updated December 1997
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urban streets
Figure 9-8 (continued).
1. Excluding lost times, one critical lane group must be moving at all times during the signal cycle, 2. At no time in the signal cycle may more than one critical lane group be moving, and 3. The critical path has the highest sum of v/s ratios. In some complex phasing situations, it may not be possible to identify critical movements using the guidelines stated above (e.g., Updated December 1997
protected-and-permitted movements from a shared lane under leftturn Case 6). In such cases, the user may need to allocate volumes in the most logical manner possible or simply omit the critical v/c determination from the analysis. These rules are more easily explained by example. Consider the case of a leading and lagging green phase plan on an arterial with exclusive left-turn lanes, as shown in Figure 9-9.
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9-25
Figure 9-8 (continued).
Figure 9-9. Critical lane group determination: leading and lagging green phase plan with exclusive left-turn lanes. Updated December 1997
9-26
urban streets
Phase 1 is discrete, with NB and SB lane groups moving simultaneously. The critical lane group for Phase 1 would therefore be chosen on the basis of the highest v/s ratio. As the v/s ratio for the NB lane group is 0.30 and that for the SB lane group is 0.25, the NB lane group is the critical lane group for this phase. Phase 2 involves overlapping leading and lagging green phases. There are two possible paths through Phase 2 that conform to the rule stated above, that is, that (except for lost times) there must be only one critical lane group moving at all times. The EB through and right-turn (T/R) lane group moves through Phases 2A and 2B with a v/s ratio of 0.30. The WB left-turn lane group moves only in Phase 2C with a v/s ratio of 0.15. The total v/s ratio for this path is therefore 0.30 + 0.15 or 0.45. The only alternative path involves the EB left-turn lane group, which moves only in Phase 2A (v/s = 0.25), and the WB T/R lane group, which moves in Phases 2B and 2C (v/s = 0.25). Because the sum of the v/s ratios for this path is 0.25 + 0.25 = 0.50, which is higher than the v/s ratio for the alternative, this is the critical path through Phase 2. Thus, the sum of critical v/s ratios for the cycle is 0.30 for Phase 1 plus 0.50 for Phase 2, for a total of 0.80. The solution for Xc also requires that the lost time for the critical path (L) through the signal be determined. Using the general rule that a movement’s lost time tL is applied when a movement is initiated, the following conclusions are reached: T The critical NB movement is initiated in Phase 1, and its lost time is applied. T The critical EB left-turn movement is initiated in Phase 2A, and its lost time is applied. T The critical WB T/L movement is initiated in Phase 2B, and its lost time is applied. T No critical movement is initiated in Phase 2C. Therefore, no lost time is applied to the critical path here. Although the WB leftturn movement is initiated in this phase, it is not a critical movement, and its lost time is not included in L. T Therefore, for this case, L = 3tL, assuming that each movement has the same lost time, tL. This problem may be altered significantly by adding a permitted left turn in both directions to Phase 2B. This is shown in Figure 9-10, with the v/s ratios resulting. Note that in this case, a separate v/s ratio is computed for the protected and permitted portions of the EB and WB left-turn movements. In essence, the protected and permitted portions of these movements are treated as separate lane groups. The analysis of Phase 1 does not change, because it is discrete. The NB lane group is still critical, with a v/s ratio of 0.30. There are now, however, four different potential paths through Phase 2 that conform to the rules for determining critical paths: WB T/R + EB left turn (protected) = 0.25 + 0.20 = 0.45. EB T/R + WB left turn (protected) = 0.30 + 0.05 = 0.35. EB left turn (protected) + EB left turn (permitted) + WB left turn (protected) = 0.20 + 0.15 + 0.05 = 0.40. EB left turn (protected) + WB left turn (permitted) + WB left turn (protected) = 0.20 + 0.22 + 0.05 = 0.47. The critical path through Phase 2 is the one with the highest total v/s ratio. This is the last choice, and yields a v/s ratio of 0.47, which when added to the 0.30 for Phase 1 results in a sum of critical v/s ratio of 0.77. Note that this is a smaller total than for Updated December 1997
Figure 9-10. Critical lane group determination: leading and lagging green phase plan with addition of permitted left turn in Phase 2B. the option without permitted left turns in Phase 2B, which is an expected result. Again, the lost time for the critical path is determined as follows: T The NB critical flow begins in Phase 1, and its lost time is applied. T The critical EB left turn (protected) is initiated in Phase 2A, and its lost time is applied. T The critical WB left turn (permitted) is initiated in Phase 2B, and its lost time is applied. T The critical WB left turn (protected) is a continuation of the WB left turn (permitted). Because the left-turn movement is already moving when Phase 2C is initiated, no lost time is applied here. T Thus, for this case, L = 3tL, assuming that each movement has the same lost time, tL. This is the same result obtained previously. Figure 9-11 shows another complex case with actuated control and a typical eight-phase plan. Although eight phases are provided on the controller, the path through the cycle cannot include more than six of these phases, as shown. The leading phases (1B and 2B) will be chosen on the basis of which left-turn movements have higher demands on a cycle-by-cycle basis. The possible critical paths through Phase 1 are as follows: EB left turn (protected) + EB left turn (permitted), EB left turn (protected) + WB left turn (permitted), EB left turn (protected) + WB T/R, WB left turn (protected) + WB left turn (permitted), WB left turn (protected) + EB left turn (permitted), and WB left turn (protected) + EB T/R. Again, the combination with the highest v/s ratio would be chosen as the critical path. A similar set of choices exists for Phase 2, with NB replacing EB and SB replacing WB. The most interesting aspect of this problem is the number of lost times that must be included in L for each of these paths. The
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Figure 9-11. Critical lane group determination: complex multiphase signal. paths involving EB left turn (protected) + EB left turn (permitted) and WB left turn (protected) + WB left turn (permitted) involve only one application of tL each, because the turning movement in question moves continuously throughout the three subphases. All other paths involve two applications of tL, because each critical movement is initiated in a portion of the phase. Note that the left turn that does not continue in Phase 1B or 2B is a discontinuous movement; that is, it moves as a protected turn in Phase 1A or 2A, stops in Phase 1B or 2B, and moves again as a permitted turn in Phase 1C or 2C. Thus, for this complex phasing, the lost time through each major phase could have one or two lost times applied, on the basis of the critical path. Therefore, for the total cycle, two to four lost times will be applied, again depending on the critical path. In general terms, up to n lost times are to be applied in the calculation of the total lost time per cycle, where n is the number of movements in the critical path through the signal cycle. For the purposes of determining n, a protected-plus-permitted movement is considered to be one movement if the protected and permitted phases are adjacent. LOS Module
In the LOS Module, the average control delay per vehicle is estimated for each lane group and averaged for all approaches and for the intersection as a whole. Level of service is directly related
to the control delay value, as shown in Table 9-1. The values derived from the formulas represent the average control delay experienced by all vehicles that arrive in the analysis period, including delays incurred beyond the analysis period when the lane group is oversaturated. The average control delay per vehicle for a given lane group is d = d1PF + d2 + d3
(9-22)
where d1 = uniform control delay component assuming uniform arrivals, sec/veh; PF = uniform delay progression adjustment factor that accounts for the effects of signal progression on delay; d2 = incremental delay component to account for the effect of random and oversaturation queues, adjusted for the duration of the analysis period and the type of signal control; this delay component assumes that there is no residual demand for the lane group at the start of the analysis period, sec/ veh; and d3 = residual demand delay to account for oversaturation queues that may have existed before the analysis period, sec/veh; this component is detailed in Appendix VI. Uniform Delay, d1
Equation 9-23 gives an estimate of delay assuming perfectly uniform arrivals and stable flow. It is based on the first term of Updated December 1997
urban streets
9-28
Webster’s delay formulation and is widely accepted as an accurate depiction of delay for the idealized case of uniform arrivals. Note that values of X beyond 1.0 are not used in the computation of d1. d1 =
0.50C(1 − g/C)2 1 − Min(1,X)g/C
(9-23)
where C = cycle length, sec [cycle length used in pretimed signal control, or average cycle length for actuated control (see Appendix II for signal timing estimation of actuated control parameters)]; g = effective green time for lane group, sec [green time used in pretimed signal control, or average green time for actuated control (see Appendix II for signal timing estimation of actuated control parameters)]; and X = v/c ratio or degree of saturation for lane group. Progression Adjustment Factor, PF. Good signal progression will result in a high proportion of vehicles arriving on the green. Poor signal progression will have a low percentage of vehicles arriving on the green. The progression adjustment factor, PF, applies to all coordinated lane groups, including both pretimed control and nonactuated lane groups in semiactuated control systems. In circumstances where coordinated control is explicitly provided for actuated lane groups, PF may also be applied to these lane groups. Progression primarily affects uniform delay, and for this reason, the adjustment is applied only to d1. The value of PF may be determined by
Rpgi /C. Arrival Type 3 should be assumed for all uncoordinated lane groups. Movements made from exclusive left-turn lanes on protected phases are not usually provided with good progression. Thus, Arrival Type 3 is usually assumed for coordinated left turns. When the actual arrival type is known, it should be used. When the coordinated left turn is part of a protected-permitted phasing, only the effective green for the protected phase should be used to determine PF since the protected phase is normally the phase associated with platooned coordination. When a lane group contains movements that have different levels of coordination, a flow-weighted average of P should be used in determining the PF. Incremental Delay d2
Equation 9-25 estimates the incremental delay due to nonuniform arrivals and temporary cycle failures (random delay) as well as that caused by sustained periods of oversaturation (oversaturation delay). It is sensitive to the degree of saturation of the lane group (X), the duration of the analysis period of interest (T), the capacity of the lane group (c), and the type of signal control as reflected by the control parameter (k). The formula assumes that there is no unmet demand causing residual queues at the start of the analysis period (T). Should that not be the case, the reader may consult Appendix VI for additional procedures that can account for the effect of a nonzero initial queue on signal delay. Finally, the incremental delay term is valid for all values of X, including highly oversaturated lane groups. The expression for d2 is
3
d2 = 900T (X − 1) + (1 − P)fP PF = 1 − (g/C)
(9-24)
where P = proportion of vehicles arriving on the green, g/C = proportion of green time available, and fP = supplemental adjustment factor for when the platoon arrives during the green. The default values for fP are 0.93 for Arrival Type 2, 1.15 for Arrival Type 4, and 1.0 for all other arrival types. The value of P may be measured in the field or estimated from the arrival type. If field measurements are carried out, P should be determined as the proportion of vehicles in the cycle that arrive at the stop line or join the queue (stationary or moving) while the green phase is displayed. PF may be computed from measured values of P using the default values for fP. Alternatively, Table 913 may be used to determine PF as a function of the arrival type based on the default values for P (i.e., Rpgi /C) and fP associated with each arrival type. If PF is estimated by Equation 9-24, its calculated value may exceed 1.0 for Arrival Type 4 with extremely low values of g/C. As a practical matter, PF should be assigned a maximum value of 1.0 for Arrival Type 4. This has already been taken into consideration in Table 9-13. Application of the adjustment factor for progression requires detailed knowledge of offsets, travel speeds, and intersection signalization. When delay for future situations involving coordination is estimated, particularly when alternatives are analyzed, it is advisable to assume Arrival Type 4 as a base condition for coordinated lane groups (except left turns), in which case P may be estimated using the Rp default values from Table 9-2 and Equation 9-7 as Updated December 1997
!(X − 1) + 2
8kIX cT
4
(9-25)
where T = duration of analysis period, hours; k = incremental delay factor that is dependent on controller settings; I = upstream filtering/metering adjustment factor; c = lane group capacity, vph; and X = lane group v/c ratio, or degree of saturation. Incremental Delay Calibration Term (k)
The calibration term (k) is included in Equation 9-25 to incorporate the effect of controller type on delay. For pretimed signals, a value of k = 0.50 is used throughout. This value is based on a queueing process with random arrivals and uniform service time equivalent to the lane group capacity. Actuated controllers, on the other hand, have the ability to tailor the green time to the cyclic demand, thus reducing the overall incremental delay component. The delay reduction depends in part on the controller’s unit extension and the prevailing v/c ratio. Recent research indicates that lower unit extensions result in lower values of k and d2. However, when v/c approaches 1.0, an actuated controller will behave in a similar manner to a pretimed controller at the maximum settings. Thus, the k parameter will converge to the pretimed value of 0.50 at X ≥ 1.0. The recommended k values for pretimed and actuated lane groups are given in Table 9-14. For unit extension values other than those listed in Table 914, k values may be interpolated. If the formula in Table 9-14 is used the kmin value (the k value for X = 0.5) should first be interpolated for the given unit extension and then the formula
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Table 9-13. Progression Adjustment Factor (PF) progression adjustment factor (PF) PF = (1 − P)fP/(1 − g/C) (see Note) arrival type (AT) green ratio (g/C)
AT-1
0.20 0.30 0.40 0.50 0.60 0.70 Default, fP Default, RP
AT-2
AT-3
AT-4
AT-5
AT-6
3
1.167 1.286 1.445 1.667 2.001 2.556
1.007 1.063 1.136 1.240 1.395 1.653
1.000 1.000 1.000 1.000 1.000 1.000
1.000 0.986 0.895 0.767 0.576 0.256
0.833 0.714 0.555 0.333 0.000 0.000
0.750 0.571 0.333 0.000 0.000 0.000
1.00 0.333
0.93 0.667
1.00 1.000
1.15 1.333
1.00 1.667
1.00 2.000
Note: 1. Tabulation is based on default values of fP and RP. 2. P = RPg/C (may not exceed 1.0). 3. PF may not exceed 1.0 for AT-3 through AT-6.
Table 9-14. Recommended k Values for Lane Groups Under Actuated and Pretimed Control UNIT EXTENSION (sec)
degree of saturation (X) ≤0.50
0.60
0.70
0.80
0.90
≥1.0
≤2.0 2.5 3.0 3.5 4.0 4.5 5.01
0.04 0.08 0.11 0.13 0.15 0.19 0.23
0.13 0.16 0.19 0.20 0.22 0.25 0.28
0.22 0.25 0.27 0.28 0.29 0.31 0.34
0.32 0.33 0.34 0.35 0.36 0.38 0.39
0.41 0.42 0.42 0.43 0.43 0.44 0.45
0.50 0.50 0.50 0.50 0.50 0.50 0.50
Pretimed or nonactuated movement
0.50
0.50
0.50
0.50
0.50
0.50
Note: For a given UE and its kmin value at X = 0.5: k = (1 − 2kmin)(X − 0.5) + kmin, k ≥ kmin, k ≤ 0.5. 1 For UE > 5.0, extrapolate to find k, keeping k ≤ 0.5.
should be used. Table 9-14 may be extrapolated for unit extension values beyond 5.0 sec, but in no case should the extrapolated k value exceed 0.5.
proach and for the intersection as a whole. In general, this is done by computing weighted averages, where the lane group delays are weighted by the adjusted flows in the lane groups. Thus, the delay for an approach is computed as
Upstream Filtering/Metering Adjustment Factor, I
The incremental delay adjustment factor, I, incorporates the effects of metering arrivals from upstream signals, as described in Chapter 11. In an isolated signal analysis in this chapter, an I value of 1.0 is used. Residual Demand Delay, d3
When a residual demand from a previous time period causes a residual queue to occur at the start of the analysis period (T), additional delay is experienced by the vehicles arriving in the period, since the residual queues must first clear the intersection. A procedure for determining this supplemental delay is described in detail in Appendix VI. If this is not the case, a d3 value of zero is used. This procedure is also extended to analyze delay over multiple time periods, each having a duration (T) in which a residual demand may be carried from one time period to the next.
dA =
o dv ov
i i
(9-26)
i
where dA = delay for approach A, sec/veh; di = delay for lane group i (on approach A), sec/veh; and vi = adjusted flow for lane group i, vph. Approach control delays can then be further averaged to provide the average delay for the intersection: dI =
odv ov
A A
(9-27)
A
where dl = average delay per vehicle for the intersection, sec/veh, and vA = adjusted flow for approach A, vph.
Aggregating Delay Estimates
The procedure for delay estimation yields the average control delay per vehicle for each lane group. It is also desirable to aggregate these values to provide average delay for an intersection ap-
LOS Determination
Intersection level of service is directly related to the average control delay per vehicle. Once delays have been estimated for Updated December 1997
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urban streets
each lane group and aggregated for each approach and the intersection as a whole, Table 9-1 is consulted, and the appropriate levels of service are determined for each component. Special Procedure for Uniform Delay with Protected-Plus-Permitted Operation
The delay estimation model just presented is based on a wellestablished formulation originally proposed by Webster and subsequently modified by others. The delay per vehicle is expressed as the sum of two terms. The first term represents the delay that would result from completely uniform arrival of vehicles over the signal cycle. The second term recognizes the tendency for occasional overflow to occur as a result of random arrivals. The first term is easily derived as a function of the area contained within the plot of queue storage as a function of time. With a single green phase per cycle, this plot assumes a triangular shape; that is, the queue size increases linearly on the red phase and decreases linearly on the green. The peak storage occurs at the end of the red phase. The geometry of the triangle depends on the arrival flow rate, the queue discharge rate, and the length of the red and green signal phases. This simple triangle becomes a more complex polygon when left turns are allowed to proceed on both protected and permitted phases. However, the area of this polygon, which determines the uniform delay, is still relatively easy to compute given the proper values for the arrival and discharge rates during the various intervals of the cycle, along with the interval lengths that determine its shape. In the following discussion, the protected phase is referred to as the primary phase and the permitted phase is referred to as the secondary phase. Specifically, the following quantities must be known to evaluate the uniform delay: T The arrival rate, qa (veh/sec), presumed to be uniform over the entire cycles; T The saturation flow rate sp (veh/sec) for the primary phase; T The saturation flow rate ss (veh/sec) for the unsaturated portion of the secondary phase (the unsaturated portion begins when the queue of opposing vehicles has been served); T The effective green time, g (sec), for the primary phase in which a green arrow is displayed to the left turns; T The green time gq (sec) during the secondary phase when the opposing through movement blocks the permitted left turns (this interval begins at the start of the permitted green and continues until the queue of opposing through vehicles has been fully discharged); T The green time gu (sec) that is available for left-turning vehicles to filter through gaps in the oncoming traffic [this interval begins when the queue of opposing through vehicles has been satisfied (i.e., at the end of gq) and continues until the end of the permitted green phase]; and T The red time r (sec) during which the signal is effectively red for the left turn. The input-output relationships that determine the shape and area of the polygon are shown in Figure 9-12. Note that the queueing polygon may assume five different shapes depending on the relationship of arrivals and departures. Slightly different mathematical formulas must be applied to determine the area for each of the different shapes. In all cases, the arrival rate must be adjusted to ensure that, for purposes of uniform delay computation, the v/c Updated December 1997
ratio is not greater than 1.0. This adjustment is also necessary for the analysis of simple protected operation as described previously. If the v/c ratio is greater than 1.0, the area contained by the polygon will not be defined. The effect of v/c ratios greater than 1.0 is expressed by the second term of the delay equation. It is first necessary to distinguish between protected-plus-permitted (leading left-turn) phasing and permitted-plus-protected (lagging left-turn) phasing. Three of the five cases shown in Figure 9-12 are associated with leading left-turn phases and the other two are associated with lagging left-turn phases. The five cases are identified as follows: Case 1—leading left-turn phase: no queue remains at the end of the protected or permitted phase. Case 2—leading left-turn phase: a queue remains at the end of the protected phase but not at the end of the permitted phase. Case 3—leading left-turn phase: a queue remains at the end of the permitted phase but not at the end of the protected phase. Note that it is not possible to have a queue at the end of both the protected and permitted phases if the v/c ratio is not allowed to exceed 1.0 for purposes of the uniform delay term. Case 4—lagging left-turn phase: no queue remains at the end of the permitted phase. In this case there will be no queue at the end of the protected phase either, because the protected phase follows immediately after the permitted phase and will therefore accommodate all of its arrivals without further delay. Case 5—lagging left-turn phase: a queue remains at the end of the permitted phase. If the v/c ratio is kept below 1.0 as just discussed, this queue will be fully served during the protected phase. Some intermediate computations are required to provide a consistent framework for dealing with all of these cases. Three queue lengths may be determined at various transition points within the cycle. These values are defined as follows: T Queue size Qa (veh) at the beginning of the green arrow, T Queue size Qu (veh) at the beginning of the unsaturated interval of the permitted green phase, and T Residual queue size Qr (veh) at the end of either the permitted or the protected phase. These queue sizes dictate the shape of the polygon whose area determines the value of uniform delay. Separate formulas will be given for computing each of the queue sizes for the five cases just described. Formulas will be provided for computing the uniform delay as a function of the queue sizes. Interpretation of Results
The results of an operational analysis will yield two key values: 1. Volume-to-capacity ratios for each lane group and for all of the critical lane groups within the intersection as a whole, and 2. Average control delays for each lane group and approach and for the intersection as a whole and the corresponding levels of service. Any v/c ratio greater than 1.0 is an indication of actual or potential breakdown and a condition requiring amelioration. When the overall intersection v/c ratio is less than 1.0 but some critical lane groups have v/c ratios greater than 1.0, the green time is generally not appropriately apportioned, and a retiming using the existing
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Figure 9-12. Queue accumulation polygons. phasing should be attempted. Appendix II may be consulted for suggestions in this regard. A critical v/c ratio greater than 1.0 indicates that the overall signal and geometric design provides inadequate capacity for the given flows. Improvements that might be considered include any or all of the following: 1. Basic changes in intersection geometry (number and use of lanes), 2. Increases in the signal cycle length if it is determined to be too short, or 3. Changes in the signal phase plan. Appendixes I and II may be consulted for suggestions with regard to these improvements. Existing state and local policies or standards should also be consulted in the development of potential improvements. It should also be noted that v/c ratios near 1.0 represent situations with little available capacity to absorb demand increases. Particularly when projected volumes are being used, normal inaccuracies in such projections can cause an intersection projected to operate near capacity to become oversaturated. Level of service is a measure of the acceptability of delay levels to motorists at a given intersection. When delays are unacceptable, the causes of delay should be carefully examined. If an unfavorable progression is the largest contributor to delay, changes in intersection design and intersection signalization will have little impact; offsets and arterial coordination should be examined for possible improvement. When progression is reasonable and unacceptable delays still exist, provision of greater capacity through geometric or signal design changes should be examined.
In some cases, delay will be high even when v/c ratios are low. In these situations, poor progression or an inappropriately long cycle length (or both), is generally present. The following point must be emphasized: unacceptable delay can exist where capacity is a problem as well as in cases in which it is adequate. Further, acceptable delay levels do not automatically ensure that capacity is sufficient. The analysis must consider the results of both the Capacity Analysis Module and the LOS Module to obtain a complete picture of existing or projected intersection operations. Because of the complexity of this methodology, detailed worksheets are provided for the computations of each analysis module. These are presented and discussed in Section III, Procedures for Application.
PLANNING ANALYSIS
The operational analysis method for signalized intersections presented in this chapter provides an extremely detailed treatment of the operation of a traffic signal. The level of precision inherent in that analysis often exceeds the accuracy of the available data. The requirement for a complete description of the signal timing plan is also a burden, especially when the method is being applied in transportation planning situations. It is possible to obtain an approximate analysis of the level of service at a traffic signal through the judicious use of assumed values for most of the data that are required. Table 9-3 contains recommended default values for several data items. For planning purposes, the only site-specific data that should be required are the traffic volumes and number of lanes for each movement toUpdated December 1997
urban streets
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Table 9-15. Intersection Status Criteria for Signalized Intersection Planning Analysis critical v/c ratio (Xcm)
relationship to probable capacity
Xcm ≤ 0.85 0.85 < Xcm ≤ 0.95 0.95 < Xcm ≤ 1.00 1.00 < Xcm
Under capacity Near capacity At capacity Over capacity
gether with a minimal description of the signal design and other operating parameters. This section sets forth a recommended technique for preparing a complete data set with minimal field data requirements. As such, it proposes a planning level methodology for the analysis of signalized intersections. Overview of Planning Method
The concept of the planning method may be best understood by comparison with the full operational analysis method already presented in this chapter. The operational analysis method is illustrated in Figure 9-3. The LOS estimates (A–F) are based on a detailed evaluation of the control delay per vehicle in each lane group. From a planning perspective, the data requirements for this procedure are usually considered somewhat excessive, and the need for an approximate analysis is apparent. The concept of the planning method is to apply the required approximation to the input data and not the computational procedures. This provides a link between the planning and operational analyses and allows the same basic computational methodology to serve both levels of analysis in estimating the level of service. A set of worksheets to be described in the next section of this chapter is used to determine the critical v/c ratio, Xcm, which has been described earlier as an approximate indicator of the overall sufficiency of the intersection geometrics. The computational method involves the summation of conflicting critical lane volumes for the intersection. The computations themselves depend on the traffic signal phasing, which in turn depends on the type of protection assigned to each left turn. The critical volume summation divided by the computed intersection capacity represents the critical v/c ratio, Xcm. Although it is not possible to assign a level of service to the intersection based on Xcm, it is possible to evaluate the operational status of the intersection for planning purposes. Table 9-15 expresses the operational status as ‘‘over,’’ ‘‘at,’’ ‘‘near,’’ or ‘‘under’’ capacity. One of the by-products of the critical volume summation is the synthesis of a ‘‘reasonable and effective’’ signal timing plan for the intersection. When this timing plan is combined with assumed values for other operating parameters, all of the data required to apply the full operational analysis will be available. As an extension of the planning analysis, it is therefore possible to obtain an estimate of the level of service on each of the lane groups and approaches and for the intersection as a whole. The accuracy of such estimates will depend heavily on the quality of the input data. If the traffic volumes are rough approximations of future conditions, the planning analysis should not be taken beyond the evaluation of intersection status. Field Data Requirements
The overall data requirements are summarized in the following discussion. It should be noted that some of the requirements may Updated December 1997
be met by assumed or default values that represent reasonable or average values for operating parameters. Other data items are sitespecific and must be obtained in the field. The objective of the planning method is to minimize the need for detailed collection of field data. The data requirements for this level of analysis may be met by using three worksheets that will be described in detail in the next section of this chapter. Much of the required data may be developed either through judgment or by cursory observation. For each approach, it is necessary to answer the following questions: 1. Will parking be allowed? 2. Will the signal be coordinated with the upstream signal on this approach? 3. How will left turns be accommodated? The treatment alternatives for left turns were described in Section I of this chapter as ‘‘permitted,’’ ‘‘protected,’’ ‘‘protected-pluspermitted,’’ and ‘‘not opposed.’’ Most of the foregoing questions may be answered easily on the basis of existing operation. If the answers are not known, the assumptions in the following sections are suggested. Parking
If the parking restrictions have not been determined, the planning method may be used as a decision tool. Both conditions (i.e., parking and no parking) may be analyzed and compared. Coordination
Without effective coordination, signals along an arterial can create poor operating conditions. The closer the spacing of signalized intersections without adequate coordination, the more delay vehicles can encounter. Conversely, closely spaced signalized intersections with good coordination can be an enhancement to arterial flow. When signalized intersections are placed far enough from each other, their effect on slowing or enhancing arterial flow may be minimal. On the major street, coordination should be assumed if the upstream signalized intersection is less than 2,000 ft away. On the minor street, the corresponding distance is 1,200 ft. Minor roads are usually shorter and their through traffic travels less distance than on major arterial roads. Requirement for Left-Turn Protection
For planning purposes the actual left-turn treatment should be used. If this is unknown, the choice should be made using local policies or practices. Many agencies use the product of the leftturning volume and the oncoming through traffic volume, which is entered on the Lane Volume Worksheet (see Figure 9-23). Although threshold values vary, one common practice suggests that left turns may require protection when this value exceeds 50,000 with one opposing lane (90,000 with two lanes, and 110,000 with three lanes) and the left-turn volume itself exceeds 90 vph. If the left-turn volume exceeds 240 vph or if more than one turning lane is provided, protection is required regardless of the magnitude of the product. Note that these thresholds should only be applied for planning purposes. For design and operational purposes there are many other factors that should be considered, including accident experience, field observations, and conditions that may exist outside of the analysis period.
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Protected left turns may also be allowed to proceed on a permitted phase (protected-plus-permitted phasing). This is an operational detail that may not be available. The existence of a permitted left-turn phase combined with a protected phase is not reflected in the planning worksheets, except that two sneakers per cycle are removed from left-turn volumes under protected-plus-permitted phasing. Unprotected left turns from exclusive lanes receive no explicit assignment of green time because they are assumed to be accommodated by the concurrent through movement. It is therefore possible to produce an unreasonably optimistic assessment of the critical v/c ratio if protected phasing is not provided for heavy left-turn volumes. The procedure to be described later includes a check for left-turn capacity.
fied on the Input Module Worksheet (see Figure 9-14). Values appropriate to the local jurisdiction should be chosen. Cycle lengths normally vary between 60 and 120 sec. In areas where heavy congestion is anticipated, cycle lengths as high as 150 sec are occasionally found. Default values of 60 sec minimum and 120 sec maximum are recommended for planning purposes. These values should be used in the absence of more specific information. The field data requirements will be satisfied by the items described above. The remainder of this discussion deals with the items that may be determined either by assuming default values or by performing worksheet computations.
Split-Phase Operation
To minimize the need for field data for planning analyses, a number of assumptions are built into the process as default values to represent generalized traffic characteristics and traffic signal operating parameters. The default values for approach grade, heavy vehicles, and bus blockage have already been presented in Table 9-3. Lane utilization adjustment factors of 1.0 are suggested, which are consistent with the requirements of a planning-level analysis. No pedestrian conflicts are considered because data at this level of detail are not usually available. These assumptions allow the determination of average conditions for each lane group. The variables area type, saturation flow rate, pedestrian crossing volume, lost time, and yellow plus all red include default values that are representative of suburban intersection conditions. The presence of traffic signal coordination must be identified on each intersection approach. On those approaches where coordination exists, Arrival Type 4 should be used. On those approaches where coordination does not exist, Arrival Type 3 should be used. Of course, any of these default values may be overridden during the analysis. Overriding a given value should produce a more accurate assessment of the capacity and level of service at the expense of consistency of treatment among intersections. There is a clear trade-off here, and the decision is up to the analyst.
Split-phase operation provides complete separation between movements in opposing directions by allowing all movements in only one direction to proceed at the same time. This alternative should only be assumed for planning purposes if 1. A pair of opposing approaches is offset; 2. Protected left-turn phasing must be provided to two opposing single-lane approaches; or 3. Both opposing left turns are protected and one of the left turns is accommodated with an exclusive lane plus an optional lane for through and left-turning traffic. In addition to the movement-specific data just described, there are three items that apply to the intersection as a whole: the area type, the peak-hour factor, and the cycle length requirements for the signal operation. Area Type
The choices offered by the operational analysis method are ‘‘central business district’’ (CBD) or ‘‘other.’’ Some judgment is required here. Unless the intersection is known to be within the CBD, the ‘‘other’’ category should be assumed.
Default Values
Peak-Hour Factor
The peak-hour factor (PHF) is used to focus the analysis on the peak 15 min of the hour. It is an important feature of the operational analysis method. However, for planning purposes, the appropriate value for the PHF will depend on the nature of the application. For near-term approximation of intersection level of service, the use of a PHF may be desirable. If no data are available, a value of 0.9 should be assumed. For longer-term projections of roadway sufficiency in heavily populated areas, the balance between hourly volumes and capacities may be of more interest. If this is the case, a PHF of 1.0 may be more appropriate. However, if 15-min peaking occurs within the hour, failure to use a PHF will result in an underestimation of delay if the planning analysis is extended to evaluate the level of service. Cycle Length Requirements
The design cycle length should be used if it is known. If it is not, the cycle length may be calculated by using the Signal Operations Worksheet presented later (see Figure 9-24). The calculations are subject to minimum and maximum values, which should be speci-
Synthesis of Signal Operation
The LOS computations for planning purposes are carried out as an optional step using the operational analysis method described in this chapter. The signal design parameters to be synthesized by the technique described here are intended as direct input data to the operational analysis method. Worksheets are presented for the computation of all of the design parameters. It is, however, anticipated that a computerized version of the technique would be employed in most practical applications. Implementation of the computations by hand would be time consuming because of the detailed nature of the process. It is not essential, nor is it practical, for planning applications to define a fully optimized signal timing plan for the intersection. It is only necessary to ensure that the analysis be based on a ‘‘reasonable and effective’’ timing plan. For purposes of this chapter, the following attributes apply to a reasonable and effective signal timing plan: 1. The timing plan must accommodate the critical movements on all lane groups at the intersection; Updated December 1997
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2. A cycle length should be chosen that is appropriate to the traffic volume levels; 3. The allocation of time among competing movements should be such that the degree of saturation is equalized for the critical movements in each phase; 4. The phasing plan should accommodate unbalanced volumes with a minimum of slack time through the use of overlap phasing; 5. The phase time for a lane group with a shared left-andthrough lane and permitted left turns should be designed to accommodate the through movement only, not the entire lane group (the adequacy of the timing with respect to the left turn should be checked if necessary in a subsequent step using the operational procedure); 6. The protected phase time for a protected-permitted left turn should accommodate the entire movement; and 7. Protected left-turn phasing should be used for all left turns that would not otherwise be accommodated. The signal operation is described in terms of a phase plan indicating which movements are able to proceed on each phase and a timing plan indicating the cycle length and the apportionment of time to each phase in the cycle. The procedure suggested here will produce a reasonable and effective timing plan by the foregoing definition, given the information mentioned previously. It is based on well-established principles of critical movement analysis and on the signal timing guidelines presented in Appendix II. The use of this technique should be limited to planning applications. It is not intended to produce an optimized operating plan for implementation in practical situations. The phase plan is chosen from a limited set of alternatives. No consideration is given to
leading versus lagging left-turn protection. The timing plan does not consider user-specified minimum green times for each phase nor does it consider the optimization of phase splits. The limitations just mentioned pose no problems for planning applications. The technique described here will generate a complete phasing and timing plan that represents a reasonable approximation of the conditions that might be expected to occur with the given traffic volumes and intersection configuration, assuming that a reasonable and effective signal timing design is employed. Other Analyses
As noted previously, the computational procedures in this chapter emphasize the estimation of level of service (delay) based on known or projected traffic demand, signalization, and geometric design. Other computational applications include determination of 1. Volume-to-capacity ratios and service flow rates associated with selected levels of service given a known signalization and geometric design; 2. Signal timing parameters when known inputs are a selected level of service, demand flow rates, and geometric design; and 3. Geometric parameters (number of lanes, lane use allocations, etc.) given selected level of service, demand flow rates, and signalization. These alternative computational sequences are discussed in the next section of this chapter and illustrated with sample computations.
III. PROCEDURES FOR APPLICATION Detailed worksheets for computations and step-by-step instructions for their use and interpretation are presented in this section. The operational analysis will be described first, followed by the less detailed planning analysis.
T Permitted left-turn operation, T Protected left-turn operation, or T A combination of protected and permitted left turns. Thus there are seven different possibilities, each of which must be handled in a slightly different manner using the worksheets.
OPERATIONAL ANALYSIS
Operational analysis is divided into five modular subanalyses: (a) Input Module, (b) Volume Adjustment Module, (c) Saturation Flow Rate Module, (d) Capacity Analysis Module, and (e) LOS Module. The computations for each of these modules are conducted or summarized on the appropriate worksheet, or both, as each module is presented. In addition to the module-related worksheets, two supplementary worksheets are provided to handle computations that are more complex. An overview of the information flow among all worksheets is presented in Figure 9-13, which shows the proper treatment of all combinations of left-turn lanes and phasing. A given lane group may have T Left turns from an exclusive lane, T Left turns from a shared lane, or T No left turns at all. When left turns are present, the signal phasing may provide Updated December 1997
Input Module
The Input Module is essentially a summary of the geometric, traffic, and signalization characteristics needed to conduct other computations. When an existing case is under study, most of these data will be obtained from field studies. When future conditions are under consideration, traffic data will be forecast, and geometric and signal designs will be based on existing conditions or will be proposed. The Input Module Worksheet is shown in Figure 9-14. The upper half of the worksheet contains a schematic intersection drawing on which basic volume and geometric data are recorded. Step 1: Record Traffic Volumes
For each movement, 15-min flow rates (vph) for the analysis period or hourly volumes are entered into the appropriate boxes shown in each corner of the intersection diagram. Left-turn,
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Figure 9-13. Worksheet information flow. (RT = right turn; LT = left turn; Prot = protected; Perm = permitted.)
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Figure 9-14. Input Module Worksheet.
Updated December 1997
signalized intersections through, and right-turn volumes are recorded below these boxes at the head of the appropriate directional arrow. The sum of the left, through, and right movements on each approach should equal the value shown in the approach volume box. Step 2: Record Geometrics
The details of lane geometrics should be shown within the intersection diagram. Details should include T T T T T T T
Number of lanes, Lane widths, Traffic movements using each lane (shown by arrows), Existence and location of curb parking lanes, Existence and location of bus stops, Existence and length of storage bays, and Other features such as channelization, and so forth.
When geometric conditions are not known, a design should be proposed based on state or local practice. Appendix I may be consulted to assist in establishing a design for analysis. When separate left-turn lanes exist, the procedures assume that the storage length is adequate. This should be checked against the criteria in Appendix I. The middle portion of the worksheet consists of a tabulation of additional traffic and roadway conditions for each movement. Step 3: Enter Traffic and Roadway Conditions
The following parameters are entered into the tabulation in the middle of the worksheet. Separate entries are required for each approach: 1. Percent grade is entered in the first column; a plus sign indicates upgrade, and a minus sign indicates downgrade. 2. Percent heavy vehicles is entered in the second column. Normally the average for the entire approach is used. When heavy vehicle presence varies significantly between movements, separate percentages may be used for left-turn, through, and right-turn movements. A heavy vehicle is defined as any vehicle with more than four tires touching the pavement. 3. The third and fourth columns describe parking characteristics for the approach. The third column indicates the presence of an adjacent parking lane at the intersection; ‘‘Y’’ or ‘‘N’’ is entered as appropriate. The fourth column indicates the number of parking maneuvers per hour occurring into and out of the parking lane within 250 ft upstream of the stop line. 4. The number of local buses stopping per hour to discharge or pick up passengers within the confines of the intersection is recorded in the fifth column. Any bus stop within 250 ft upstream or downstream from the stop line is considered to be within the confines of the intersection. 5. The peak-hour factor is entered in the sixth column. This will be used to convert hourly values to 15-min flow rates in the event that 15-min flow rates were not entered. PHF values of 1.0 should be used for 15-min flow entries. 6. The number of pedestrians per hour using the crosswalk and conflicting with right turns from the subject approach is recorded in the seventh column. For the NB approach, this is the east crosswalk; for the SB approach, the west crosswalk; for the EB approach, the south crosswalk; and for the WB approach, the north crosswalk. 7. The eighth and ninth columns describe pedestrian controls at the intersection. In the eighth column, the existence of a pedestrian
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pushbutton detector on the subject approach is indicated by a ‘‘Y’’ or ‘‘N’’ entry. The ninth column gives the minimum green time required for a pedestrian to cross the street, computed from Equation 9-8: Gp = 7.0 + (W/4.0) − Y 8. The tenth and last column is used to indicate the quality of signal progression. Either the value P, the proportion of vehicles arriving on green, or the arrival type (1–6) is entered here. When data for some of these variables are not available or forecasts cannot be adequately established, default values may be used as an approximation. These may be established by judgment, or the default values in Table 9-3 may be used when they cannot be established by other means. Step 4: Enter Signal Phasing Design
The sequence of signal phases is diagrammed in the eight boxes at the bottom of the Input Module Worksheet. Up to an eightphase signal design may be shown. Each box is used to show a single phase or subphase during which the allowable movements remain constant. 1. For each phase, the allowable movements are shown with arrows. Permitted turns are shown with a dashed arrow, and protected turns are shown with solid arrows. Conflicting pedestrian flows should be shown with dashed lines. 2. For each phase, the actual green (G) time and the actual yellow-plus-all-red (Y) time should be shown (in seconds) on the line labeled ‘‘Timing.’’ 3. Each phase should be identified as pretimed (P) or actuated (A) in the appropriate box. When signal design is not known, two decisions should be made at this point: what type of control is going to be assumed for analysis, and what phase sequence will be used? These two questions are important, because they will influence the determination of lane groups for analysis. This portion of the signal design should be projected on the basis of state or local practice. For additional suggestions on establishing the type of control and phase sequence, Appendix II may be consulted. The timing of the signal will not be known when signal design is to be established. It may or may not be known when actuated signals are in place, depending on whether average phase durations were observed in the field. Appendix II contains recommendations for establishing phase times based on an assumed signal type and phase sequence and for estimating the average phase lengths of actuated signals when observations are not available. These estimates, however, cannot be computed until the first half of the Capacity Analysis Module is complete. Other computations may proceed without this information. Because the establishment of signal timing will usually involve iterative computations, it is preferable to simply specify a complete signal timing for analysis using trial-and-error computations to determine an appropriate final timing. As an alternative, the timing plan may be synthesized using the planning method described previously. If a fully implementable timing plan is required, a variety of professionally accepted signal timing optimization models may be used. Some of these models apply the methodology of this chapter iteratively. Updated December 1997
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The second major analysis module focuses on (a) adjustment of hourly movement volumes to flow rates for a peak 15-min period within the hour and (b) establishment of lane groups for analysis. The Volume Adjustment Module results in the preparation of demand flows in a form amenable to further analysis and provides values used in subsequent analysis modules. A worksheet for volume adjustment computations is shown in Figure 9-15. Step 1: Enter Hourly Volumes
Hourly movement volumes or 15-min flow rates (vph) are entered in Column 3 of the worksheet. These are taken directly from the intersection diagram on the Input Module Worksheet. Step 2: Convert Hourly Volumes to Peak Flow Rates
If hourly volumes are used, the peak-hour factor (PHF) for each movement is entered in Column 4. If 15-min flow rates are used, 1.0 is entered. Hourly volumes are divided by the PHF to compute peak flow rates: vp = V/PHF where vp is the flow rate for the peak 15-min analysis period. The result is entered in Column 5 of the worksheet. Step 3: Establish Lane Groups for Analysis
Lane groups for analysis should be established on the basis of recommendations cited in Section II, Methodology. Exclusive turn lanes are always established as separate lane groups. Where shared left-turn and through lanes exist on an approach with additional lanes for through traffic, they should be checked to determine whether they operate in a shared equilibrium mode or as de facto left-turn lanes. This check involves determining the proportion of left turns in the shared lane. If this value equals or exceeds 1.0, the shared lane should be considered an exclusive left-turn lane. The proportion of left turns in the shared lane will be determined later as a part of the Saturation Flow Rate Module. Lane groups are shown in Column 6 of the worksheet by entering arrows illustrating the lanes and movements included in the group. Permitted turning movements are shown with dashed arrows, and protected turning movements are shown with solid arrows. When a turn has a protected and a permitted phase, both types of arrows should be shown. Step 4: Enter Adjusted Lane Group Rate
Once lane groups have been established, the flow rates for included movements must be entered in Column 7 of the worksheet as the adjusted lane group flow rate, v. Step 5: Enter Proportion of Left or Right Turns in Lane Group
Column 8 is provided for entering the proportion of left or right turns, or both, in the lane group volume. These values may be computed as PLT = vLT/v PRT = vRT/v where PLT and PRT are the proportions of left- and right-turning vehicles using the lane group, expressed as a decimal. Left- and Updated December 1997
right-turn flow rates are obtained from Column 5 of the worksheet, and the total lane group flow rate is given in Column 7.
Saturation Flow Rate Module
In the Saturation Flow Rate Module, the total saturation flow rate that can be accommodated by the lane group under prevailing conditions is computed. A worksheet for this module is shown in Figure 9-16. Step 1: Enter Description of Lane Groups
Column 2 of the worksheet is used to identify the lanes and movements included in each lane group. These are the same as the entries in Column 6 of the Volume Adjustment Module Worksheet, where lane groups are established. Step 2: Enter Ideal Saturation Flow Rate
The ideal saturation flow rate per lane is entered in Column 3 of the worksheet. For most computations, this value will be taken to be 1,900 passenger cars per hour of green time per lane (pcphgpl), unless local data indicate that another value is appropriate. Appendix IV contains guidelines for conducting local studies to determine the prevailing saturation flow rate for purposes of calibrating the ideal saturation flow rate. Step 3: Enter Adjustment Factors
The ideal saturation flow rate is multiplied by the number of lanes in the lane group and by nine separate adjustment factors, as follows: 1. Enter the number of lanes in the group in Column 4 of the worksheet. 2. Enter the lane width factor, fw, obtained from Table 9-5, in Column 5. 3. Enter the heavy vehicle factor, fHV, obtained from Table 96, in Column 6. 4. Enter the grade factor, fg, obtained from Table 9-7, in Column 7. 5. Enter the parking factor, fp, obtained from Table 9-8, in Column 8. 6. Enter the bus blockage factor, fbb, obtained from Table 9-9, in Column 9. 7. Enter the area type factor, fa, obtained from Table 9-10, in Column 10. 8. Enter the lane utilization adjustment factor, fLU, computed using Equation 9-11, in Column 11. 9. Enter the right-turn factor, fRT, obtained from Table 9-11, in Column 12. 10. Enter the left-turn factor, fLT, obtained from Table 9-12 or computed using the special procedure described in Section II, Methodology, for permitted left turns made from exclusive or shared lanes, in Column 13. Factors for each lane group are determined separately from the prevailing conditions for the lane group. Information for these determinations is taken from the Input Module Worksheet. The proportion of left or right turns, or both, is taken from the last column of the Volume Adjustment Module Worksheet.
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Figure 9-15. Volume Adjustment Module Worksheet.
Determination of right-turn factors for protected-plus-permitted phasing will require an assumption of the proportion of rightturning vehicles using the protected portion of the phase. This is basically judgmental and should be guided by field observations where possible. Step 4: Special Procedure for Estimating the Left-Turn Adjustment Factor for Permitted Left Turns
Figures 9-17 and 9-18 show worksheets that are used in the computation of the left-turn adjustment factor when permitted left turns are made. These worksheets are applied to the permitted portion of left turns, including permitted-only and protected-plus-
permitted phasing, whether made from an exclusive or shared lane, for Cases 2, 3, and 5. Figure 9-17 is used in cases in which the subject approach is opposed by an approach with more than one lane. Figure 9-18 is used in cases in which the subject approach is opposed by a single-lane approach. The basic methodology for each worksheet assumes that the subject approach is a multilane approach if the opposing approach is a multilane approach (Figure 9-17) and that the subject approach is a single-lane approach if the opposing approach is a single-lane approach (Figure 9-18). For cases in which the two approaches are not of the same type as well as cases of protected-plus-permitted phasing and a phasing in which the opposing through moveUpdated December 1997
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Figure 9-16. Saturation Flow Rate Module Worksheet.
ment has a lead phase, the worksheets may still be used, but the special instructions cited in Section II, Methodology, must be followed carefully. There is a column for each approach on the worksheets, although only those approaches with permitted left-turn conditions would be included. Since the worksheets are quite similar, they are discussed together here, noting the exceptions and differences where appropriate. The first set of entries consists of input variables that should be entered directly from values appearing on previous worksheets, as follows: 1. The cycle length is entered from the Input Module Worksheet. 2. The actual green time for the permitted phase is entered from the Input Module Worksheet. If the permitted phase is part of a protected-plus-permitted phasing or the opposing approach has a lead phase, see the special instructions in Section II, Methodology. Updated December 1997
3. The effective green time for the permitted phase is entered. This is generally the actual green time (above) from the Input Module Worksheet plus the yellow plus all-red change-and-clearance interval minus the movement’s lost time. If the permitted phase is part of a protected-plus-permitted phasing or the opposing approach has a lead phase, see the special instructions in Section II, Methodology. 4. The effective green time for the opposing approach is entered for the permitted phase. This is generally the actual green time from the Input Module Worksheet plus the yellow plus all-red change-and-clearance interval minus the movement’s lost time. If the permitted phase is part of a protected-plus-permitted phasing or the opposing approach has a lead phase, see the special instructions in Section II, Methodology. 5. The number of lanes in the subject lane group is entered from the Input Module Worksheet. If the left turn is opposed by a multilane approach (Figure 9-17), the number of lanes in the opposing lane group is entered from the Input Module Worksheet
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Figure 9-17. Supplemental Worksheet for Permitted Left Turns: Multilane Approach. Updated December 1997
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Figure 9-18. Supplemental Worksheet for Permitted Left Turns: Single-Lane Approach. Updated December 1997
signalized intersections as well. If left or right turns are made from exclusive turn lanes on the opposing approach, these lanes are not included in the number of opposing lanes. 6. The adjusted left-turn flow rate is entered from the Volume Adjustment Module Worksheet. 7. The proportion of left turns in the lane group is entered from the Volume Adjustment Module Worksheet. When an exclusive left-turn lane group is involved, PLT = 1.0. If the left turn is opposed by a single-lane approach (Figure 9-18), the proportion of left turns in the opposing flow is entered from the Volume Adjustment Module Worksheet. 8. The adjusted opposing flow rate is entered from the Volume Adjustment Module Worksheet. If left or right turns are made from exclusive turn lanes on the opposing approach, these adjusted volumes are not included in the opposing flow rate. 9. The lost time for the left-turn lane group is entered as determined from the Input Module Worksheet. The equations used in subsequent computations are shown on the remaining rows of the worksheet; these equations are based on the input variables that were entered above. Some of these computations deserve some further discussion, as follows. T The opposing platoon ratio Rpo may be determined in two different ways. If the arrival type of the opposing traffic appears on the Input Module Worksheet, the default platoon ratio from Table 9-2 is used. If the proportion of arrivals on green appears on the Input Module Worksheet, Equation 9-7 based on the g/C ratio is used instead. T The equation shown for gf in Figure 9-17 assumes that the subject approach is a multilane approach like the opposing approach. If the subject approach is a single-lane approach, the equation for gf from Figure 9-18, which assumes a single-lane approach, should be used. Conversely, the equation shown for gf in Figure 9-18 assumes that the subject approach is a single-lane approach like the opposing approach. If the subject approach is a multilane approach, the equation for gf from Figure 9-17, which assumes a multilane approach, should be used. In either case, if the subject lane group is an exclusive left-turn lane, then gf = 0. T For multilane lane groups (Figure 9-17), PL is computed as the proportion of left turns in the left-hand lane of the lane group. If this value is determined to be 1.0 or higher, the lane groups for the approach should be reassigned showing this left-hand lane as an exclusive left-turn lane (a de facto left-turn lane), since it is occupied entirely by left-turning vehicles. This requires redoing all of the computations for this approach. If a multilane lane group is opposed by a single-lane approach, Figure 9-18 should be used, but a value of PL should be estimated and substituted for PLT, as described in Section II, Methodology. In this case, the same de facto left-turn check should be applied. T Figure 9-7 is used to determine the value of EL1 based on the opposing flow rate and the lane utilization factor of the opposing flow. For the single-lane approach (Figure 9-18), EL2 is computed by formula, not by Figure 9-7. T The value of fm is computed as shown. The maximum value is 1.0 and the minimum value is 2(1 + PL)/g. These limits are used if the computed value falls outside this range. T The left-turn adjustment factor, fLT, is computed as shown. For a single-lane lane group, fLT = fm. If a multilane lane group is opposed by a single-lane approach, Figure 9-18 is used, but fLT is calculated on the basis of fm and the number of lanes as shown in
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Figure 9-17 except when the subject lane group contains multiple exclusive left-turn lanes. Step 5: Compute Adjusted Saturation Flow Rates
The adjusted saturation flow rate for each lane group is computed by multiplying the ideal saturation flow rate by the number of lanes in each lane group and by each of the nine adjustment factors determined in Steps 3 and 4. This is done in accordance with Equation 9-10: s = so N fw fHV fg fp fbb fa fLU fRT fLT Capacity Analysis Module
In the Capacity Analysis Module, information and computational results from the first three modules are combined to compute the capacity of each lane group and v/c ratios for each lane group and for the intersection as a whole. A worksheet for these computations is shown in Figure 9-19. Step 1: Enter Lane Group Description
Column 1 of the worksheet is once again for the description of lane groups. Lanes and movements included in each lane group are entered as on the Saturation Flow Rate Module Worksheet. Step 2: Enter Phase Type
Column 2, Phase Type, is included to accommodate exclusivelane left turns that have both protected and permitted phases. In this case, the protected phase will be the primary phase and the permitted phase will be the secondary phase. The primary and secondary phases must be represented by separate row entries on this worksheet, and certain quantities, such as lane group capacity, must be computed as the sum of the primary and secondary phase values. Primary phase entries should be designated ‘‘P’’ in this column. Secondary phase entries should be designated ‘‘S,’’ and the row containing the total values should be designated ‘‘T.’’ Note that lane groups with shared left-turn lanes have only a primary phase, as do lane groups with only protected or only permitted phasing. Step 3: Enter Adjusted Flow Rate for Each Lane Group
The adjusted flow rate for each lane group is obtained from the Volume Adjustment Module Worksheet and entered in Column 3 of the worksheet. In the case of lane groups with both primary and secondary phases, the flow rate for the lane group should be entered in a row identified ‘‘T’’ in Column 2. For computation of the critical v/c ratio, Xc, it is necessary to apportion the total flow rate between the primary and secondary phases. As indicated in Section II, Methodology, it is appropriate to consider whichever phase is displayed first to be fully saturated by left-turn traffic and to apply any residual flow to the phase that is displayed second. Step 4: Enter Adjusted Saturation Flow Rate for Each Lane Group
The adjusted saturation flow rate for the primary phase for each lane group is obtained directly from the Saturation Flow Rate Module Worksheet and entered in Column 4. It is not necessary to enter a saturation flow rate value in Row T when a secondary phase is involved, because this value has no significance. Updated December 1997
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Figure 9-19. Capacity Analysis Module Worksheet.
signalized intersections Step 5: Compute Flow Ratio for Each Lane Group
The flow ratio for each lane group is computed as v/s and entered in Column 5 of the worksheet. This should be done for rows representing both primary and secondary phases but not for the row that represents the total. Step 6: Enter Green Ratio for Each Lane Group
The g/C ratio for each lane group, the effective green time divided by the cycle length, is computed and entered in Column 6 of the worksheet. The actual green times and the cycle length may be obtained from the Input Module Worksheet. Effective green times can be taken to be equal to the actual green time plus the change-and-clearance interval minus the lost time for the movement as determined from the Input Module Worksheet. When signal timing is to be determined for cases involving permitted left turns, these computations will be iterative. Step 7: Compute Capacity of Each Lane Group
The capacity of each lane group is computed from Equation 93 as the saturation flow rate times the green ratio: ci = si (gi /C) The result is entered in Column 7 of the worksheet. Values should be computed for both primary and secondary phases, and the sum of the values for each phase should be entered in the row designated ‘‘T’’ in Column 2. A minimum capacity value based on sneakers per cycle must be imposed as a practical matter for all permitted left-turning movements. This value may be computed as 3,600 (1 + PL) C Step 8: Compute v/c Ratios for Each Lane Group
The v/c ratio for the lane group is the ratio of adjusted flow to capacity: Xi = vi /ci These values are computed and entered in Column 8 of the worksheet. Entries should be made for all rows, including those designated ‘‘P,’’ ‘‘S,’’ and ‘‘T,’’ in Column 2. Step 9: Identify Critical Lane Groups
At this point in the computations, critical lane groups and lost time per cycle may be identified according to the guidelines discussed in Section II, Methodology. A critical lane group is defined as the lane group with the highest flow ratio in each phase or set of phases. When overlapping phases exist, all possible combinations of critical lane groups must be examined for the combination producing the highest sum of flow ratios, as discussed previously. Critical lane groups are identified by a check placed in Column 9 of the worksheet. The lost time per cycle is entered as the value L in the appropriate space at the bottom of the worksheet. Step 10: Compute Critical v/c Ratio
The flow ratios for critical lane groups (i.e., those checked in Column 9) are summed. The result is entered as the value Yc in the appropriate space at the bottom of the worksheet.
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The critical v/c ratio, Xc, which indicates the degree of saturation associated with the geometrics, volumes, and signal phasing, is computed as Xc = Yc[C/(C − L)] The results are entered in the appropriate space at the bottom of the worksheet. At the completion of this module, the capacity characteristics of the intersection have been defined. These characteristics must be evaluated in their own right as well as in conjunction with the delays and levels of service resulting from the next module. Although the interpretation of capacity results is discussed in Section II, Methodology, some key points are summarized here: 1. A critical v/c ratio of greater than 1.0 indicates that the signal and geometric design cannot accommodate the combination of critical flows at the intersection. The given demand in these movements exceeds the capacity of the intersection to handle them. The condition may be ameliorated by any or all of the following: increased cycle length, changes in the phasing plan, and basic changes in geometrics. Note, however, that computations should be conducted using arrival volumes. When the v/c ratios are less than 1.0, arrival and departure volumes are the same. When v/c ratios are greater than 1.0, either for an individual phase or for the overall intersection, departure volumes are less than arrival volumes. Future volume forecasts are also arrival volumes, by definition. When counts of actual departure volumes are used in analysis, the actual v/c ratio cannot be greater than 1.0. Observed departure volumes cannot exceed capacity. In such cases, computations should be checked for errors. If v/c ratios greater than 1.0 persist for actual departure volumes, it is an indication that the intersection operates more efficiently than anticipated by these computational techniques. 2. When the critical v/c ratio is acceptable but the v/c ratios for critical lane groups vary widely, the green time allocation should be reexamined, because disproportionate distribution of available green is indicated. 3. If permitted left turns result in extreme reductions in saturation flow rate for applicable lane groups, protected phasing might be considered. 4. If the critical v/c ratio exceeds 1.0, it is unlikely that the existing geometric and signal design can accommodate the demand. Changes in either or both should be considered. 5. When v/c ratios are unacceptable and signal phasing already includes protective phasing for significant turning movements, it is probable that geometric changes will be required to ameliorate the condition. The capacity of an intersection is a complex variable depending upon a large number of prevailing traffic, roadway, and signalization conditions. Suggestions on interpretation are not meant to be exhaustive or complete, but merely to point out some of the more common problems that can be identified from the Capacity Analysis Module results.
LOS Module
The LOS Module combines the results of the Volume Adjustment, Saturation Flow Rate, and Capacity Analysis modules to find the average control delay per vehicle in each lane group. The Updated December 1997
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level of service is directly related to delay and is found from Table 9-1. The worksheet for this module is shown in Figure 9-20. Delay is found from Equations 9-22, 9-23, and 9-25, presented in Section II. These equations are restated below for convenience. d = d1PF + d2 + d3 d1 =
3
PF =
(9-22)
0.50C(1 − g/C)2 1 − Min(1,X)g/C
d2 = 900T (X − 1) +
vehicles arriving on the green) is used in lieu of the arrival type, PF may be computed as
(9-23)
!(X − 1) + 2
8kIX cT
4
(9-25)
The worksheet is designed for computation of the uniform and incremental delay terms separately. The uniform delay is then multiplied by the progression adjustment factor (PF) to account for the impact of progression on delay. The values of PF and k are obtained from Tables 9-13 and 914, respectively. For purposes of this chapter, the upstream filtering/metering adjustment factor (I) is normally set equal to 1.0 for an isolated signal analysis. When no unserved demand exists from a previous time period, the residual delay term, d3, is equal to zero. When an initial unserved queue of vehicles exists at the start of the analysis period (observed at the beginning of red), the procedures in Appendix VI are to be used to modify the calculation of d1, to calculate d3, and to determine delay and level of service. Step 1: Enter Lane Group Description
As in the case of previous worksheets, Column 1 is used to enter the description of the lanes and movements included in the lane group. This description will be the same as that shown on the Volume Adjustment Module Worksheet. Step 2: Find Uniform Delay
The first term of the delay equation (Equation 9-23) accounts for uniform delay, that is, the delay that results in a lane group if arrivals are uniformly distributed and if no cycles experience oversaturation. It is dependent upon the v/c ratio (X) for the lane group, the green ratio (g/C) for the lane group, and the cycle length (C), which is entered at the top of the worksheet. It is found as follows: 1. Enter the v/c ratio for each lane group in Column 2 of the worksheet. These may be obtained from the Capacity Analysis Module Worksheet. 2. In Column 3 enter the effective green ratio for each lane group from the Capacity Analysis Module Worksheet. 3. Compute the first-term delay and enter the result in Column 4. a. For lane groups with only primary phases indicated on the Capacity Analysis Module Worksheet, compute this value in accordance with Equation 9-23. b. For the groups with both primary and secondary phases indicated on the Capacity Analysis Module Worksheet, use the supplemental worksheet for lane groups with primary and secondary phases presented in Figure 9-21 (see discussion in the next section).
(1 − P)fP 1 − (g/C)
(9-24)
where fP = 0.93 for Arrival Type 2, 1.15 for Arrival Type 4, and 1.0 for all other arrival types. For this purpose, the arrival type may first be determined from Table 9-2 after calculating Rp = PC/g. Because fP is greater than 1.0 for Arrival Type 4, it is possible to compute a value of PF greater than 1.0 using this equation when g/C is very low. Because Arrival Type 4 reflects ‘‘favorable progression,’’ the value of PF should be reduced to 1.0 under this condition. Enter the value of PF in Column 5 of the worksheet. Step 4: Find Incremental Delay
The second term of the delay equation accounts for the ‘‘incremental delay,’’ that is, the delay over and above uniform delay due to arrivals’ being random rather than uniform and due to cycles that fail. It is based on the v/c ratio (X) and the capacity (c) for the lane group. Incremental delay is found as follows: 1. Enter the lane group capacity in Column 6 of the worksheet. 2. Determine the incremental delay calibration factor (k) from Table 9-14. This value is a function of the controller type and degree of saturation. Enter the value of k in Column 7. 3. Compute the second-term delay from Equation 9-25. Enter the result in Column 8. Step 5: Find Delay and Level of Service for Each Lane Group
Delay and level of service are found by multiplying the uniform delay by the progression factor and adding the result to the incremental delay, in accordance with Equation 9-22. The result is entered in Column 9 of the worksheet. The level of service corresponding to this delay, taken from Table 9-1, is entered in Column 10. In the event that the analysis period starts with an initial queue, the procedures in Appendix VI must be used to modify the calculation of d1 and to calculate the additional term, d3. Furthermore, if the analysis period is oversaturated or results in a final unmet demand at the end of the analysis period, an additional analysis of the subsequent analysis period should be made to assess its delay. Step 6: Find Delay and Level of Service for Each Approach
The average delay per vehicle is found for each approach by adding the product of the lane group flow rate and the delay for each lane group on the approach and dividing by the total approach flow rate. The weighted-average delay is entered in Column 11 of the worksheet for each approach. Level of service is determined from Table 9-1 and entered in Column 12. As in Step 5, if the analysis period starts with an initial queue, the delay and level of service for each approach will be determined using the procedures in Appendix VI.
Step 3: Determine the Progression Adjustment
Step 7: Find Delay and Level of Service for Intersection
The progression adjustment factor, PF, as indicated in Table 913, is a function of the arrival type and g/C ratio for lane groups with coordinated control. If the value of P (i.e., the proportion of
The average delay per vehicle for the intersection as a whole is found by adding the product of the approach flow rate and the approach delay for all approaches and dividing the sum by the
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Figure 9-20. LOS Module Worksheet.
total intersection flow rate. This weighted-average delay is entered in the appropriate space at the bottom of the worksheet. The overall intersection level of service is found from Table 9-1 and entered in the appropriate space at the bottom of the worksheet. As in Step 6, if the analysis period starts with an initial queue, the delay and level of service for the intersection will be determined using the procedures in Appendix VI. The result of this module is an estimation of the average control delay per vehicle in each lane group as well as average values for
each approach and for the intersection as a whole. Level of service is directly related to delay values and is assigned on that basis. LOS and delay values are best analyzed in conjunction with the results of the Capacity Analysis Module. Although the discussion below is clearly not exhaustive, some of the more common situations are as follows. 1. The level of service is an indication of the general acceptability of delay to drivers. It should be noted that this is somewhat Updated December 1997
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subjective: what is acceptable in a large CBD is not necessarily acceptable in a less-dense environment. 2. When delay levels are acceptable for the intersection as a whole but are unacceptable for certain lane groups, the phase plan, allocation of green time, or both might be examined to provide for more efficient handling of the disadvantaged movement or movements. 3. When delay levels are unacceptable but v/c ratios are relatively low (Capacity Analysis Module), the cycle length may be too long for prevailing conditions, the phase plan may be inefficient, or both. It should be noted, however, that when signals are part of a coordinated system, the cycle length at individual intersections is determined by system considerations, and alterations at isolated locations may not be practical. 4. When both delay levels and v/c ratios are unacceptable, the situation is critical. Delay is already high, and demand is near or over capacity. In such situations, the delay may increase rapidly with small changes in demand. The full range of potential geometric and signal design improvements should be considered in the search for improvements in such cases. Delay and level of service, like capacity, are complex variables depending on a wide range of traffic, roadway, and signalization conditions. The operational analysis techniques presented here are useful in estimating the performance characteristics of the intersection and in providing basic insights into probable causal factors. These procedures do not, however, account for all possible conditions. The influences of such characteristics as specific curbcorner radii, intersection angle, combinations of grades on various approaches, odd geometric features (offset intersections, narrowing on the departure lanes, etc.), and other unusual site-specific conditions are not addressed in the methodology. Field studies may be conducted in such cases to determine delay directly (see Appendix III) and or to calibrate the prevailing saturation flow rate (see Appendix IV). Unusual delays may result from blockages, such as illegally parked or stopped vehicles or other factors. The analyst may also gain additional insights into intersection operations by observing them in the field in addition to making the analyses prescribed in this chapter. There are also a number of more complex and microscopic modeling techniques that could provide important supplementary analyses for problems that are beyond the scope of the methods described here.
Supplemental Uniform Delay Worksheet
Left turns from exclusive lanes that are allowed to proceed on both protected and permitted phases in the signal sequence must be treated as a special case for purposes of computing the uniform delay. Such movements are analyzed for both phases on the Capacity Analysis Module Worksheet, on which the protected phase is identified as the primary phase and the permitted phase is identified as the secondary phase. This terminology will be continued in the following description of the Supplemental Uniform Delay Worksheet, which follows the procedures outlined in Section II, Methodology. The worksheet is presented in Figure 9-21. Certain input data must first be obtained from other worksheets and entered here, namely, the adjusted left-turn volume from the Volume Adjustment Module Worksheet (Figure 9-15) and the v/c ratio, X, for the lane Updated December 1997
group, obtained from Row T, Column 8, on the Capacity Analysis Module Worksheet (Figure 9-19). The following signal timing intervals must also be obtained from previous computations: 1. Primary-phase effective green, g, from the Capacity Analysis Module Worksheet (Figure 9-19); 2. Secondary-phase effective green intervals, gq and gu, from the supplemental worksheets for permitted left turns (Figure 9-17 or 9-18); and 3. Red time (in seconds), r, computed as C − (g + gq + gu), where C is the cycle length (in seconds). These values are entered in the appropriate rows on the worksheet. Note that extremely heavy opposing traffic may reduce gu to zero, which means that all of the left turns on the permitted phase will be accommodated as sneakers. The effect of sneakers was approximated on the Saturation Flow Rate Module Worksheet (Figure 9-16) by imposing a lower limit on the value of fLT. Because of the lower limit on fLT, a lower limit must also be imposed on the value of gu to be entered on the Supplemental Uniform Delay Worksheet. The necessary time should be transferred from gq to gu to ensure that the value of gu does not fall below 4 sec. The delay computations begin with determination of the arrival and departure rates in units of vehicles per second for compatibility with the remaining worksheet computations. The arrival rate is determined by dividing the left-turn volume, v, by 3,600. This value must be adjusted to ensure that for purposes of uniform delay computation, the arrivals do not exceed the capacity of the intersection. If the v/c ratio, X, exceeds 1.0, the arrival rate must be divided by X, as indicated on the worksheet. Two departure rates must be determined: 1. The primary-phase departure rate, sp = s/3,600, where s is the adjusted saturation flow rate for the primary phase, is obtained from the Capacity Analysis Module Worksheet (Figure 9-19); and 2. The secondary-phase departure rate, ss, which must be computed as ss = s (gq + gu)/(gu × 3,600) where s is the adjusted saturation flow rate for the secondary phase from the Capacity Analysis Module Worksheet (Figure 9-19) and the other values have already been determined as described above. When gu is very short, the secondary-phase departures will be mostly sneakers. Since sneakers move with very low headway, it is possible to have extremely high values of ss. As a practical matter, the per-lane value of ss should not exceed the ideal saturation flow rate for the lane group divided by 3,600. Next, the v/c ratios for the primary and secondary phases, Xprot and Xperm, must be determined from the equations given on the worksheet. Note that different equations are used for leading and lagging left-turn phases. Because of the adjustment of the arrival rate performed in the last step, it will not be possible for both Xprot and Xperm to exceed 1.0. It will, however, be possible for one or the other to exceed 1.0. It is possible to define five separate cases for delay computation, depending on which of the X values exceed 1.0 and on the left-turn phasing (leading or lagging). The case number, 1–5, should now be determined and entered on the worksheet. When the case number is known, the size of the queue at three transition points—Qa, Qu, and Qr—may be determined from the
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Figure 9-21. Supplemental Uniform Delay Worksheet for Left Turns from Exclusive Lanes with Primary and Secondary Phases. Updated December 1997
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formulas given at the bottom of the worksheet. When these values have been computed and entered on the worksheet in their respective rows, it is possible to determine the uniform delay, d1, using the formulas given at the bottom of the worksheet. Note that the formula is different for each of the five cases. PLANNING ANALYSIS
The planning analysis is intended for use in sizing the overall geometrics of the intersection or in identifying the general capacity sufficiency of an intersection for planning purposes. It is based on the sum of critical lane volumes and requires minimum input information, mainly the demand volumes and intersection geometrics. Three worksheets are provided for planning analysis. Figure 9-22 is the basic worksheet on which all input information is entered, and Figure 9-23 is the lane volume worksheet used to establish the individual lane volumes on each approach. Figure 9-24 is the signal operations worksheet used to synthesize the signal timing plan and to determine the operational status of the intersection for planning purposes. Worksheet Operations
The relationship between the lane volume worksheet (Figure 923) and the signal operations worksheet (Figure 9-24) is shown in Figure 9-25. Note that one lane volume worksheet is required for each of the four approaches. This will determine the equivalent hourly lane volume for each approach. The hourly volumes are then combined on the signal operations worksheet to determine the critical movement sum and the intersection status. Optionally, the cycle length and phase times may also be determined. Computational Requirements
The computations must be based on the traffic volumes and lane configuration of each approach to the intersection. The steps in performing the analysis are as follows: 1. Determine the lane volumes for each movement. The detailed instructions for the lane volume worksheet describe this process. 2. Determine the type of left-turn protection for each direction. For planning applications, the actual left-turn protection should be used if known. A left turn is considered to be protected if it is able to proceed at some point in the cycle while the oncoming through movement is stopped. If the actual left-turn protection is unknown, a simple method will be presented later for determining an appropriate choice. 3. From six alternative plans, select the phase plan that will provide the desired degree of left-turn protection and will accommodate the observed left-turn volume balance. 4. Determine the sum of the critical volumes for each phase and the intersection status (under, near, at, or over capacity). This completes the planning portion of the analysis. If an estimate of the level of service based on control delay is desired, it is necessary to establish the signal timing plan. Two additional steps are involved: 5. Determine the cycle length that will accommodate the observed volumes with a specified degree of saturation. A saturation level of 90 percent is assumed. Updated December 1997
6. Apportion the total cycle time among the conflicting phases in the phase plan on the basis of the principle of equalizing the degree of saturation for the critical movements. When all of these steps have been completed, the signal timing will be specified to the level of detail required for operational analysis using the method given previously in this chapter. The data to be entered on the Planning Method Input Worksheet are self-explanatory. The following discussion covers the main aspects of the lane volume and signal operations worksheets, as well as the default values. Also covered are the underlying theory and a description of the most pertinent items.
Lane Volume Worksheet
Description
The purpose of the lane volume worksheet (Figure 9-23) is to establish the individual lane volumes (vehicles per hour per lane) on all of the approaches. This information will be used on the signal operations worksheet to synthesize the signal timing plan. The lane volume worksheet contains additional items such as leftturn treatment alternatives, parking adjustments, left-turn equivalence, adjustment factors for shared lanes with permitted left turns, and a quick method to determine the type of left-turn protection if unknown. Note that the items are numbered (1–20) and that a separate worksheet must be completed for each of the four approaches. The directional designations refer to the movements as they approach the intersection. This is consistent with the terminology used throughout this chapter. Computational formulas are presented on the worksheet for each data item that is computed as a function of other data items, the step number being shown in square brackets; for example, [11]/[12] indicates that the required data item will result from dividing the value determined in Step 11 by the value determined in Step 12. Note that some data fields contain fixed values such as 0 or 1.0. Others are shaded to indicate that a particular value does not apply to all treatment alternatives. This allows the same basic worksheet to be used for all treatment alternatives. For purposes of this analysis, only exclusive lanes are entered for turning movements. Shared lanes are included with the through lanes. Right-turn volumes from shared lanes are simply added to the through volumes at one point on the worksheet. Left-turn volumes in shared lanes are adjusted for their through-vehicle equivalence, and the proportion of the shared lane that they require is removed from the through-lane capacity. Shared lanes with ‘‘not opposed’’ left turns are treated as shared right-turn lanes. Each of the three left-turn treatment alternatives identified previously must be processed differently in computing the lane volumes. Therefore, the lane volume worksheet contains three columns, each of which represents one of the alternatives. Only one of the three columns should be used for each approach. For planning purposes the actual left-turn treatment should be used. If this is unknown, the choice should be made using local policies or practices. A quantitative method for identifying an appropriate treatment on the basis of the product of the volumes for left turns and opposing through movements is described in Section II, Methodology. Failure to provide protected phasing for heavy left-turn volumes will become evident in the operational analysis in the form of very
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Figure 9-22. Planning Method Input Worksheet.
high v/c ratios for these movements. These problems will not, however, appear in the planning-level results because unprotected left turns are not considered in the synthesis of the traffic signal timing plan. Therefore, failure to assume protected phases for heavy left-turn volumes will generally produce an unreasonably optimistic assessment of the critical v/c ratio. Above all, the planning analysis presented here should never be used by itself to determine the need for protected left-turn phasing.
The lane volume worksheet does not consider the case of exclusive plus shared lanes for turning movements. It is possible to have either an exclusive lane or a shared lane for either a left or a right turn. The case of one exclusive lane plus an optional lane is a complicated situation that does not lend itself to the approximations involved in this technique. The treatment of shared-lane permitted left turns is a very complex process. It is, however, possible to approximate the signal Updated December 1997
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Figure 9-23. Planning Method Lane Volume Worksheet.
timing parameters that will handle this situation effectively. Table 9-16 sets forth the computations for the planning-method left-turn factor for permitted and protected-plus-permitted operation. The shared-lane protected treatment alternative is only valid when one of the two opposing left turns is protected, and the Updated December 1997
through movement in the same direction must move during the same phase as the protected left turn. This method does not deal with simultaneous opposing left turns from shared lanes. If the opposing through movement exists, the protected left turn will be considered protected plus permitted. If the opposing through
signalized intersections
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Figure 9-24. Planning Method Signal Operations Worksheet.
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Figure 9-25. Planning method worksheet relationships.
Table 9-16. Shared-Lane Left-Turn Adjustment Computations for Planning-Level Analysis permitted left turn Lane groups with two or more lanes: [17] = {[13] − 1 + e (−[13]*[1]*[16]/600)}/[13] Subject to a minimun value that applies at very low left-turning volumes when some cycles will have no left-turn arrivals: [17] = {[13] − 1 + e (−[1]*Cmax/3600)}/[13] Lane groups with only one lane for all movements: [17] = e−{0.02* ([16]+10*[15])*[1]*Cmax/3600} protected-plus-permitted left turn (one direction only) If [2] < 1220 [17] = 1/{1 + [(235 + 0.435∗[2])∗[15]]/(1400 − [2])} If [2] ≥ 1220 [17] = 1/(1 + 4.525∗[15])
movement does not exist, the protected left turn will be ‘‘not opposed,’’ and therefore will move on the same phase as a permitted movement. The opposing through movement may be considered not to exist in cases of one-way streets, T-intersections, and split-phase operation. The protected-plus-permitted shared lane is handled by a simple lookup procedure described previously as Case 6 in Table 9-12. The same procedure is repeated in Table 9-16 for the planning method. The permitted case is much more difficult because it is necessary to know the signal timing, which is the final product of the computational process described here. The operational analysis method described previously involves complex supplemental worksheets (Figures 9-17 and 9-18) for this purpose that would have to be applied iteratively to resolve the mutual dependence between the left-turn factor and the signal Updated December 1997
timing design. This is clearly not practical, and a single-pass approximation technique must therefore be sought. The method presented here offers a crude approximation that is based on the through-vehicle equivalents for left turns, obtained from Figure 9-7. In this model, the portion of the shared lane available to through traffic decreases as a negative exponential function of the through-vehicle equivalent of the left-turn volume. When this value is high, the shared lane will function as a de facto left-turn lane. Otherwise, the through traffic will be able to occupy a portion of the shared lane. The rate at which through-vehicle capacity is lost depends on the number of lanes. As the number of through lanes increases, it is natural to expect that through vehicles will desert the shared lane more readily. The case of a single shared lane (i.e., one lane that accommodates all movements in the lane group) must be treated differently. In this situation, the through vehicles do not have the option of deserting the shared lane. Therefore it is never possible to achieve a de facto left-turn lane regardless of the left-turn volume. A separate equation appears in Table 9-16 to accommodate this condition. The negative exponential model is retained in this case, but different parameters are applied to reflect captivity of the through traffic by the shared lane. The parameters given in Table 9-16 for both the single-lane and multiple-lane models were selected to produce close agreement with the results of the operational analysis obtained by the full application of the supplemental worksheets presented earlier to specific examples. In computing the left-turn factor, it must be recognized that left turns in shared lanes have no effect on through traffic during signal cycles in which no left turns arrive. Therefore, the minimum value of the left-turn factor is 1.0 minus the probability of zero leftturn arrivals. The minimum value for the left-turn factor is also determined from Table 9-16. The minimum value will occasionally govern the calculations when very low left-turn volumes are opposed by a very heavy opposing through traffic. Instructions
The following instructions cover the step-by-step procedure for
signalized intersections completing all of the items on the lane volume worksheet. Note that each step is numbered to correspond with each row on the worksheet. 1. Left-Turn Volume: The first item is the left-turn volume (in vehicles per hour) on the approach. In the case of protected-pluspermitted phasing with an exclusive left-turn lane, two vehicles per cycle should be removed from the left-turn volume to account for the effect of sneakers. If the cycle length has not been established, the maximum cycle length should be used. To prevent unreasonably short protected left-turn phase durations, this volume adjustment step should not reduce the left-turn volume to a value below four vehicles per cycle. 2. Opposing Mainline Volume: Opposing mainline volume was defined earlier in this chapter as the total approach volume minus the left-turn volume from exclusive lanes or from a single lane (in vehicles per hour). The cross product ([2] × [1]) may now be computed by multiplying the opposing mainline volume by the left-turn volume. This gives a value for comparison to determine if a protected phase should be assumed. 3. Number of Exclusive Left-Turn Lanes: This would be the number of lanes exclusively designated to accommodate the leftturn volumes. 4. Left-Turn Adjustment Factor: The left-turn adjustment factor applies only to protected left turns from exclusive left-turn lanes or to left turns that are not opposed. This factor is derived from Table 9-12 as 0.95 for single lanes and is further reduced by Table 9-4 to 0.92 for dual lanes. If the left-turn movement is not opposed because of a one-way street or T-intersection, pedestrian interference must be considered. The corresponding value of 0.85 for one lane and 0.75 for two lanes should be used as given in Table 911 and reduced in Table 9-4. 5. Left-Turn Lane Volume ([1]/([3] ∗ [4])): The total left-turn volume from Step 1 should be divided by the product of the number of exclusive left-turn lanes (Step 3) and the left-turn adjustment factor (Step 4). The left-turn volume should be entered directly if there is no exclusive left-turn lane. The result is expressed in vehicles per hour per lane. Zero should always be entered if the left turns are permitted. 6. Right-Turn Volume: Right-turn volumes (in vehicles per hour) from either a shared through and right-turn lane or from an exclusive turn lane or lanes should be entered. The right-turn-onred volume should be subtracted in accordance with the guidelines presented in Section II of this chapter. 7. Exclusive Lanes: This is the number of lanes assigned exclusively for right turns, if any. 8. Right-Turn Adjustment Factor: The right-turn adjustment factor is derived from Table 9-11 as 0.85 for a single lane or a shared lane and reduced by Table 9-4 to 0.75 for two lanes. 9,10. Right-Turn Lane Volume ([6]/([7] ∗ [8])): The total rightturn volume from Step 6 should be divided by the product of the number of exclusive right-turn lanes (Step 7) and the right-turn adjustment factor (Step 8). If there is no exclusive right-turn lane, a value of 1.0 should be used for Step 7. The result is entered as Step 9 if one or more exclusive right-turn lanes exist or as Step 10 if right turns must share the lane. 11. Through Volume: Total through volume for the approach, excluding left and right turns, should be placed in the appropriate column to correspond with the applicable treatment for left turns (permitted, protected, or not opposed).
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12. Parking Adjustment Factor: The parking adjustment factor should be placed in the appropriate column, as explained in Step 11. This factor corresponds to the assumed value of 20 parking maneuvers per hour applied to Table 9-8. It is dependent on the number of through lanes available. The values are 0.800, 0.900, and 0.933 for one, two, and three lanes, respectively. If no parking exists, the factor equals 1.0. 13. Number of Through Lanes Including Shared Lanes: This step is self-explanatory. Exclusive turn lane or lanes should be excluded. At this point it is necessary to distinguish between exclusive left-turn lanes and shared left-turn lanes. The procedure for exclusive left-turn lanes will be described first. Note that Steps 15 and 17 do not apply to exclusive left-turn lanes. 14. Total Approach Volume (([10] + [11])/[12]): The total approach volume is the total of the shared lane right-turn volumes plus the through volumes. Note that the through volumes are adjusted (increased) by the parking adjustment factor to account for the effect of parking on through volumes, for example, momentary lane blockage. Note also that left-turn volumes are excluded because they are not a part of the lane group. 15. Not applicable to exclusive left-turn lanes. 16. Left-Turn Equivalence: Left-turn equivalence, determined from Figure 9-7, is not used in lane volume calculations when exclusive left-turn lanes exist. This step is, however, required for permitted left turns to assess the adequacy of the left-turn treatment in Step 20. 17. Not applicable to exclusive left-turn lanes. 18. Through-Lane Volume ([14]/[13]): The total approach volume should be divided by the number of lanes to obtain volume per lane, which is the basis for computing critical lane volumes. 19. Critical Lane Volume: Step 19 is normally the same as Step 18 except when the right turn has an exclusive lane or the left turn is not opposed and either of these movements is more critical than the through movement. If both conditions apply, the critical lane volume will be Max ([5], [9], [18]). If a shared lane exists for the right turn, Step 9 should be eliminated. If the left turn is permitted or protected, Step 5 should be eliminated. The case of shared left-turn lanes is more complicated and therefore requires a more detailed procedure. Steps 14 through 18 are used to approximate the effect that left-turning vehicles have in reducing available lanes for through volumes. Left-turning vehicles blocking the shared left-turn and through lane will prevent through vehicles from proceeding until the turning vehicles have been able to make the turn. 14. Total Approach Volume: The total approach volume is computed in nearly the same manner as in Step 14 for exclusive leftturn lanes, that is, ([10] + [11])/[12]. The difference is that the volume from Step 5 must be added to the through volume in Step 11 if the left turn is not opposed. 15. Proportion of Left Turns in Lane Group: Step 15 is selfexplanatory. This data item is required for the follow-up computations. 16. Left-Turn Equivalence: Determined from Figure 9-7, this is one of the factors needed to compute the applicable formulas from Table 9-15 for shared-lane permitted left turns. It is not used at all when the left turn is protected. Updated December 1997
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17. Left-Turn Adjustment Factor for Through Traffic fDL: The appropriate formula in Table 9-15 should be used. This is a reduction factor applied to the through volumes to account for the effect of left-turn vehicles waiting for a gap in the opposing traffic to make the turn. Note that for lanes that are not opposed, the factor must be 1.0 because these vehicles will have gaps in which to turn. 18. Through-Lane Volume: Total through volume in the approach should be divided by the number of through lanes. Note that the number of lanes is reduced by the factor obtained in Step 17 to account for the effect of the left-turning vehicles. 19. Critical Lane Volume: The critical lane volume is the maximum of either the value computed by Step 18 or the right-turn volume from an exclusive right-turn lane as computed in Step 9. 20. Left-Turn Check: If one or more left turns have been designated as permitted (i.e., no protected phase has been assigned), the need for a protected phase should be reexamined at this point. If the cross product ([2] × [1]) exceeds the adopted thresholds, a protected left-turn phase should be assigned for planning purposes unless existing traffic volumes have been used and it is known that such a phase does not exist. When the level of opposing traffic is such that permitted left turns have difficulty finding acceptable gaps, the permitted leftturn capacity is derived substantially from sneakers and is therefore limited to approximately two vehicles per cycle. For planning level analysis, it should be assumed that this capacity limitation will apply whenever the left-turn equivalence exceeds a value of 3.5. Therefore, if the left-turn equivalence [16] is greater than 3.5 and the left-turn volume is greater than two vehicles per cycle (i.e., [1] > 7,200/Cmax), it is most likely that the subject left turn will not have adequate capacity without a protected phase.
Signal Operations Worksheet
Of the six steps involved in the planning method, only the first two are carried out by the lane volume worksheet. The last four steps are included in the signal operations worksheet, which is shown in Figure 9-24. To facilitate the use of the signal operations worksheet, the lane volumes are transferred from the lane volume worksheet before the computations begin. Note that the throughmovement lane volume is taken as the heavier of the through or right-turning movement when an exclusive right-turn lane is present. In other words, if the volume of a right turn from an exclusive lane is heavier than that of the through movement, the right-turn lane volume will be considered as the through volume for design purposes. 1. Transcribed Data Items: The peak-hour factor (PHF) was entered on the Planning Method Input Worksheet. The appropriate value is discussed in connection with the description of that worksheet. The left-turn treatment is also transcribed to the signal operations worksheet from the input worksheet. Note that it is not necessary to specify whether the treatment includes a permitted phase for the left turn in addition to a protected phase. The synthesis of the signal timing plan does not consider protected-pluspermitted operation. That, of course, does not preclude specification of this type of operation in the analysis. At this time, only determination of reasonable values for the cycle length and phase times is of interest. 2. Phase Plan Selection: The phase plan is selected from six alternatives that cover the full range of left-turn protection requireUpdated December 1997
ments. A phase plan deals with only one street at a time. The complete signal sequence will involve two phase plans: one for the east-west street and one for the north-south street. The choice between phase plans is made by examining the left-turn protection for both pairs of opposing left turns. The alternatives include the following: T Plan 1: No left-turn protection in either direction. In this case, the phase plan includes only one phase, in which all through and left-turn movements may proceed, with the left turns yielding to the opposing through traffic. T Plans 2a and 2b: These two plans involve left-turn protection for only one of the two opposing left turns. Two phases will be involved in this case. In the first phase, the protected left turn will proceed with the through movement in the same direction. In the second phase, the two through movements will proceed. Plans 2a and 2b differ only in terms of which of the two opposing left turns is protected. T Plans 3a and 3b: Both opposing left turns are protected here. In the first phase, the two opposing left turns will proceed. In the second, the dominant left turn will continue with the through movement in the same direction. In the third, the two through movements will proceed. Plans 3a and 3b differ only in terms of the dominant left turn that governs the display in the second phase. T Plan 4: This is generally known as ‘‘split-phase’’ operation. Two phases are involved, with the through and left-turn movements from one of the two opposing directions proceeding on each phase. This has the effect of full directional separation between the two approaches. From a capacity analysis point of view, it is equivalent to two one-way streets that meet at a common point. The selection criteria are presented in a table on the signal operations worksheet. Note that the selection is made on the basis of the user-specified left-turn protection and the dominant left-turn movement identified from the lane volume worksheet. 3. Critical Phase Volume, CV: When the phase plan has been selected, the movement codes, critical phase volumes (CVs), and lost time per phase may be entered on the worksheet. The appropriate choice for critical lane volumes is given in the phase plan summary shown in Table 9-17, along with a code that identifies the movements that are allowed to proceed on each phase. The movement codes are defined in a note to Table 9-17. For example, ‘‘NST’’ indicates that the northbound and southbound through movements have the right-of-way on the specified phase. The corresponding code for the two opposing left turns moving concurrently is ‘‘NSL.’’ If the northbound through and left turns are moving together, the code is ‘‘NTL.’’ Note that Table 9-17 also indicates the lost time to be assigned to each phase. Thus, the movement codes and CVs must be determined for each phase from Table 9-17 and entered on the signal operations worksheet. When all phases have been completed, the critical sum (CS) of the CVs must be entered on the next line. 4. Lost Time Determination: For planning purposes, it is assumed that there is a lost time value of 4 sec per phase in which any movement is both started and stopped. For one- and two-phase plans, there is a lost time associated with each phase. For threephase plans (Plans 3a and 3b), the second phase requires no lost time because none of the movements are both started and stopped. Thus, as a simple rule, phase Plan 1 involves 4 sec of lost time per cycle, and all other plans require 8 sec.
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Table 9-17. Phase Plan Summary for Planning Analysis east-west critical sum
north-south
phase plan
phase no.
lost time
movement code
1
1
4
EWT
Max(ET,EL,WT,WL)
movement code NST
Max(NT,NL,ST,SL)
critical sum
2a
1 2
4 4
WTL EWT
WL Max(WT-WL,ET)
STL NST
SL Max(ST-SL,NT)
2b
1 2
4 4
ETL EWT
EL Max(ET-EL,WT)
NTL NST
NL Max(NT-NL,ST)
3a
1 2 3
4 0 4
EWL ETL EWT
WL EL-WL Max(WT,ET-(EL-WL))
NSL NTL NST
SL NL-SL Max(ST,NT-(NL-SL))
3b
1 2 3
4 0 4
EWL WTL EWT
EL WL-EL Max(ET,WT-(WL-EL))
NSL STL NST
NL SL-NL Max(NT,ST-(SL-NL))
4
1 2
4 4
ETL WTL
Max(ET,EL) Max(WT,WL)
NTL STL
Max(NT,NL) Max(ST,SL)
Note: EWT = eastbound and westbound through; ETL = eastbound through and left; WTL = westbound through and left; NST = northbound and southbound through; STL = southbound through and left; NTL = northbound through and left; ET = eastbound through; EL = eastbound left; WT = westbound through; WL = westbound left; NT = northbound through; NL = northbound left; ST = southbound through; SL = southbound left.
When the lost times have been determined for each phase, the total lost time per cycle (TL) may be computed and entered on the worksheet. 5. Critical v/c Ratio, Xcm: The planning-level critical v/c ratio, Xcm, is the ratio of the critical sum, CS, to the sum of the critical lane volumes that could be accommodated at the maximum cycle length, computed as (1 − TL /Cmax) * 1,900 * CBD * PHF The intersection status is determined directly from Xcm using the threshold values given in Table 9-15. 6. Timing Plan Development: The development of a timing plan is optional. For many planning applications, a knowledge of the intersection status is sufficient. The timing plan is only required if the planning analysis is to be extended to estimate the level of service. The cycle length may be determined from the following formula: C=
TL 1 − [Min(CS,RS)/RS]
where RS is the reference sum of phase volumes representing the theoretical maximum value that the intersection could accommodate at an infinite cycle length. The recommended value for the reference sum is (1,710 * PHF). This value should be reduced by 10 percent in CBD locations. The value of 1,710 is 90 percent of the ideal saturation flow rate of 1,900 pcphgpl. It will attempt to produce a 90 percent v/c ratio for all critical movements. The cycle length determined from this equation should be checked against reasonable minimum and maximum values. The determination of appropriate values is discussed in connection with the Planning Method Input Worksheet. The lost time per cycle must be subtracted from the total cycle time to determine the effective green time per cycle, which must then be apportioned among all the phases. This is based on the proportion of the critical phase volume sum for each phase determined in a previous step. The phase time should be entered on the worksheet. As a final step, the lost time must be added to the effective green time for each phase to determine the total phase time per
cycle. The phase times for all of the phases should be equal to the cycle length and should be entered on the last line of the worksheet.
Limitations of Planning Method
The planning analysis technique described in this chapter offers a method for synthesizing a reasonable and effective signal timing plan based on the traffic volumes and lane utilization at an intersection. It is possible using the worksheets included here to determine the approximate status of the operation of a signalized intersection with respect to its capacity. It is also possible to take the analysis considerably farther and obtain the level of service for each lane group by the operational analysis method. Software has already been developed that will implement the worksheets and invoke the operational analysis method. This development introduces a very powerful capability, one from which the numerical precision of the results may greatly exceed the accuracy of the original data. In particular, great caution should be employed when traffic volumes are projected to some point in the future. Unless there is strong confidence in the validity of the traffic data, this method should not be taken beyond the worksheet stage. Caution must also be used in interpreting the results of the operational analysis, even with reliable traffic data. In particular, it must be recognized that the overall intersection level of service represents the average of all approaches to the intersection. When highly directional peak periods are involved, the relatively inconsequential movements on the lightly traveled approaches will have minimal delay. Thus, it is possible to see a favorable average delay and level of service for the intersection even when the critical approaches are heavily congested. The planning-level critical v/c ratio Xcm is used as an indicator of the status of the intersection with respect to its capacity. This measure may also be used as an indicator of the additional demand volume that could be accommodated. Although lower values of Xcm indicate that larger increases in demand volumes could be absorbed, it is important to realize that the relationship is not linear. Updated December 1997
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Therefore, linear projections of the maximum allowable increase in demand volumes based solely on Xcm might not be accurate. PROCEDURES FOR OTHER ANALYSES
As noted in Section II, Methodology, by starting with a known or desired level of service, it is possible to sequence the computations of the operational analysis procedure to solve for three unknowns: (a) v/c ratios, service flow rates, or both; (b) signalization; or (c) geometric features. In such computations, the steps of an operational analysis are rearranged in recognition of the fact that level of service, and therefore average stopped delay per vehicle, is a known quantity. Given knowledge of any two of the other three unknowns noted above, the remaining variable may then be calculated. Solutions for any of the above may be handled through iterative computations using the standard sequence of calculations. Delay results are then tabulated versus various trial values of the variable of interest. It is also possible, though computationally difficult, to work backward through the procedure, starting with a known delay. This is complex because relationships deal primarily with individual lane groups, and changes to one virtually always imply changes in the operation of others at the intersection. Further, geometric and signalization parameters must often change in relation to one another, such as an exclusive left-turn phase requiring an exclusive left-turn lane. Nevertheless, reverse computations are feasible and are best carried out using computer programs designed by the analyst for the specific objective. Figure 9-26 illustrates the computational path for such alternative analyses. In Figure 9-26(a), a v/c ratio or service flow rate is calculated for a given level of service. Calculations are made in the normal sequence through the computation of capacity for each lane group. Delay equations, however, are solved for a known delay commensurate with the selected level of service with the v/c ratio (X) as the unknown. Service flow rates may be computed as the v/c ratio times the capacity of the lane group.
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In Figure 9-26(b), the signal timing for a given level of service (delay) is desired. In this case, computations through the Saturation Flow Rate Module are performed in the normal sequence. As in all signal timing exercises, the phase plan must be established before computations are made. As indicated in Figure 9-26(b), however, determination of the signal timing for a given level of service requires some iterative calculations. This is because signal timing affects both capacity and delay, whereas capacity also affects delay. Further, the delay equations include g/C, C, c, and X, all of which are influenced by signal timing. Thus, no one variable can be directly computed without checking its effect on the others. In this approach, signal timing is estimated on the basis of the recommendations of Appendix II or local practice, and iterations are pursued to produce the desired delay value. In Figure 9-26(c), the number of lanes in a given lane group is to be computed. This is also an iterative process. For any given signal timing, the capacity of the lane group may be estimated using the delay equations (with c as the unknown). The delay equations, however, also require v/c ratios that depend heavily on capacity. Therefore, once again it is more practical to iterate the number of lanes, comparing the resulting delay for several trial values. The relative complexity of these other approaches makes a manual solution difficult, and therefore the operational analysis procedure is presented in the mode of solving for level of service. A sample calculation is included, however, illustrating how these alternative approaches may be accomplished. As with any analysis, v/c ratio and level of service must be considered as two important measures of performance. Any analysis yielding v/c ratios exceeding 1.0 should immediately trigger consideration of alternatives. High v/c ratios in the 0.95 to 1.0 range may also cause such consideration. This is an important point that can save a good deal of analysis effort. In many analyses [Figure 9-26(b) and (c)], v/c ratios will be obtained before delays and level of service. If an intersection is operating in an unacceptable v/c range, completing computations to find delay and level of service may be a fruitless exercise.
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Figure 9-26. Alternative computations using operational analysis.
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IV. SAMPLE CALCULATIONS This section presents six numerical examples that illustrate the computational principles set forth in this chapter. Sample Calculations 1 through 5 demonstrate the estimation of delay with given values for all the required field data items and operating parameters. Sample Calculation 6 demonstrates the reverse process of seeking the maximum traffic volume that may be accommodated within a specified level of service. A wide range of operational configurations, from simple to complex, is represented in the examples. In some cases, the timing plan as well as certain operating parameters, such as the type of left-turn protection, must be determined as a part of the exercise. When data items are not specified, the default values given in Table 9-3 are used. The planning method described earlier in this chapter will be used for all computations of timing plan parameters (cycle length and phase times) required by the sample calculations. Minimum cycle lengths of 60, 70, and 80 sec will be applied to two-, three-, and four-phase operation, respectively. Minimum phase times are generally determined by pedestrian requirements with assumed walking speeds. Absolute minimums of 10 and 15 sec per phase (including change and clearance intervals) have been imposed to provide a consistent treatment among sample problems. The total intergreen time (yellow plus all red) will be assumed to be 4 sec for each phase. RTOR volumes are assumed to be zero. The use of a particular design configuration or parameter does not imply endorsement of its suitability for field implementation under all conditions. Many agencies have their own policies and practices regarding design configurations and parameters. It is not the intent of this section to influence these policies or practices nor to prescribe design procedures but simply to illustrate the computational principles set forth here for evaluating delay and level of service. The worksheets shown in Section III and Appendix V of this chapter will be used to illustrate all of the computations. Each of the main worksheets will be presented in graphic form the first time it appears in this section. To conserve space and make the computations easier to follow, tabular equivalents will be used when appropriate for all subsequent presentations of the same worksheet, and worksheets that are not essential to the discussion will be omitted. Because of their complex nature, supplemental worksheets and planning method worksheets will always be presented in tabular form.
CALCULATION 1: OPERATIONAL ANALYSIS OF EXISTING PRETIMED, TWO-PHASE SIGNAL
The intersection of Third Avenue and Main Street is located in the central business district (CBD) of a small urban area. Figure 9-27 is the Input Module Worksheet for the problem, which illustrates the geometry and flows that exist at the intersection. Third Avenue is a two-lane street and Main Street is a four-lane arterial. The signal has a simple two-phase sequence, with phase times as shown on the worksheet. There are 5 percent heavy vehicles on all movements of the eastbound (EB) and westbound (WB) approaches and 8 percent on all movements of the northbound (NB) and southbound (SB) approaches. The peak-hour factor (PHF) is 0.90 for all movements. Updated December 1997
There is no parking within the confines of the intersection, and pedestrian flows average 100 peds/hr/crosswalk. The computations for each module of the procedure are described below in detail. Input Module Worksheet for Calculation 1
Most of the information on the Input Module Worksheet for Calculation 1 (Figure 9-27) is given. One item, however, must be calculated—the minimum green time for pedestrians, Gp, is computed as Gp = 7.0 + (W/4.0) − Y where W is the width to be crossed and Y is the yellow-plus-allred interval. Common practice is to take W as the distance from the curb to the midpoint of the farthest lane to be crossed. For the Main Street green (crossing Third Avenue), this is about 23 ft. For Third Avenue (crossing Main Street), this is about 39 ft. Then Gp (Main) = 7.0 + (23/4.0) − 4 = 8.8 sec Gp (Third) = 7.0 + (39/4.0) − 4 = 12.8 sec These values are entered in the appropriate boxes on the worksheet. Volume Adjustment Module Worksheet for Calculation 1
The computations for the Volume Adjustment Module Worksheet for Calculation 1 are shown in Figure 9-28. Each approach has one lane group that will be carried through the entire analysis. The hourly volumes are divided by the PHF to provide peak flow rates for subsequent computations. Proportions of left- and right-turning traffic are found by dividing the appropriate turning flow rates by the total lane group flow rate. Saturation Flow Rate Module Worksheet for Calculation 1
The computations for the Saturation Flow Rate Module are shown in Figure 9-29. Note the following entries: 1. Lane width adjustment factors are obtained from Table 9-5. For EB and WB approaches, 11-ft lane widths result in a factor of 0.967, and for the NB and SB approaches, with 15-ft lanes, the factor is 1.10. 2. The heavy vehicle adjustment factors of 0.952 and 0.926 are obtained from Table 9-6 and reflect 5 and 8 percent heavy vehicles present in each lane group. 3. Grade (level), parking conditions (none), and local bus traffic (none) are all ideal at this intersection, and therefore each has a factor of 1.00, which can be verified by consulting Tables 9-7, 9-8, and 9-9, respectively. 4. The area-type adjustment factor is 0.90, reflecting the CBD location of the intersection, as given in Table 9-10. 5. The lane utilization adjustment factor is applied here, at least initially, so the analysis will seek to establish the conditions in the worst lane within each lane group. If this factor were not applied, the results would reflect the average of all lanes of the defined lane groups. The lane utilization factor is 1.0 for the single-lane ap-
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Figure 9-27. Input Module Worksheet for Calculation 1.
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Figure 9-28. Volume Adjustment Module Worksheet for Calculation 1. proaches (NB and SB) and 0.95 for the two-lane approaches (EB and WB). 6. Right-turn adjustment factors are obtained from Tables 9-11a and 9-11b. Both EB and WB right turns fall under Case 5, and both NB and SB right turns fall under Case 7. The factors are based upon the proportion of right turns being made and the pedestrian crosswalk flow with which they conflict. 7. Because all left turns are permitted, the special procedure and worksheet for such turns must be used to obtain the left-turn adjustment factor. The supplemental worksheets for permitted left turns (Figures 9-17 and 9-18) must be implemented with some care, because they are complex and may involve a number of special cases. The current problem is the most straightforward case for which this worksheet is used, that is, permitted turns from a shared lane in which the green indications for the subject left turn and the opposing traffic are displayed simultaneously. Updated December 1997
Computations for this example follow the worksheet exactly with no special cases. The EB and WB approaches are multilane approaches opposed by multilane approaches and use the worksheet in Figure 9-30a. The NB and SB approaches are singlelane approaches opposed by single-lane approaches and use the worksheet shown in Figure 9-30b to determine the left-turn adjustment factor. It should be remembered that the value of fm must be converted to fLT for multilane approaches. This conversion is done on the last line of the worksheet. The top of each worksheet contains the input information transcribed from the Input Module Worksheet. The Rpo values are determined from the arrival type using Table 9-2. It should be remembered that each column refers to the value of Rpo for the opposing flow. Thus, for the EB column, the WB value of Rpo is used, and for the WB column, the EB value of Rpo is used. When all factors are entered onto the worksheet, the ideal saturation flow rate of 1,900 pcphgpl is multiplied by the number of
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Figure 9-29. Saturation Flow Rate Module Worksheet for Calculation 1.
lanes in the lane group and by each of the nine adjustment factors shown on the worksheet. The result is the prevailing adjusted saturation flow rate for each approach. Capacity Analysis Worksheet for Calculation 1
The capacity analysis computations for this problem are shown in Figure 9-31. Lane group volumes are entered from the Volume Adjustment Module Worksheet, and saturation flow rates are entered from the Saturation Flow Rate Module Worksheet. With these two values, v/s ratios can be computed and entered onto the worksheet. Once v/s ratios are obtained, the critical lane groups must be identified. Since there are no overlapping phases to consider, the highest v/s ratio between EB and WB approaches defines one critical lane group, and the highest v/s ratio between NB and SB approaches defines the other. The EB lane group, with v/s of 0.378,
is critical, as is the SB lane group, with a v/s of 0.455. The sum of critical v/s ratios is therefore 0.378 + 0.455 = 0.833. From this determination and the known signal timing parameters, the critical v/c ratio, Xc, can be computed. Note that for a simple two-phase signal and an assumption of 4.0 sec of lost time per movement, L = 8.0 sec/cycle and the resulting Xc = 0.940. Green ratios are entered onto the worksheet by dividing the effective green times by the 70-sec cycle length. Lane group capacities and v/c ratios may then be computed as shown on the worksheet. The results of the Capacity Analysis Module should be studied carefully for insights into operational problems, should they exist. In this case, the eastbound lane group v/c ratio is above 100 percent, indicating oversaturation. This problem will require further consideration, but the remainder of the computations will be completed first. Note that the v/c ratios for the two critical lane groups are not equal, indicating that green time is not proportionally allocated. Updated December 1997
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Figure 9-30a. Supplemental left-turn worksheets for EB and WB approaches (multilane). Updated December 1997
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Figure 9-30b. Supplemental left-turn worksheets for NB and SB approaches (single lane). Updated December 1997
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Figure 9-31. Capacity Analysis Module Worksheet for Calculation 1.
Updated December 1997
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Figure 9-32. LOS Module Worksheet for Calculation 1.
The EB critical lane group has a v/c ratio of 1.017, whereas the SB critical lane group has a v/c ratio of 0.885. A reallocation of green time may be considered but should not be made without consideration of the results of the delay computations in the next module. LOS Module Worksheet for Calculation 1
Level of service and delay are determined on the worksheet shown in Figure 9-32. Key values needed for this computation are entered from previous worksheets, and the formulas for uniform
delay, progression adjustment factor, and incremental delay are implemented. The resulting lane group delays vary from LOS B to E on the basis of the criteria in Table 9-1. Because there is only one lane group per approach, approach delays and levels of service are the same as the lane group delays and levels of service. The overall intersection delay is computed as 35.4 sec, resulting in an intersection level of service of D. In general, the intersection operation is marginal and could be improved. Note that the EB v/c ratio of 1.017 indicates that subUpdated December 1997
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Figure 9-33. Saturation Flow Adjustment Module Worksheet with no lane utilization factor for Calculation 1.
Figure 9-34. LOS Module Worksheet with no lane utilization factor for Calculation 1.
stantial queueing will take place on this approach during the peak 15 min of the peak hour. The overall allocation of green appears to result in an inequitable service to vehicles on all approaches. Some further consideration of the operation at this intersection could be considered. It should be recalled that because the lane utilization adjustment factor was used, the results reflect the operation in the worst of two lanes. Also, it was suggested earlier in this chapter that multiple lanes tend to be much more evenly utilized at high v/c ratios. It would therefore be quite appropriate to repeat the analysis without the lane utilization factors, that is, to consider the operation as averaged over all lanes in the lane group. This, of course, would make no difference to the NB and SB approaches because only single lanes are involved. However, saturation flow rates on the EB and WB approaches were decreased by 5 percent because of the two-lane approaches. The effect of eliminating this adjustment is seen in the Saturation Flow Rate Module Worksheet with no lane utilization factor (Figure 9-33). Note that the EB saturation flow, which was critical in the previous analysis, has been increased from 2,118 to 2,281 vphg. The effect of this increase is propagated through all of the worksheets and is evident in the LOS Module Worksheet with no lane utilization factor (Figure 9-34). Note that the EB v/c ratio dropped Updated December 1997
from 1.017 to 0.945 and the delay dropped to 39.7 sec/vehicle. The overall intersection delay is the weighted average of the approach delays with the approach flow rates used as the basis for weighting and is 29.7 sec/veh. The net effect was an improvement in the overall intersection level of service to LOS C. If it can be accepted that drivers on the EB approach would change lanes to maintain equilibrium in the lane distribution rather than suffering considerable extra delay per vehicle, it is reasonable to conclude that the revised analysis is appropriate. The given signal timing of 40 sec for the NB and SB traffic and 30 sec for the EB and WB traffic (total phase time) has not balanced the delay or v/c ratios among the competing movements. A more equitable design would require a small amount of time to be taken from the N-S phase and given to the E-W phase. This can only be accomplished using an iterative trial-and-error procedure. Although this would normally be carried out with one of several available traffic signal timing design programs that implement the methodology of this chapter, it is possible, given enough time, to arrive at a manual solution using the worksheets. Since the arrival types specified on the Input Module Worksheet indicate that this intersection is part of a coordinated system, it is logical to retain the 70-sec cycle throughout the process of reallo-
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Figure 9-35. LOS Module Worksheet with timing modifications for Calculation 1.
cating green time. It can be demonstrated that an equal v/c solution would be obtained with total phase times of 39.2 and 30.8 sec to the N-S and E-W phases, respectively. The final LOS Module Worksheet shown in Figure 9-35 indicates that the v/c ratios for the two critical movements (SB and EB) will be equalized at 0.905 under these conditions. At this point, the operation could be considered acceptable. The v/c ratios are balanced on the critical approaches. There is no apparent need for phasing changes or geometric improvements. CALCULATION 2: OPERATIONAL ANALYSIS OF THREEPHASE, PRETIMED SIGNAL
The intersection of Sixth Street and Western Boulevard is shown on the worksheet in Figure 9-36. Sixth Street is a one-way local street in an outlying area, and Western Boulevard is a four-lane arterial. Because Sixth Street is one way, signalization must address the existence of left turns (in this case, a heavy movement) in one direction only on Western Boulevard by providing an exclusive left-turn lane and protected-plus-permitted phasing for the EB left turn. The intersection is to be analyzed for the impact of volumes expected as a result of new development in the vicinity. The individual computational modules for this problem are discussed in the sections that follow.
analysis of this phasing will be a key part of this example. Note that signal timing is not specified and must be estimated as part of the solution. 4. The volumes shown represent future conditions, and the details of signal progression are not yet known for this case. As a base for analysis, random arrivals will be assumed, in which case the appropriate arrival type is 3. All other conditions shown on the Input Module Worksheet are straightforward. Sixth Street NB is on a 2 percent downgrade and has parking on both sides of the street. The parking activity of 20 movements per hour represents the total number of movements on both sides of the street, which is the appropriate value to use in determining the total impact of both parking lanes on saturation flow. Volume Adjustment Module Worksheet for Calculation 2
Input Module Worksheet for Calculation 2
The Volume Adjustment Module Worksheet for this calculation is shown in Figure 9-37. All items are straightforward for these computations. Movement volumes are divided by the PHF to find peak demand flow rates. Determination of lane groups is also straightforward: the EB left-turn lane must be established as a separate lane group, with remaining EB lanes forming a second lane group; WB and NB approaches form one lane group each. There are no de facto left-turn lanes because there are no opposed left turns from the WB or NB approaches. Left-turn and right-turn proportions are found by dividing the appropriate turning flow rate by the total lane group flow rate.
Several items are worthy of note on the Input Module Worksheet for Calculation 2 (Figure 9-36):
Saturation Flow Rate Module Worksheet for Calculation 2
1. Sixth Street is a one-way street as noted. Thus, left turns from Sixth Street do not have an opposing flow. Their principal conflict is with pedestrians, as is the case for right turns. Therefore, in the selection of a left-turn adjustment factor for Sixth Street, left turns will be treated using the right-turn adjustment factor table (Tables 9-11A and 9-11B). 2. Western Boulevard has local bus traffic stopping within the confines of the intersection. An appropriate adjustment factor will account for this condition. 3. The signal timing provides for a protected-plus-permitted left-turn phase from an exclusive lane in the EB direction. The
Figure 9-38 shows the Saturation Flow Rate Module Worksheet for this calculation. All adjustment factors are obtained directly from the appropriate tables except for the left-turn adjustment factor for the EB left-turn lane group, which is complex. The other factors are found as follows: 1. All lane widths are 12 ft, which is the ideal condition. Therefore, fw = 1.00 for all lane groups. 2. There are 10 percent trucks in each EB and WB lane group and 5 percent in the NB lane group. From Table 9-6, fHV = 0.909 and 0.952, respectively. Updated December 1997
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Figure 9-36. Input Module Worksheet for Calculation 2. Updated December 1997
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Figure 9-37. Volume Adjustment Module Worksheet for Calculation 2.
Figure 9-38. Saturation Flow Rate Module Worksheet for Calculation 2. 3. The grade is level for the EB lane groups and the WB lane group ( fg = 1.00). The NB lane group is on a 2 percent downgrade. From Table 9-7, fg = 1.01. 4. There is no parking on the EB and WB lane groups ( fp = 1.00). On the NB lane group, there is parking with 20 movements/ hr. From Table 9-8, fp = 0.90. 5. There are 20 local buses per hour stopping within the EB through lane group and the WB lane group. From Table 9-9, fbb = 0.96 for these groups. For the other lane groups, with no bus activity, fbb = 1.00. 6. The area type is not a CBD. From Table 9-10, fa = 1.00 for all lane groups. 7. There are no right turns from the EB left-turn lane group or the EB through lane group. Thus, fRT = 1.00 for these cases. For the WB and NB lane groups, Tables 9-11a and 9-11b are used with the proportion of right turns and 50 peds/hr in conflicting movements to obtain the factors shown on the worksheet. 8. The left-turn adjustment factor for the NB approach is obtained from Table 9-12, treating left turns from the one-way street as right turns. For the EB through and WB lane groups, there are no left turns, and fLT = 1.00. The left-turn adjustment factor for the EB left-turn lane group is more complex. Since it involves permitted left turns, the special procedure for such cases must be applied. Moreover, since a protected left-turn phase is also provided for this movement, separate
values of fLT must be computed for the protected and permitted portions of the movement. Since no signal timing was given for this example, it will be necessary to estimate the cycle length and phase times before proceeding further. The planning methodology will be used for this purpose. Since this is a three-phase operation, the cycle length range will be 70 to 100 sec as prescribed earlier in this section. The input data for the planning method normally come from the simplified Planning Method Input Worksheet presented in Figure 9-22. That worksheet will be omitted from this discussion because all of the information may be found in the Input Module Worksheet for Calculation 2 (Figure 9-36). The planning method worksheets for this calculation are shown in Figures 9-39 (lane volume worksheet) and 9-40 (signal operations worksheet). For simplicity, the results of the computations for all the lane volume worksheets are shown on a single table in Figure 9-39. It should be kept in mind that a manual implementation of this procedure using the worksheet originally presented in Figure 9-23 would require a separate worksheet for each direction. Because of the one-way street, only the NB and EB left turns exist. The following data items merit some discussion: 1. One of the first items to be specified is the left-turn treatment type, which includes both the signal protection (protected, permitted, or not opposed) and the left-turn lane assignment (shared or Updated December 1997
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Figure 9-39. Lane Volume Worksheet for Calculation 2.
exclusive). Only the EB left turn has an exclusive lane. The NB left turn operates from a shared lane, and the other two left turns do not exist. The EB left turn is protected, and the NB left turn is not opposed. For purposes of this worksheet, all movements that do not exist should be considered permitted, because they require no special treatment in the signal phasing. 2. There is no need for left-turn adjustment factors (Figure 923, line 17) here. Left-turn adjustment factors apply only to permitted left turns from shared lanes in the planning analysis. Permitted left turns from exclusive lanes are not represented in the signal timing plan synthesis. Protected left turns are adjusted in line 4 of the worksheet in Figure 9-23. 3. The critical lane volumes for the lane groups with through traffic are based on the through volume in each case. If the rightturn lane volume on any approach were heavier than the through volume, the right-turn volume would be considered critical. The critical through and right-turn lane volumes of 490, 409, and 474 vph for the EB, WB, and NB lane groups, respectively, and the lane volume for the EB left turn (126 vph) must now be Updated December 1997
transferred to the signal operations worksheet shown in Figure 940. The process for determining the signal timing is as follows: 1. The phase plane for N-S movements and for the E-W movements is determined from the type of left-turn protection for each movement. A choice of six phase plans is available; the selection criteria are given in Table 9-16. The appropriate choices are Plan 2b for the E-W approaches and Plan 1 for the N-S approaches. Note that all movements are assumed to exist in Table 9-16. Those movements that do not actually take place in the field are considered to exist with zero volume. This simplifies the selection process considerably. 2. The full sequence of phases is then established by specifying the movements that proceed on each phase using the codes in Table 9-16. The three phases are labeled ‘‘ETL,’’ ‘‘EWT,’’ and ‘‘NST.’’ This is consistent with the information presented on the Input Module Worksheet for Calculation 2 (Figure 9-36). Note that the ‘‘NST’’ code used for the third phase assumes that SB traffic would be allowed to move on that phase if it existed. This greatly simplifies the analysis without affecting the generality of the results.
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Figure 9-40. Signal Operations Worksheet for Calculation 2.
3. The critical phase volume (CV) for each phase is now determined using the critical sums given in Table 9-16 for the chosen phase plan. 4. The critical sum (CS), determined as the sum of the critical phase volumes for all phases, is 1,009 vph. 5. The critical v/c ratio Xcm is determined as 0.64 using the formula given in Note 4 of the signal operations worksheet (Figure 9-24). 6. The intersection status, obtained from Table 9-14, is under capacity. 7. The reference sum (RS) is determined using the formula given in Note 6 of the signal operations worksheet as 1,624 vph. This is the value of the critical sum that could be accommodated at an infinite cycle length with 90 percent v/c ratio. This value will be used later in the estimation of the cycle length. 8. The lost time for each phase is determined from Table 9-16 on the basis of the selected phase plan. 9. The cycle length is determined using the formula given in Note 7 of the signal operations worksheet. Because of the low v/c ratio, the specified minimum cycle length of 70 sec will govern in this example. 10. The phase times are determined using the formula given in Note 8 of the signal operations worksheet. The phase times are 11.2 sec (ETL), 27.5 sec (EWT), and 31.3 sec (NST). Two important observations may be made from the planning worksheets. The first is that the intersection should operate well
below its capacity. It would be expected that this fact would be reflected in the operational analysis when it has been completed. Second, the timing plan synthesized by the planning method appears to satisfy all of the minimum green requirements and should therefore be considered to be reasonable for implementation, providing that the assumed minimum greens are acceptable to the operating agency. Note that this is an initial signal timing established to allow the analysis to continue to completion. When v/c ratios and levels of service are established, the timing may have to be reconsidered and altered. Once the signal timing has been established, the value of fLT must be calculated using the special worksheet for permitted left turns, which is illustrated in Figure 9-41 for this calculation. Note the following input information: 1. The total lane group flow rate is entered as 126 vph from the Volume Adjustment Module Worksheet. 2. The proportion of left turns in the EB left-turn lane group flow is 1.0. 3. The cycle length is 70 sec, as estimated above. 4. There is no lost time applied for the permitted phase here, because the EB left turn is already proceeding as a protected movement at the beginning of the permitted phase. This is a special case that applies to multiple-phase left turns. Normally a lost time would be applied to the permitted phase. 5. The adjusted opposing flow is 842 vph, the total flow in the WB lane group, taken from the Volume Adjustment Module Updated December 1997
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Figure 9-41. Supplemental left-turn worksheet for Calculation 2.
Worksheet. The proportion of left turns in this opposing flow is zero. 6. The opposing platoon ratio is 1.0 because of the assumption of Arrival Type 3. This makes the opposing queue ratio equal to the proportion of red time for the opposing movement, or 0.66. 7. There is one lane in the EB left-turn lane group and there are two opposing lanes. 8. For exclusive lanes, gf is set at 0.0, because the first vehicle in the queue is always a left-turning vehicle. 9. The portion of green time blocked by oncoming traffic, gq, is determined by the equation given on the worksheet to be 15.19 sec. The remainder of the green time, or 12.31 sec, is the unsaturated green time, gu, and is considered to be available for left turns to filter through the oncoming traffic. 10. Subsequent computations of fm and fLT are made as indicated on the worksheet. For a one-lane group, fm = fLT. The value fLT may now be entered on the Saturation Flow Rate Module Worksheet, and the prevailing saturation flow rates for each lane group are computed as in Equation 9-10: s = so N fw fHV fg fp fbb fa fLU fRT fLT The results are shown in the last column of the Saturation Flow Rate Module Worksheet for Calculation 2 (Figure 9-38). Capacity Analysis Module Worksheet for Calculation 2
The capacity analysis worksheet for this calculation is shown in Figure 9-42. Lane group flow rates are entered in the third column of this worksheet from the Volume Adjustment Module Worksheet, and prevailing adjusted saturation flow rates are enUpdated December 1997
tered in the fourth column from the Saturation Flow Rate Module Worksheet. These are then used to compute the v/s ratios for each lane group. Critical lane groups must now be identified. The NB lane group, with a v/s ratio of 0.290, is clearly critical, because it is the only one moving during Phase 3 of the sequence, which has no overlaps. For the purpose of critical lane group determination, the protected and permitted phases of the EB left-turn lane group should be considered as separate lane groups. The EB left-turn primary phase is the only lane group moving exclusively in Phase 1. The EB left-turn secondary lane group and the WB lane group move exclusively in Phase 2. The WB v/s (0.273) is greater than that of the EB left-turn secondary, and therefore would be chosen. The combination of EB left-turn (primary) and WB gives a v/s sum of 0.35. The EB through lane group moves in both Phases 1 and 2 and has a v/s ratio of 0.328. The EB left-turn (primary) lane group and the WB lane group are critical. Thus, the sum of critical lane group v/s ratios is 0.290 + 0.077 + 0.273 = 0.640. The determination of lost time per cycle is simple for this case. All the critical lane groups effectively start and stop in a single phase. Each of the critical lane groups contributes 4 sec to the total lost time, to give a lost time per cycle of 12 sec. Had the EB left-turn secondary been critical instead of the WB, it would be assumed that the left turn did not stop at the interface of Phases 1 and 2 and therefore would not add any additional lost time to the sum. Using the critical lane group values, the critical v/c ratio for the intersection, Xc, is computed as 0.640 × (70)/(70 − 12) = 0.772. Green ratios g/C are now entered in the sixth column of the worksheet. The EB left-turn secondary phase is assumed to experience no lost time. For this lane group, g/C = 0.393.
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Figure 9-42. Capacity Analysis Module Worksheet for Calculation 2.
Figure 9-43. LOS Module Worksheet for Calculation 2.
Lane group capacities are then computed as s(g/C), and lane group v/c ratios are computed. All of the lane group v/c ratios are acceptable. The low v/c ratio for the EB left-turn lane group suggests that protected-plus-permitted phasing may have been overkill. In subsequent trials, the feasibility of a simple two-phase signal at this intersection might be investigated. A ‘‘protectedonly’’ left turn might also be feasible within the same cycle length. The critical v/c ratio is also somewhat low, suggesting that a shorter cycle length might accommodate all of the traffic; however, minimum green times must also be recognized. None of these insights should be acted on before the delay results of the final analysis module are considered. LOS Module Worksheet for Calculation 2
The LOS worksheet for Calculation 2 is shown in Figure 9-43. Values of cycle length, green ratio, v/c ratio, and lane group capacity are entered on the worksheet from previous results. Since random arrivals have been assumed as a base condition, the progression adjustment factor, PF, is taken to be 1.00 and may be entered directly on the worksheet without performing the computation.
Because of the protected-plus-permitted EB left turn, a special procedure for computing the uniform delay must be used as shown on the Supplemental Uniform Delay Worksheet for Calculation 2 (Figure 9-44). This worksheet implements the computations required for estimating the uniform delay as described previously in this chapter. The worksheet will be explained in more detail later in this discussion. Uniform, incremental, and total delay for each lane group are computed as indicated on the worksheet, and appropriate levels of service are selected from Table 9-1. The EB left-turn and EB through lane groups are then aggregated to obtain an approach delay and level of service. The average delay for these two lane groups is weighted on the basis of lane group demand flow. The overall intersection delay and level of service are determined as 21.4 sec/vehicle (LOS C) by computing the weighted average of the approach delays. The level of service at the intersection with the trial signal timing is generally quite good. The WB approach has the poorest LOS (C) and also has the highest v/c ratio (0.814), but both are in the acceptable range. Minor modifications could be considered, but the balance of this discussion will focus instead on the left-turn phasing alternatives. The objective will be not Updated December 1997
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Figure 9-44. Supplemental Uniform Delay Worksheet for Calculation 2.
Figure 9-45. Capacity Analysis Module Worksheet for protected-only phasing for Calculation 2.
to improve the intersection operation, but to gain a better perspective on the complex nature of the process by which left turns must be modeled. This provides an excellent opportunity to examine the special procedure for protected-plus-permitted phasing in more detail and to compare the results with the ‘‘protected-only’’ alternative. The Input Module Worksheet shown in Figure 9-36 indicates that the EB left turn proceeds on a green arrow in the first phase and on a solid green in the second phase. Suppose that this movement were only allowed to proceed on the green arrow, facing a red indication in Phase 2 instead of a green indication. Suppose also that the length of each signal phase does not change. These suppositions would make no difference in the Volume Adjustment Module Worksheet, and the only difference in the Saturation Flow Rate Module Worksheet would be the elimination of the computations for fLT for the EB permitted left turn. The Capacity Analysis Module Worksheet would remain the same for all movements except the EB left turn, as indicated in Figure 9-45. Note that the EB left turn is now served only by the primary Updated December 1997
phase, and the secondary phase no longer exists. The capacity is thereby reduced from 272 to 169 vph. The reduction in capacity for this movement should cause an increase in the delay. The delay is now estimated directly from Equation 9-24 instead of the special procedure in Figure 9-21. The revised LOS worksheet shown in Figure 9-46 indicates that the delay for the EB left turn has increased from 17.3 to 56.0 sec/ vehicle. Note that supplemental worksheets were not required for the left-turn saturation flow adjustment fLT nor for the uniform delay computations because no permitted movements were involved. A better understanding of this comparison may be seen in Figure 9-47, which shows the queue accumulation polygons that determine the value of the uniform delay. The area contained under the large lightly shaded triangle represents the delay for a protectedonly left turn that would be computed using Equation 9-24. The area under the two smaller and heavily shaded triangles represents the delay for a protected-plus-permitted left turn that would be computed by the Supplemental Uniform Delay Worksheet (Figure
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Figure 9-46. LOS Module Worksheet for protected-only phasing for Calculation 2.
Figure 9-47. Queue accumulation polygons for protected and protected-plus-permitted phasing for Calculation 2. 9-21). Note that the altitudes of the two heavily shaded triangles (0.53 and 1.24 vehicles, respectively) were computed previously on the Supplemental Uniform Delay Worksheet for Calculation 2 (Figure 9-44). The effect of this difference is propagated through to the capacity analysis worksheet for protected-only phasing and the LOS worksheet for protected-only phasing presented in Figures 9-45 and 9-46, respectively. Now that protected left-turn phasing has been compared with protected-plus-permitted (leading) phasing, it is perfectly logical to ask what would happen to the delay and level of service with permitted-plus-protected (lagging) left-turn phasing. The Supplemental Uniform Delay Worksheet differentiates between these two phasing alternatives. Further differences will be found in the saturation flow rate and capacity computations because of the relative position of the green phase for the two opposing directions. Reversing the order of the EB and WB phases to provide lagging left-turn protection for the EB left turn will have no effect on the operation if the left turn is protected only. The results will be identical to those presented for the leading protected-only case
shown in Figures 9-45 and 9-46. There will, however, be a noticeable difference if permitted-plus-protected phasing is used. To illustrate this difference, the order of the EB and WB phases is reversed, keeping the same cycle length and total phase times as in the original example. This will have no effect on the Volume Adjustment Module Worksheet for Calculation 2 (Figure 9-37); the values shown there will still apply. The changes in the Saturation Flow Rate Module Worksheet will be limited to a new fLT that results from minor changes in the computations performed on the Supplemental Worksheet for Permitted Left Turns (Figure 9-48). As shown in Figures 9-48 and 9-49, the fLT will increase from 0.15 (Figure 9-41) to 0.18 (Figure 9-48). The capacity will increase from 272 vph (Figure 9-42) to 366 vph (Figure 9-49). The Supplemental Uniform Delay Worksheet for permittedplus-protected (lagging) left-turn phasing (Figure 9-50) indicates an increase in the uniform delay from 11.75 sec/vehicle (Figure 9-44) to 19.72 sec/vehicle, reflecting the difference between leading and lagging left-turn protection. The second term of the delay equation is very small in both cases, because the v/c ratios are Updated December 1997
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Figure 9-48. Supplemental Worksheet for Permitted Left Turns: permitted-plus-protected (lagging) left-turn phasing for Calculation 2.
Figure 9-49. Capacity Analysis Module Worksheet for permitted-plus-protected (lagging) left-turn phasing for Calculation 2. low. The overall delay and level of service are computed on the LOS worksheet shown in Figure 9-51. The comparison of the queue accumulation and discharge polygons between protected-only phasing and permitted-plus-protected (lagging) left-turn phasing, shown in Figure 9-52, provides a graphical insight into the modeling process. A similar comparison for leading left-turn phasing was given in Figure 9-47. The difference between these phasing alternatives is apparent. It should be remembered that the uniform delay is given by the area contained under the queue accumulation polygon for the specified phasing alternative. Note how this area is reduced to a greater extent in the case of leading left-turn protection. Updated December 1997
This sample calculation has exercised several features of the analysis methodology presented in this chapter. All of the computations indicate that traffic volumes are well below capacity and that delays are minimal. No operational problems would be predicted under the specified conditions.
CALCULATION 3: OPERATIONAL ANALYSIS OF MULTIPHASE ACTUATED SIGNAL
The intersection of Fifth Avenue and Twelfth Street is a major CBD junction of two significant arterials. Both facilities have four
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Figure 9-50. Supplemental Uniform Delay Worksheet for permitted-plus-protected (lagging) left-turn phasing for Calculation 2.
Figure 9-51. LOS Module Worksheet for permitted-plus-protected (lagging) left-turn phasing for Calculation 2.
lanes, with exclusive left-turn lanes provided at the intersection on all four approaches. The signal is fully actuated, with standard protected-plus-permitted phasing on Fifth Avenue and simple permitted phasing on Twelfth Street. The signal is relatively isolated from adjacent signals, and arrivals can be assumed to be random for all practical purposes. Input Module Worksheet for Calculation 3
Figure 9-53 shows the Input Module Worksheet for this sample calculation. Most of the information is self-explanatory. There are 5 percent heavy vehicles on Twelfth Street and 2 percent on Fifth Avenue. There is parking on Twelfth Street with 5 movements/hr activity, and no parking on Fifth Avenue. PHFs are different for the two streets because of the slightly differing traffic characteristics. There are heavy pedestrian crossing volumes on Fifth Avenue and more moderate crossing volumes on Twelfth Street. Again, since arrivals are assumed to be random, Arrival Type 3 will be used for all approaches. The average signal timings observed in the field are
shown in Figure 9-53, and the unit extension for each phase is 2.5 sec. Balanced lane utilization was also observed in the field. Volume Adjustment Module Worksheet for Calculation 3
The Volume Adjustment Module Worksheet for Calculation 3 is shown in Figure 9-54. Movement volumes are divided by the appropriate PHF to obtain peak flow rates. The designation of lane groups is straightforward, with each approach consisting of an exclusive left-turn lane group and the through and right-turn lane group. The analysis will proceed with eight separate lane groups. The proportions of left and right turns are obtained by dividing the individual left- and right-turn flow rates by the total flow rate in each lane group. Saturation Flow Rate Module Worksheet for Calculation 3
The Saturation Flow Rate Module Worksheet for Calculation 3 is shown in Figure 9-55. The following adjustment factors are taken directly from the appropriate tables: Updated December 1997
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Figure 9-52. Queue accumulation polygons for protected and permitted-plus-protected phasing for Calculation 2.
1. The 10-ft lane widths on Twelfth Street call for an fw of 0.933. Fifth Avenue has standard 12-ft lanes, for which the factor is 1.00. 2. Twelfth Street has 5 percent heavy vehicles and from Table 9-6, fHV = 0.952. Fifth Avenue has 2 percent heavy vehicles and a factor of 0.980. 3. All grades are level, so fg = 1.00 for all lane groups. 4. EB and WB through lane groups have adjacent parking lanes with relatively low activity (5 movements/hr). From Table 9-8, fp = 0.938 for this case. Other lane groups do not have adjacent parking lanes and thus have a factor of 1.00. 5. There are no local buses on any approach, and fbb = 1.00. 6. Because the intersection is located in a CBD, fa = 0.90. 7. Because of the observed balanced lane utilization, fLU = 1.0. 8. Right-turn adjustment factors are found in Tables 9-11a and 9-11b for the appropriate proportion of right turns and conflicting pedestrian movements. For all left-turn lane groups, the value is 1.00. Values for through lane groups are shown on the worksheet. 9. The left-turn adjustment factor is 1.00 for all through lane groups. For left-turn lane groups, the special procedures involving permitted left turns must be implemented to compute the adjustment factor. The special worksheet for computing the left-turn adjustment factor for permitted left turns is shown in Figure 9-56. The EB and WB left-turn lanes involve simple permitted phasing, and the worksheet is followed easily, except that gf is set at 0.0 because the first vehicle in the queue is always a left-turner. The resulting left-turn adjustment factors are then recorded in the bottom rows of the worksheet. Note that the proportion of vehicles arriving on the green (for the opposing flow) is assumed to be equal to the opposing g/C ratio. In this case, the EB and WB g/C ratios are equal. NB and SB left-turn lane groups involve protected-plus-permitted phasing, and one modification must be applied in following the worksheet. The difference is that no lost time is applied to the permitted phase because the left turns already have a green indication at the beginning of the phase. Note that a 4-sec lost time is Updated December 1997
applied to the EB and WB left turns because no such phase is present for these movements. The resulting left-turn factors are very low for the NB and SB movements. This is primarily because the turns are made from exclusive lanes facing very heavy oncoming traffic. It is expected that most of the capacity for these movements will have to come from the protected phase and the sneakers. The fLT values are all entered on the Saturation Flow Rate Module Worksheet.
Capacity Analysis Module Worksheet for Calculation 3
The Capacity Analysis Module Worksheet for Calculation 3 is shown in Figure 9-57. Lane group flows are entered from the Volume Adjustment Module Worksheet (Figure 9-54), and saturation flow rates from the Saturation Flow Rate Module Worksheet (Figure 9-55). Flow ratios, v/s, are then computed and reviewed to identify critical lane groups. In this case, there are no overlaps in the phasing, which simplifies the determination of critical lane groups. Because both left turns in the N-S direction are protected plus permitted, both left turns are split into two lane groups. In the first phase, only the left-turn primaries move. The critical lane group is the SB leftturn primary (0.090). In the second phase, the NB through lane group has the highest v/s ratio (0.522). There is a single phase in the E-W direction. The critical lane group is the EB left turn with a v/s ratio of 0.224. This accounts for all phases. The sum of the v/s ratios is 0.836. The lost time is taken to be 4.0 sec/phase. Since each of the critical lane groups defines a single phase, there is time lost in the cycle at each phase. The total lost time is 12 sec/cycle. The critical v/c ratio is 0.836 × [90/(90 − 12)] = 0.964. Green ratios are entered in Column 6 of the worksheet, and lane group capacities are computed as s × g/C. Lane group v/c ratios are then computed as shown.
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Figure 9-53. Input Module Worksheet for Calculation 3. Updated December 1997
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Figure 9-54. Volume Adjustment Module Worksheet for Calculation 3.
Figure 9-55. Saturation Flow Rate Module Worksheet for Calculation 3.
LOS Module Worksheet for Calculation 3
The LOS Module Worksheet for Calculation 3 is shown in Figure 9-58. Relevant values of C, v/c, g/C, and c are entered from previous results. Lane group delays are computed as shown, and levels of service are obtained from Table 9-1. Delays are then aggregated by approach and for the intersection as a whole, and appropriate levels of service are assigned. A supplemental uniform delay worksheet is required for the NB and SB left turns. This worksheet is shown in Figure 9-59. The SB left turn will experience more delay than the NB left turn because there is heavier movement, which is opposed by more oncoming traffic. The NB movement is blocked by oncoming traffic for 15.35 sec of the permitted phase, and the SB movement is blocked for 36.48 sec as indicated by their respective gq values. Updated December 1997
This results in larger queues that create a greater area for the queue accumulation polygon discussed in detail in connection with Calculation 2. The uniform delays are computed as 6.27 sec/vehicle NB and 25.05 sec/vehicle SB. LOS values range from F for the WB left-turn lane group to A for the NB left-turn lane group. The wide range of delay for the critical movements suggests that the signalization is far too favorable to some movements, reinforcing the results of the capacity analysis. The disparate delay and v/c values suggest that the signal timing is inefficient and inequitable. The critical v/c ratio of 0.964 suggests that the overall intersection will operate near capacity. It is likely that a redistribution of the time allocation among the phases will produce a workable operation in the near-capacity v/c range.
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Figure 9-56. Supplemental Worksheet for Permitted Left Turns for Calculation 3.
Figure 9-57. Capacity Analysis Module Worksheet for Calculation 3.
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Figure 9-58. LOS Module Worksheet for Calculation 3. In this example, a trial-and-error procedure will again be applied to seek an acceptable solution using the planning method results as an initial solution. The EB and WB phases clearly need more green time. The NB and SB left-turn movements have ample green time; however, it is only possible to reduce this phase a small amount without violating the minimum green time for these movements. Some time will therefore have to be transferred from the NB and SB through phase or the cycle length must be increased, or both. As a result of a trial-and-error process of phase time redistribution, the following timing plan was formulated. Lane Group NB and SB left turn NB and SB through EB and WB left turn Total
Phase Time (sec) 12.4 49.9 27.7 90
Skipping the intermediate computations, the effect of the green time redistribution is shown in the LOS worksheet presented in Figure 9-60. Note that a better balance of delay among the competing movements has been achieved, with the worst delays in each phase balanced at 49 sec. The overall delay for the intersection is approximately 37 sec/vehicle. This delay value reflects LOS D. This sample problem has examined the effect of the signal timing plan on intersection performance. The initial plan was first evaluated and then modified by trial and error to produce a more satisfactory operation. It was mentioned earlier in this chapter that a separate and more detailed procedure for estimating signal timing parameters at traffic-actuated intersections is presented in Appendix II. The analysis of this intersection will be continued in Appendix II to illustrate the procedure. The effect of changes in controller operating parameters will also be demonstrated. CALCULATION 4: PLANNING ANALYSIS OF INTERSECTION WITH MULTILANE APPROACHES
The intersection of Tenth Avenue and First Street is currently a minor intersection of two 2-lane, lightly used streets. In 20 years, major development is expected to cause both streets to be reconUpdated December 1997
structed as multilane facilities, and the intersection will experience substantial demand. Figure 9-61, the input worksheet for the planning analysis, contains a diagram of the expected intersection layout and the forecast volumes for the intersection. Note that leftturn lanes are expected to be incorporated on each approach. Will the capacity of the design be adequate? This is an ideal application for the planning analysis. Some preliminary assumptions must be made about the signal phasing. All left turns are heavy and face heavy opposing traffic and will therefore be assumed to be protected. For planning purposes several years in the future, it is probably appropriate to assume that protected-only phasing will be used. There is no guarantee that protected-plus-permitted operation will be practical. For example, crash rates at this or nearby intersections could dictate the use of simple left-turn protection, and it could be very optimistic to count on the extra capacity of the permitted phase. Figure 9-62 shows the composite lane volume worksheet for this intersection, and Figure 9-63 shows the signal operations worksheet. For planning purposes, the main item of interest is the intersection status, which is given as near capacity, with a critical v/c ratio of 0.92. The estimated cycle length is 120 sec. The near-capacity rating could be interpreted to mean that it is uncertain whether the demand would exceed the capacity. It should be kept in mind that the 20-year traffic volume projections are no doubt based on some coarse assumptions and approximations. Although this status might be considered acceptable with nearterm volume projections, many agencies would be more comfortable with a design that was rated as under capacity to provide additional assurance that the capacity will not be exceeded. The suggestions in Appendix I indicate that intersection design should attempt to keep the per-lane volumes to 450 vph or less. This is not the case for the EB approach in the proposed design of Figure 9-61. Note that the right-turn volume is extremely high on this approach. If an exclusive right-turn lane were provided, lane volumes on the remainder of the approach could be brought below the suggested 450 vph. That alternative can be examined with the planning method. The composite lane volume worksheet with modified geometry is shown in Figure 9-64. This worksheet is very similar to the
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Figure 9-59. Supplemental Uniform Delay Worksheet for Calculation 3.
Figure 9-60. LOS Module Worksheet with revised signal timing for Calculation 3.
corresponding worksheet for the original design in Figure 9-62. Note, however, that the right turn is now the critical movement. The reduced lane volume resulting from the additional lane, when analyzed on the signal operations worksheet in Figure 9-65, indicates a reduction in the v/c ratio to 0.87. There is some question at this point about whether it is appropriate to proceed with the operational analysis on the basis of volumes projected so far into the future. It is certainly mechanically possible to perform the analysis; the problem lies with the degree of confidence in the results. Therefore the operational analysis will be carried out with that limitation in mind. The signal timing plan synthesized by the planning method in Figure 9-65 cannot be transferred directly into the operational
analysis without violating the minimum green time for the WB left turn. This problem may best be overcome by forcing the EB and WB left turns to move simultaneously by absorbing the 2.7 sec EB through and left-turn phase into the 9.5-sec EB and WB left-turn phase to create a 12.2-sec phase for both the EB and WB left turns. The timing plan to be used in the operational analysis will thus include five phases as follows: Movement EWL EWT NSL NTL NST
Phase (sec) 12.2 36.4 17.7 4.1 29.6 Updated December 1997
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Figure 9-61. Planning Method Input Worksheet for Calculation 4.
Using default values for the rest of the data items and skipping the worksheets showing intermediate computations, the discussion proceeds directly to the LOS Module Worksheet for Calculation 4 (Figure 9-66). The v/c ratios are reasonably well balanced and in the range indicated by the planning analysis. In general, the planning analysis tends to be a better approximation of the operational analysis when default values are used in the operational analysis and when permitted left turns are avoided. This is the case in the example that has just been examined. It is reasonable Updated December 1997
to conclude that both the planning and operational analyses indicate that the intersection would perform acceptably under the specified conditions. CALCULATION 5: PLANNING ANALYSIS OF INTERSECTION WITH SINGLE-LANE APPROACHES
A large area of a semirural community has been developing rapidly, requiring a considerable planning effort to provide addi-
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Figure 9-62. Lane Volume Worksheet for Calculation 4.
tional capacity at numerous intersection of low-type, formerly rural highway facilities. The intersection of Eighth Avenue and Main Street is one such location. It is an intersection of a two-lane roadway with a four-lane roadway. No turning lanes are present on any approach. The intersection is shown in Figure 9-67, along with projected traffic volumes. Is it likely that the capacity will be exceeded at this intersection, and if so, what countermeasures should be implemented? It will be difficult to evaluate phase plans with protected left turns at this intersection because none of the approaches is shown to have an exclusive left-turn lane. The single-lane approaches for NB and SB traffic preclude consideration of any alternative lane use. Protected left-turn phasing on these approaches would require split-phase operation. The EB and WB approaches each have two lanes, so it is possible to assign one lane as an exclusive left-turn lane and the other as a shared lane for through and right-turn traffic. Inspection of the EB and WB traffic volumes suggests that this is definitely necessary and probably practical on the WB approach. On the EB approach, a single-lane group with a shared lane for left turns is likely to be more appropriate. Therefore the initial solution is to use protected left-turn
phasing for the WB approach and a shared-lane permitted treatment on all of the other approaches. To provide a conservative assessment, protected-only phasing will be used for the WB left turn. The composite lane volume worksheet for this initial analysis is shown in Figure 9-68. The critical lane volumes appear to be very high, and this observation is confirmed on the signal operations worksheet (Figure 9-69). The critical v/c ratio is computed as 0.97, producing an at-capacity status. Some countermeasures should probably be considered. Since the EB through and right-turn lane group volume is critical, and since this lane group includes moderately heavy right-turn movement, it is logical to examine the addition of an EB right-turn lane as a countermeasure. The exclusive right-turn lane is easily incorporated into this analysis. The lane volume and signal operations worksheets shown in Figures 9-70 and 9-71, respectively, indicate that the critical v/c ratio would be reduced to 0.82 by this improvement, and the intersection status would be under capacity. This could be considered the final solution to the problem, but the NB and SB left turns merit further consideration. It would be desirable to avoid the problem of significant left-turn volumes in a pair of opposing single-lane approaches, if possible. For this reason, Updated December 1997
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urban streets
Figure 9-63. Signal Operations Worksheet for Calculation 4.
split-phase operation on the NB and SB approaches will be examined. Under split-phase operation, there would be a complete directional separation between the traffic from the two opposing directions because their lane groups would proceed on different phases. The planning method worksheets provide for split-phase operation, which is identified on the signal operations worksheet as Phase Plan 4. The lane volume worksheet for this alternative is shown in Figure 9-72. Note that the NB and SB per-lane volumes are reduced because there is no interference from the left turns in the single lane. However, as shown in Figure 9-73, these reduced volumes must now be added into the critical sum because they each move on different phases. Previously, only the heavier of the two volumes was reflected in the critical sum, because the two lane groups proceeded on the same phase. The net result is an increase in the critical v/c ratio to 1.02. Therefore, it would be difficult to recommend split-phase operation at this intersection as a desirable solution from a capacity standpoint. To provide a protected phase for the NB and SB left turns, it will be necessary to widen the approaches to the intersection to construct an additional lane for exclusive left turns. This alternative is easy to examine with the planning method. The composite lane volume worksheet shown in Figure 9-74 indicates a substantial reduction in the per-lane volume for the NB and SB through movements. The effect on the critical v/c ratio, as shown in Figure 9-75, is a reduction to the under-capacity level. Updated December 1997
CALCULATION 6: DETERMINING v/c AND SERVICE FLOW RATES—AN ALTERNATIVE USE OF OPERATIONAL ANALYSIS PROCEDURE Description
A two-lane through movement at one approach to a signalized intersection has a cycle length of 90 sec with a g/C ratio of 0.50. The arrival type is currently 3 (random), but this could be improved by altering the progression. What is the maximum service flow rate that could be accommodated at LOS B (20 sec/veh delay) on this approach? Solution
Delay is based on the v/c ratio, X; the green ratio, g/C; the cycle length, C; the lane group capacity, c; and the progression factor, PF. The lane group capacity may be computed as the saturation flow rate for the lane group times the g/C ratio, which is known. Assume that a standard analysis using the Saturation Flow Rate Module Worksheet has been conducted and that the saturation flow rate for the lane group has been found to be 3,200 vphg and the capacity 3,200 × 0.50 = 1,600 vph. If delay is set at 20.0 sec/veh and the known values of C, g/C, and c are inserted into Equations 9-22, 9-23, and 9-25, the following relationship is established:
signalized intersections
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Figure 9-64. Lane Volume Worksheet for Calculation 4 with geometric modifications. 20.0 = d1 PF + d2 + d3 d1 = 0.5(90)(1 − 0.50)2/(1 − 0.50X ) d2 = 225[(X − 1) + √(X − 1)2 + (X/100)] d3 = 0 Various combinations of PF and X that result in 20.0 sec of delay may now be solved for. If the level of service (delay) were to be allowed to vary as well, a tabular array of X versus delay and arrival type could be developed for the subject approach. Table 9-18 is such an array. Two presentation formats are shown in Table 9-18. The upper portion tabulates delay for various arrival types and v/c ratios (X). The lower portion tabulates v/c ratio versus delay and arrival type.
For the solution to this problem, the lower table is most useful. For a delay of 20 sec, maximum v/c ratios are given for Arrival Types 1–6. Service flow rates, SF, are computed as the v/c ratio times the lane group capacity of 1,600 vph. Thus, for LOS B, the approach can carry a maximum service flow rate of 1,126 vph under the existing arrival type (3), but could be increased to as much as 1,491 vph for Arrival Type 5 with improved progression and even up to 1,571 for Arrival Type 6 with near-perfect progression. This calculation is intended to illustrate the potential for alternative computational sequences using the basic operational analysis format. It should be noted, however, that this calculation addresses only one lane group and that computations become far more complex when multiple lane groups are to be considered simultaneously. Nevertheless, the procedure is capable of determining service flow rates, as shown here, or geometric or signal parameters based on a desired level of service.
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urban streets
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Figure 9-65. Signal Operations Worksheet for Calculation 4 with geometric modifications.
Figure 9-66. LOS Module Worksheet for Calculation 4.
Updated December 1997
signalized intersections
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Figure 9-67. Planning Method Input Worksheet for Calculation 5.
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Figure 9-68. Lane Volume Worksheet for Calculation 5.
Figure 9-69. Signal Operations Worksheet for Calculation 5.
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urban streets
Figure 9-70. Lane Volume Worksheet with additional EB right-turn lane for Calculation 5.
Figure 9-71. Signal Operations Worksheet with additional EB right-turn lane for Calculation 5.
signalized intersections 9-93
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Figure 9-72. Lane Volume Worksheet with NB and SB split-phase operation for Calculation 5.
Figure 9-73. Signal Operations Worksheet with NB and SB split-phase operation for Calculation 5.
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urban streets
Figure 9-74. Lane Volume Worksheet with added NB and SB left-turn lanes for Calculation 5.
Figure 9-75. Signal Operations Worksheet with added NB and SB left-turn lanes for Calculation 5.
signalized intersections 9-95
Updated December 1997
urban streets
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Table 9-18. Service Flow Rate Solutions for Calculation 6 X
flow rate
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0 160 320 480 640 800 960 1,120 1,280 1,440 1,600
los
max delay
A B C
D
E
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
delay d1
d2
AT = 1
AT = 2
AT = 3
AT = 4
AT = 5
AT = 6
11.25 11.84 12.50 13.24 14.06 15.00 16.07 17.31 18.75 20.45 22.50
0.00 0.12 0.28 0.48 0.75 1.12 1.67 2.58 4.30 8.51 22.50
18.75 19.87 21.12 22.54 24.19 26.12 28.46 31.43 35.55 42.61 60.01
13.95 14.81 15.78 16.89 18.19 19.72 21.60 24.04 27.55 33.88 50.40
11.25 11.97 12.78 13.72 14.81 16.12 17.74 19.88 23.05 28.97 45.00
8.63 9.21 9.87 10.63 11.53 12.62 14.00 15.85 18.68 24.20 39.76
3.75 4.07 4.44 4.89 5.43 6.11 7.02 8.34 10.54 15.33 29.99
0.00 0.12 0.28 0.48 0.75 1.12 1.67 2.58 4.30 8.51 22.50
X
SFmax
AT = 1 SFmax
177 707 1043 1259 1381 1462 1508 1554 1600
AT = 2
0.11 0.44 0.65 0.79 0.86 0.91 0.94 0.97 1.00
191 824 1164 1342 1451 1499 1548 1596
AT = 3 X
0.12 0.51 0.73 0.84 0.91 0.94 0.97 1.00
SFmax
663 1126 1333 1450 1500 1550 1600
AT = 4 X
SFmax
0.41 0.70 0.83 0.91 0.94 0.97 1.00
348 1046 1318 1448 1500 1551
AT = 5 X 0.22 0.65 0.82 0.91 0.94 0.97
AT = 6
SFmax
X
SFmax
X
513 1241 1429 1491 1546
0.32 0.78 0.89 0.93 0.97
1307 1457 1514 1571
0.82 0.91 0.95 0.98
V. REFERENCES The methodology in this chapter is based in part on the results of an NCHRP study conducted by JHK & Associates (2,3). Critical movement capacity analysis techniques have been developed in the United States (1,4,5), Australia (6), Great Britain (7), and Sweden (8). Background for delay estimation procedures was developed in Great Britain (7), Australia (9,10), and the United States (11). Updates to the original methodology were subsequently developed (12–20). 1. Messer, C.J., and Fambro, D.B., ‘‘Critical Lane Analysis for Intersection Design.’’ Transportation Research Record 644, Transportation Research Board, Washington, D.C. (1977). 2. ‘‘NCHRP Signalized Intersection Capacity Method.’’ National Cooperative Highway Research Program, Project 328(2), JHK & Associates, Tucson, Ariz. (Feb. 1983). 3. ‘‘Signalized Intersection Capacity Study.’’ Final report, National Cooperative Highway Research Program, Project 328(2), JHK & Associates, Tucson, Ariz. (Dec. 1982). 4. Berry, D.S., ‘‘Other Methods for Computing Capacity of Signalized Intersections.’’ Paper presented at the 56th Annual Meeting of the Transportation Research Board, Washington, D.C. (Jan. 1977). Updated December 1997
5. Berry, D.S., and Gandhi, P.K., ‘‘Headway Approach to Intersection Capacity.’’ Highway Research Record 453, Transportation Research Board, Washington, D.C. (1973). 6. Miller, A.J., ‘‘The Capacity of Signalized Intersections in Australia.’’ Australian Road Research Bulletin 3, Australian Road Research Board, Kew, Victoria, Australia (1968). 7. Webster, F.V., and Cobbe, B.M., Traffic Signals. Her Majesty’s Stationary Office, London, England (1966). 8. Petersen, B.E., and Imre, E., Swedish Capacity Manual. Stockholm, Sweden (Feb. 1977). 9. Akcelik, R. (Ed.), ‘‘Signalized Intersection Capacity and Timing Guide.’’ Signalized Intersection Capacity Workshop— Papers, Australian Road Research Board, Kew, Victoria, Australia (1979). 10. Akcelik, R., ‘‘Traffic Signals: Capacity and Timing Analysis.’’ Australian Road Research Report 123, Australian Road Research Board, Kew, Victoria, Australia (1981). 11. Reilly, W.R., Gardner, C.C., and Kell, J.H., ‘‘A Technique for Measurement of Delay at Intersections.’’ FHWA Report No. RD-76-135/137, Federal Highway Administration, Washington, D.C. (1976).
signalized intersections 12. Fambro, D.B., Chang, E.C.P., and Messer, C.J., ‘‘Effects of the Quality of Traffic Signal Progression on Delay,’’ National Cooperative Highway Research Program, Project 3-28C, Texas Transportation Institute, Texas A&M University, College Station (Aug. 1989). 13. Roess, R.P., Papayannoulis, V.N., Ulerio, J.M., and Levinson, H.S., ‘‘Levels of Service in Shared-Permissive LeftTurn Lane Groups at Signalized Intersections,’’ Federal Highway Administration, Transportation Training and Research Center, Polytechnic University, Brooklyn, New York (Sept. 1989). 14. Prassas, E.S., and Roess, R.P., ‘‘The Left-Turn Adjustment for Permitted Turns from Shared Lane Groups: Another Look,’’ paper presented at the mid-year meeting of TRB Committee A3A10, Transportation Training and Research Center, Polytechnic University, Brooklyn, New York (July 1992). 15. Bonneson, J.A., and McCoy, P.T., ‘‘Operational Analysis of Exclusive Left-Turn Lanes with Protected/Permitted Phasing,’’ Transportation Research Record 1114, Transportation Research Board, Washington, D.C. (1987).
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16. Hagen, L.T., and Courage, K.G., ‘‘Comparison of Macroscopic Models for Signalized Intersection Analysis,’’ Transportation Research Record 1225, Transportation Research Board, Washington, D.C. (1989). 17. Strong, D.W., ‘‘Real-World Use of the 1985 HCM—Analysis of Signalized Intersections,’’ Compendium of Technical Papers, Institute of Transportation Engineers, Washington, D.C. (Sept. 1989). 18. Fambro, D.B., Rouphail, N., Sloup, P., Daniel, J., and Li, J., ‘‘Highway Capacity Manual Revisions of Chapters 9 and 11.’’ Final Report FHWA-RD-96-088 (Jan. 1996). 19. Courage, K., Fambro, D.B., Akcelik, R., Lin, P., Anwar, M., and Viloria, F., ‘‘Capacity Analysis of Traffic-Actuated Intersections.’’ Final report NCHRP Project 3-48 (Dec. 1996). 20. Powell, J.L., ‘‘Field Measurement of Signalized Intersection Delay for the 1997 HCM.’’ Parsons Transportation Group, Chicago, Ill., unpublished paper (July 1997).
APPENDIX I INTERSECTION GEOMETRICS—SUGGESTIONS FOR ESTIMATING DESIGN ELEMENTS This appendix summarizes suggestions for establishing the geometric design of an intersection when it has not been defined by existing conditions or by state or local practice. These suggestions may also be applied when analysis indicates intersection deficiencies that are to be corrected by changes in geometric design. Nothing in this appendix, however, should be construed as constituting strict guidelines or standards. This material should not be used in place of applicable state and local standards, guidelines, policies, or practice. The geometric design of an intersection involves several critical decisions about the number and use of lanes to be provided on each approach, as discussed in the following sections.
approach. A method for estimating the required length of the storage bay is summarized in Figure I.9-1 and Table I.9-1.
EXCLUSIVE LEFT-TURN LANES
EXCLUSIVE RIGHT-TURN LANES
Left-turn lanes are provided to accommodate heavy left-turn movements without disruptions to through and right-turning vehicles. The provision of an exclusive left-turn lane (or lanes) allows for the use of protected left-turn phasing and provides storage for queued left-turn vehicles without disruption to other flows. The following suggestions are made concerning the provision of exclusive left-turn lanes:
Although right turns are generally made more efficiently than left-turn movements, exclusive right-turn lanes are often provided, for many of the same reasons that left-turn lanes are used. Right turns may face a conflicting pedestrian flow, but do not face a conflicting vehicular flow. In general, an exclusive right-turn lane should be considered when the right-turn volume exceeds 300 vph and the adjacent main-line volume exceeds 300 vphpl.
1. Where fully protected left-turn phasing is to be provided, an exclusive left-turn lane should be provided. 2. Where space permits use of a left-turn lane, it should be considered when left-turn volumes exceed 100 vph. Left-turn lanes may be provided for lower volumes as well on the basis of the judged need and state or local practice, or both. 3. Where left-turn volumes exceed 300 vph, provision of a double left-turn lane should be considered. 4. The length of the storage bay should be sufficient to handle the turning traffic without reducing the safety or capacity of the
Figure I.9-1 shows the relationship between the left-turn volume [expressed in passenger car equivalents (PCEs)] and the length of the turn storage bay. The relationship is based on random arrivals and 5 percent probability of storage bay overflow. Left-turn PCE factors, EL1, are obtained from Figure 9-7. The values obtained from Figure I.9-1 are for a cycle length of 75 sec and a v/c ratio of 0.80. For other values, the length obtained from Figure I.9-1 is multiplied by a correction factor obtained from Table I.9-1. The v/c ratio for left-turn lane groups is computed on the operational analysis Capacity Analysis Module Worksheet.
NUMBER OF LANES
The number of lanes required on an approach depends on a variety of factors, including the signal design. In general, enough main roadway lanes should be provided such that the total of the through plus right-turn volume (plus left-turn volume, if present) does not exceed 450 vphpl. This is a very broad suggestion. Higher volumes can be accommodated on major approaches when a substantial portion of available green time can be allocated to the Updated December 1997
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urban streets Table I.9-1. Left-Turn Bay Length Adjustment Factors v/c ratio, X 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95
cycle length, C (sec) 60
70
80
90
100
0.70 0.71 0.73 0.75 0.77 0.82 0.88 0.99 1.17 1.61
0.76 0.77 0.79 0.81 0.84 0.88 0.95 1.06 1.26 1.74
0.84 0.85 0.87 0.89 0.92 0.98 1.05 1.18 1.40 1.92
0.89 0.90 0.92 0.94 0.98 1.03 1.11 1.24 1.48 2.03
0.94 0.95 0.97 1.00 1.03 1.09 1.17 1.31 1.56 2.14
Source: C. J. Messer, ‘‘Guidelines for Signalized Left-Turn Treatments,’’ Implementation Package FHWA-IP-81-4, Federal Highway Administration, Washington, D.C., 1981, Table 1.
subject approach. When the number of lanes is unknown, the foregoing value represents a reasonable starting point for analysis computations. OTHER FEATURES
Figure I.9-1. Left-turn bay length versus turning volume. (Source: C. J. Messer, ‘‘Guidelines for Signalized Left-Turn Treatments,’’ Implementation Package, FHWA-IP-81-4, Federal Highway Administration, Washington, D.C. 1981, Fig. 2.)
When lane widths are unknown, the 12-ft standard lane width should be assumed unless known restrictions prevent such width. Parking conditions should be assumed to be consistent with local practice. When no information exists, no curb parking and no local buses should be assumed for analysis purposes.
APPENDIX II SUGGESTIONS FOR ESTABLISHING SIGNAL DESIGN IN ANALYSIS The design of traffic signal operation is a complex process involving three important decisions: 1. Type of signal controller to be used; 2. Phase plan to be adopted, and 3. Allocation of green time among the various phases. Each of these decisions is heavily influenced by state and local policies, guidelines, and standards, all of which may vary considerably from location to location. This appendix presents the alternatives available to the analyst along with a general discussion of the range in which they are employed. This discussion is intended only to assist the analyst in establishing an initial signal design for study and does not represent established standards or guidelines.
TYPE OF SIGNAL
Traffic engineering textbooks describe three types of traffic signal controllers: 1. Pretimed Controllers: A preset sequence of phases is displayed in repetitive order. Each phase has a fixed green time and Updated December 1997
a change-and-clearance interval that are repeated in each cycle to produce a constant cycle length. 2. Fully Actuated Controllers: The timing on all of the approaches to an intersection is influenced by vehicle detectors. Each phase is subject to a minimum and a maximum green time, and some phases may be skipped if no demand is detected. The cycle length for fully actuated control will vary from cycle to cycle. 3. Semiactuated Controllers: Some approaches (typically on the minor street) have detectors, and some do not. The earliest form of semiactuated control was designed to confine the green indication to the major street in the absence of minor-street actuation. Once actuated, the minor-street green is displayed for a period just long enough to accommodate the traffic demand. Although these equipment-based definitions have persisted in traffic engineering terminology, the evolution of traffic control technology has complicated their function from the analyst’s perspective. For purposes of capacity and LOS analysis, it is no longer sufficient to consider the controller type as a global descriptor of the intersection operation. Instead, an expanded set of these definitions must be applied individually to each lane group. Each lane group may be served by a phase that is either actuated or nonactuated. Nonactuated phases may be coordinated with
signalized intersections neighboring signals on the same route, or they may function in an isolated mode without influence from other signals. Nonactuated phases generally operate with fixed minimum green times, which may be extended by reassigning unused green time from actuated phases with low demand if such phases exist. Actuated phases, on the other hand, may be used at intersections at which other phases are coordinated, but they may not, for purposes of this appendix, be coordinated themselves. Actuated phases are subject to being shortened on cycles with low demand. On cycles with no demand, they may be skipped entirely or they may be displayed for their minimum duration. In systems where the nonactuated phases are coordinated, the actuated phases are also subject to early termination (force-off) to accommodate the progression design for the system. If all the phases at an intersection are nonactuated, the length of each phase, and consequently the cycle length, will be fixed for purposes of analysis. This is pretimed operation, Type 1 above. In current practice, one or more phases under this type of control will usually be coordinated. In general, if the intersection is sufficiently removed from its neighbors to operate in an isolated mode, actuated operation will produce lower delays and a better level of service. The analysis procedures prescribed earlier in this chapter will indicate the degree to which the delays may be reduced by actuated control on any phase. If all the phases at an intersection are actuated, the length of each phase, and consequently the cycle length, will vary with each cycle. This is Type 2, fully actuated operation. No coordination with neighboring signals is possible under this control mode. Fully actuated signals are generally used only at intersections where distances are such that coordination would not be expected to be beneficial. The analysis procedures prescribed in this chapter will support an evaluation of the comparative benefits of coordinated operation versus actuated operation. Type 3, semiactuated control, includes all of the cases that do not fit into either the pretimed or fully actuated category. The majority of coordinated arterial systems must be treated as systems of semiactuated controllers with coordinated nonactuated phases serving the arterial approaches and isolated actuated phases serving the cross-street approaches. The cross-street approaches include minor movements such as protected left turns from all approaches. The cycle length is constant at coordinated semiactuated intersections and variable at isolated semiactuated intersections. The analysis procedures presented earlier in this chapter are based on the assumption of a fixed sequence of phases, each of which is displayed for a predictable time. In the case of pretimed control (i.e., no actuated phases), the length of each phase is assumed to be fixed and constant from cycle to cycle. Actuated phases must be approximated for analysis purposes by their average green time, recognizing that the actual time may differ from cycle to cycle. For a given timing plan (i.e., constant or average green times), the differences between actuated and nonactuated phases are recognized by the parameters used in the incremental term of the delay equation.
PHASE PLANS
The most critical aspect of any signal design is the selection of an appropriate phase plan, which involves determination of the number of phases to be used and the sequence in which they are implemented. As a general guideline, simple two-phase control
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should be used unless conditions dictate the need for additional phases. Because the change interval between phases contributes to lost time in the cycle, as the number of phases increases, the percentage of the cycle made up of lost time generally increases also. Figure II.9-1 shows a number of common phase plans that may be used with either pretimed or actuated controllers, and Figure II.9-2 illustrates an optional phasing scheme that typically can be implemented only with actuated controllers. These and other phase plans are discussed in the sections that follow. Two-Phase Control
Two-phase control is the most straightforward and the simplest of the available phase plans. Each of two intersecting streets is given a green phase during which all movements on the street are allowed to proceed. All left and right turns are made on a permitted basis against an opposing vehicle or pedestrian flow. The twophase plan is shown in Figure II.9-1(a). This phase plan is generally used unless turn volumes require protected phasing. Multiphase Control
Multiphase control is adopted at any intersection where it is determined that one or more left or right turns require protected phasing. It is generally the left-turn movement that requires a partially or fully protected left-turn phase. Local policy and practice are again critical determinants of this need. Most agencies have guidelines for left-turn volumes that require protected phasing. These threshold volumes are generally in the range of 100 to 200 vph turning left. Protected left-turn phasing is also considered when the speed of opposing traffic is greater than 40 mph. Multiphase control can be provided in a wide variety of ways, depending on the number of turns requiring protected phasing and the sequence and overlaps used. Figure II.9-1(b), (c), and (d) presents three common plans for multiphase control. Figure II.9-1(b) shows a three-phase plan in which an exclusive left-turn phase is provided for both left-turn movements on the major street. It is followed by a through phase for both directions of the major street, during which left turns in both directions may be permitted on an optional basis. The use of permitted left-turn phases following protected leftturn phases is very much a matter of local practice. Some agencies use protected-plus-permitted phasing extensively, whereas others prefer protected-only phase plans. The phasing illustrated in Figure II.9-1(b) can be used in either mode. Exclusive left-turn phases provide for simultaneous movement of opposing left turns and are most efficient when the opposing left-turn volumes are nearly equal. When volumes are unequal, or in cases in which only one left turn requires protected phasing, other phase plans are more efficient. The three-phase plan may be expanded to a four-phase sequence if both streets require left-turn phases. Such a sequence is shown in Figure II.9-1(d). As described previously, left turns may be continued on a permitted basis during the through phases if desired. It should be noted that all approaches having an exclusive leftturn phase should have an exclusive left-turn lane as well. Figure II.9-1(c) shows what is commonly referred to as ‘‘leading and lagging green’’ phasing. The initial phase is a through-plusleft-turn phase for one direction of the major street, followed by Updated December 1997
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urban streets
Figure II.9-1. Phase plans for pretimed and traffic-actuated control.
Figure II.9-2. Dual-ring concurrent phasing scheme with assigned movements. a through phase for both directions of the major street during which left turns in both directions may be permitted on an optional basis. (Note that many operating agencies do not, as a matter of policy, use the optional permitted left turn with this type of phasing because of safety considerations.) The direction of flow started in the first phase is then stopped, providing the opposing direction with a through-plus-left-turn phase. The final phase accommodates all movements on the minor street. Such phasing is extremely flexible. When only one left turn requires a protected phase, a leading green can be provided without a lagging green phase. When left-turn volumes are unequal, the lengths of the leading and lagging green can be adjusted to avoid excessive Updated December 1997
green time for one or both left-turn movements. Leading or lagging green phases, or both, can even be used where no left turn exists as long as turns are permitted to continue during the through phase. The phasing in Figure II.9-1(c) may also be expanded to incorporate leading or lagging green phases on both streets. All the phase plans discussed to this point can be implemented with pretimed or actuated controllers. The only difference in operation would be the manner in which green time is allocated to the various phases: for pretimed controllers, green times are preset, whereas for actuated controllers, green times vary on the basis of detector actuations. At this point, it is necessary to recognize the differences in the
signalized intersections way that modern traffic-actuated controllers actually implement the phase plan. The phase plans shown in Figure II.9-1 are singlering, sequential phase plans in which a single phase is used to indicate the combination of all movements that are proceeding at a given point in time. Modern traffic-actuated controllers do not use this scheme. Instead, they implement dual-ring, concurrent phasing, in which each phase controls only one movement but two phases are generally being displayed concurrently. The dual-ring concurrent concept is illustrated in Figure II.9-2. Note that eight phases are shown, each of which accommodates one of the through or left-turning movements. A barrier separates the north-south phases from the east-west phases. Any phase in the top group (Ring 1) may be displayed with any phase in the bottom group (Ring 2) on the same side of the barrier without introducing any traffic conflicts. For simplicity, the right turns are omitted and assumed to proceed with the through movements. The definition of a phase as presented in Figure II.9-2 is not consistent with that in Figure II.9-1 nor with the definition given in the introduction to this chapter. It is, however, a definition that is universally applied in the traffic control industry. It is the responsibility of the analyst to recognize which definition is applicable to any given situation. For purposes of the capacity and delay analysis procedures presented elsewhere in this chapter, each lane group is considered to be controlled separately by a phase with specified red, green, yellow, and all-red times, so either definition could apply. The examples shown throughout the chapter are based on the single-ring sequential concept. However, the dualring definition must be used for estimating the timing plan at traffic-actuated intersections with the method presented later in this appendix. The dual-ring phases that accommodate left turns will only be used if the left turns are protected. Left turns with compound protection will proceed with their concurrent through movements. For example, none of the left-turn phases would be used by a dualring controller to implement the two-phase plan shown in Figure II.9-1(a). All the other phase plan examples shown in Figure II.91 may be created by selectively omitting left-turn phases and by reversing the order in which the through and left-turn phases are displayed in either ring. The advantage of the dual-ring concept is that it is able to generate the optimal phase plan for each cycle in response to the traffic demand. Pretimed controllers, and earlier versions of trafficactuated controllers, are more constrained in this regard. The maximum flexibility is provided by allowing the first (usually left-turn) phases in Rings 1 and 2 to terminate independently after their respective demands have been satisfied. It is also possible to constrain these phases to terminate simultaneously in emulation of the older, less efficient equipment. For example, simultaneous termination of the northbound and southbound left-turn phases in Figure II.9-2 would produce the phasing example shown in Figure II.9-1(b). Independent termination of the two left turns would introduce an overlap phase between the leftturn phase and the through movement phase in Figure II.9-1(b). The overlap phase would accommodate the heavier of the two left turns together with the concurrent through movement, thereby making more effective use of the green time. The degree of benefit obtained from phase overlaps of this nature depends on the degree of difference in the opposing left-turn volumes. Establishment of a phase plan is the most creative part of signal design and deserves the careful attention of the analyst. A good phase plan can achieve great efficiency in the use of available
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space and time, whereas an inappropriate plan can create great inefficiency. The phase plans presented and discussed in this appendix represent a sampling of the more common forms used. They may be combined in a large number of innovative ways on various approaches to an intersection. Again, local practice is an important determinant in the selection of a phase plan. Also, system considerations should be included when phase plans are established. Phasing throughout an area should generally be relatively uniform; for example, it may confuse drivers if protected-plus-permitted phasing is introduced at one location in an area where left turns are generally handled in exclusive left-turn phases.
ALLOCATION OF GREEN TIME
The allocation of green time is an important input to the methodology presented earlier in this chapter for the estimation of delay. It is necessary to know the average cycle length and effective green time for each lane group to be analyzed. The most desirable way to obtain these values is by field measurement; however, there are many cases when field measurement is not possible. For example, the comparison of hypothetical alternatives precludes field measurements. Even for the evaluation of existing conditions, the required data collection is beyond the resources of many agencies. A procedure for estimating signal timing characteristics is therefore an important traffic analysis tool. Such a procedure is also useful in designing timing plans that will optimize some aspect of the signal operation. In this respect, pretimed and actuated control must be treated differently, because the design and analysis objectives are different. For pretimed control, the objective is to design an implementable timing plan as an end product. In traffic-actuated control, the timing plan is generated by the controller itself on the basis of operating parameters that are established for each phase. This creates two separate objectives for traffic-actuated control. The first is to determine how the controller will respond to a specified combination of operating parameters and traffic conditions. The second is to provide some indication of the optimal values for the key operating parameters.
TIMING PLAN DESIGN FOR PRETIMED CONTROL
The design of an implementable timing plan is a complex and iterative process that is generally carried out with the assistance of computer software. Several popular software products are available for this purpose, some of which employ the methodology of this chapter at least in part. There are, however, several aspects of signal timing design that are beyond the scope of this manual. One such aspect is the choice of the timing strategy itself. Three basic strategies are commonly used for designing timing plans at pretimed signals: 1. Equalize the v/c ratios for critical lane groups: This is the simplest strategy and the only one that may be implemented without excessive iteration. It will be described briefly in the next section of this appendix. It is also employed in the timing plan synthesis procedures of the planning method presented earlier in the chapter and in the sample calculations presented in Section IV. Under this strategy, the green time is allocated among the Updated December 1997
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various signal phases in proportion to the flow ratio of the critical lane group for each phase. 2. Minimize total delay to all vehicles: This strategy is generally proposed as the ‘‘optimal’’ solution to the signal timing problem, often in combination with other measures such as minimization of stops and fuel consumption. Many signal timing models offer this optimization feature. Some use a delay estimation procedure identical to that proposed in this chapter, whereas others employ minor departures. 3. Balance the level of service for all critical lane groups: This strategy promotes a level of service on all approaches that is consistent with the overall intersection level of service. Both of the previous strategies tend to produce a higher delay per vehicle, and therefore a less favorable level of service, for the minor movements at an intersection. This causes some difficulty in representing the overall intersection level of service because of the imbalance in level of service for critical lane groups. The sample calculations presented in Section IV illustrate this phenomenon. This problem is another example of one that can only be solved iteratively. EQUALIZING DEGREE OF SATURATION
Once a phase plan and signal type have been established, the allocation of green time may be estimated: Xi = viC/(sigi) Xc =
o (v/s) i
ci
(9-4)
[C/(C − L)]
(9-5)
Equation 9-5 may be manipulated to solve for the cycle length: C = LXc /[Xc −
o (v/s) ] i
ci
(II.9-1)
Equation 9-4 may be manipulated to solve for the green time for a particular phase, gi: gi = viC/siXi = (v/s)i(C/Xi)
(II.9-2)
where C = cycle length, sec; L = lost time per cycle, sec; Xc = critical v/c ratio for the intersection; Xi = v/c ratio for lane group i (note that the target v/c ratio is a user-specified input with respect to this procedure; the default value suggested in the planning method described in this chapter is 0.90); (v/s)i = flow ratio for lane group i; and gi = effective green time for lane group i, sec. Cycle lengths and green times may be estimated by using these relationships, the flow ratios computed as part of the Capacity Analysis Module, and the desired v/c ratios. For pretimed signals, fixed green times and cycle lengths may be estimated using Equations II.9-1 and II.9-2. The procedure will be illustrated using a sample calculation. Consider the two-phase signals shown below.
The flow ratios are shown, and it is assumed that lost times equal the change-and-clearance interval, which is 4 sec for each phase, or 8 sec/cycle. The cycle length is computed from Equation II.91 for the desired v/c ratio, Xc, which must be selected by the analyst. The shortest cycle length that will avoid oversaturation may be computed using Xc = 1.00. C(minimum) = LXc /[Xc −
o (v/s) ] ci
i
(II.9-3)
C(minimum) = 8 (1.0)/[1.0 − (0.45 + 0.35)] = 8/0.2 = 40 sec This cycle length has no direct value in the design of implementable timing plans; however, it is commonly used as a departure point for iterative procedures that seek to minimize or equalize delay among lane groups. If a v/c ratio of no more than 0.8 were desired, the computation would become C = 8 (0.80)/[0.8 − (0.45 + 0.35)] = 6.4/0 = infinity This computation indicates that a critical v/c ratio of 0.8 cannot be provided for the demand levels existing at the intersection. Any cycle length of greater than 40 sec may be selected. For purposes of illustration, assume a cycle length of 60 sec. In all cases, the cycle length assumed would be rounded to the nearest 5 sec for values between 30 and 90 sec and to the nearest 10 sec for higher values. The actual critical v/c ratio provided by a 60-sec cycle is Xc =
o (v/s) C/(C − L) i
(II.9-4)
i
Xc = (0.45 + 0.35)(60)/(60 − 8) = 0.923 A number of different policies may be employed in allocating the available green time. A common policy for two-phase signals is to allocate the green such that the v/c ratios for critical movements in each phase are equal. Thus, for the example problem, the v/c ratio for each phase would be 0.923, and gi = (v/s)i(C/Xi) g1 = 0.45 (60/0.923) = 29.3 sec g2 = 0.35 (60/0.923) = 22.7 sec Lost time
(II.9-5)
52.0 sec = 8.0 sec 60.0 sec
Another common policy would be to allocate the minimum required green time to the minor approach and assign all remaining green to the major approach. In that case, the v/c ratio for Phase 2 would be 1.0, and g2 = 0.35(60/1.0) = 21.0 sec g1 = 60 − 8 − 21 = 31.0 sec Lost time
52.0 sec = 8.0 sec 60.0 sec
Note that in both cases the entire 60-sec cycle is fully allocated among the green times and the lost time. The procedure for timing may be summarized as follows: 1. Estimate the cycle length for full saturation using Equation II.9-1 and Xc = 1.0. Updated December 1997
signalized intersections 2. Estimate the cycle length for the desired critical v/c ratio, Xc, using Equation II.9-1. 3. From the results of Steps 1 and 2, select an appropriate cycle length for the signal. When system constraints determine the cycle length, Steps 1 and 2 may be eliminated. 4. Estimate the green times using Equation II.9-2 and v/c ratios, Xi, appropriate to the proportioning policy adopted. 5. Check the timing to ensure that the sum of the green times and the lost time equals the cycle length. Include overlapping green times only once in this summation.
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Worksheets are presented in the NCHRP Project 3–48 Final Report (1) to describe each step of the computational process. The primary purpose of these worksheets is to provide a clear and concise description of the computations for software development purposes. The process is highly iterative, and productive application of the manual worksheets is not practical. Only the input data worksheet will be discussed in detail in this appendix. This worksheet, presented as Worksheet 1 in Figure II.9-3, gathers together all data required by the analytical model. Approach-Specific Data
TIMING PLAN ESTIMATION FOR TRAFFIC-ACTUATED CONTROL
A procedure for estimating the timing plan generated by a traffic-actuated controller was developed under NCHRP Project 3-48. This procedure is described fully in the final report for the project (1). In this appendix, the procedure is summarized and examples of its application are presented. The procedure encompasses both a traffic-actuated control model and an analytical structure for implementation of the model. Functional Requirements of Model
A practical traffic-actuated control model must be functionally capable of providing reasonable estimates of the operating characteristics of traffic-actuated controllers under the normal range of design configurations at both isolated and coordinated intersections. It must also be sensitive to common variations in design parameters. Examples of design parameters include 1. Traffic-actuated controller settings (initial interval, allowable gap, maximum green time), 2. Conventional actuated versus volume-density control strategies, 3. Detector configuration (length and setback), 4. Pedestrian timing (Walk signal and flashing Don’t Walk signal), 5. Left-turn treatment (permitted, protected, permitted and protected, not opposed), and 6. Left-turn phase position (leading or lagging).
Data Requirements
The information that is already required by the procedure in this chapter is used to the extent possible to avoid the need for new data. Most of the additional data items relate to the operation of the controller itself. The model structure is based on the standard eight-phase dual-ring control scheme illustrated in Figure II.9-2. This scheme is more or less universally applied in the United States. From a capacity and LOS point of view, less complex phasing concepts (including simple two-phase operation) may generally be represented adequately as a subset of the dual-ring scheme. For the purposes of this discussion, the scheme for assignment of movements to phases presented in Figure II.9-2 will be adopted. This will greatly simplify the illustration of all modeling procedures without affecting the generality of the results.
The top portion of Worksheet 1 summarizes the approach-specific information. A separate column is used for each of the four approaches. The required items are discussed in the following sections. Left-Turn Treatment Codes. The logic of the proposed model requires that the left-turn treatment be identified explicitly. The codes used here are consistent with the definitions presented elsewhere in this chapter: 0 = does not exist, 1 = permitted, 2 = simple protection, 3 = compound protection, and 4 = not opposed. The term ‘‘simple left-turn protection’’ will refer to treatment code 2, in which the left turn moves only on the protected phase. The term ‘‘compound left-turn protection’’ will be used to denote either protected-plus-permitted or permitted-plus-protected treatment. Position Codes. Position codes are required to distinguish between leading and lagging left-turn protection. The terms ‘‘leading’’ and ‘‘lagging’’ apply equally to the cases of simple and compound left-turn protection. These terms do not apply if the left turn is not protected. The worksheet offers a simple choice of ‘‘Lead’’, ‘‘Lag,’’ or ‘‘N/A.’’ The definition is simple: leading left turns precede the movement of the opposing through traffic, and lagging left turns follow it. Sneakers. This term describes the number of left turns per cycle that may be dismissed at the end of a permitted phase. An implicit default of two per cycle is built into the supplemental permitted left-turn worksheets for purposes of determining the minimum saturation flow rate. Since any vehicles that rest in the detection zone will extend their respective phases, a more detailed treatment of sneakers will be required for traffic-actuated control. Free Queue. The current pretimed model assumes that the first permitted left turn at the stop line will block a shared lane. However, through vehicles in the shared lane are often able to squeeze around one or more left-turning vehicles that constitute the free queue. The lack of a free queue parameter is a definite deficiency of the pretimed model, but it is especially critical with trafficactuated control, because vehicles in the free queue do not occupy the detector and therefore do not extend the green phase. A permitted left turn stopped on the detector must be treated entirely differently in the modeling process than one that is stopped beyond the detector. Approach Speed. The speed of vehicles on a signalized intersection approach (SP) is not important to the current methodology Updated December 1997
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Figure II.9-3. Worksheet 1: traffic-actuated control input data.
in this chapter. It is, however, required in the analysis of trafficactuated operation. This speed determines the passage time between the detector and the stop line as well as the portion of intervehicle headways during which a presence detector is occupied. It is a common custom in modeling the operation of vehicles at a traffic signal to assume a single value for speed that applies throughout the cycle. Termination of Rings 1 and 2. The nature of dual-ring control requires that the second phases of Rings 1 and 2 terminate simultaneously because they yield control to approaches with conflicting traffic. However, control may pass from the first phase to the second phase of either ring without causing conflict. Independent termination of the first phases improves efficiency in the allocation of time among competing movements and is generally exploited Updated December 1997
for this reason. The type of operation created by independent termination is sometimes referred to as ‘‘phase overlap.’’ It is, however, not essential that the phases terminate independently. Older single-ring controller operation may be approximated by requiring that the first phases of each ring (i.e., Phases 1 and 5 or 3 and 7) terminate simultaneously. In some situations involving coordination of controllers on arterial routes, it is common to force both rings out of their first phase simultaneously. The model to be developed must consider simultaneous or independent termination as legitimate alternatives. It is possible that one or more of the first phases will not be used because their associated left turns are not protected. In this case, the question of simultaneous or independent termination will not apply. This is another multiple-choice entry on the worksheet. The alternatives are ‘‘Simultaneous,’’ ‘‘Independent,’’ and ‘‘N/A.’’
signalized intersections Phasing and Detector Design Parameters
The bottom portion of the worksheet includes all the data items that are specific to each of the eight phases represented in Figure II.9-2. A separate column is provided on the worksheet for each phase. The first group of data items includes the design parameters relating to phasing and detector placement that will affect operation. These data items are discussed in the following sections. Phase Type. Phase type is the first of several phase-specific inputs that are required. A phase that is not active will not be recognized in any subsequent computations. Inactive phases are indicated by an X in the appropriate column of the worksheet. A left-turn phase will be considered active only if it accommodates a protected left turn. A through phase will be considered active if it accommodates any traffic at all, whether through, left, or right. Active phases will be designated as follows: L = phase accommodates a protected left turn on a green arrow; T = phase accommodates through and right-turning traffic only; in this case, all left turns are accommodated entirely on another phase (i.e., simple left-turn protection); G = any left turns accommodated on this phase are opposed by oncoming traffic (phases with permitted left turns and those with compound left-turn protection); and N = phase accommodates, in addition to other movements, left turns that are not opposed at any time in the phase sequence (T intersections, one-way streets, and cases in which the phasing completely separates all movements on opposing approaches). Note that right turns are not referenced specifically in these designations. Right turns are assumed to proceed concurrently with through traffic. Phase Reversal. Normally the first (odd-numbered) phase in each ring on each side of the barrier handles protected left turns and the second (even-numbered) phase handles the remaining traffic. This creates a condition of leading left-turn protection. When lagging left-turn protection is desired, the movements in the first and second phases are interchanged. Most controllers provide an internal function to specify phase reversal. For the purposes of this discussion, two phases may be swapped only if both phases are active. Detector Length. Detector length (DL) is the effective distance, measured parallel to the direction of travel, through which a vehicle will occupy the detector. It is a user-specified design parameter influenced by local practice. The detector length influences the choice of other parameters, such as the allowable gap in traffic that will terminate the phase. Detector Setback. Detector setback (DS) is the space between the downstream edge of the detector and the stop line. Controller Settings
The controller itself has several operating parameters that must be specified for each phase. Collectively, these will be referred to as the ‘‘controller settings’’ because they must be physically set in the controller with switches, keypads, or some other electrical means. The following settings will exert a significant influence on the operation of the intersection and must therefore be recognized by the analysis methodology.
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Maximum Initial Interval. Used only when the initial interval is extended under volume-density control, the maximum initial interval (MxI) must be long enough to ensure that a queue of vehicles released at the beginning of green will be in motion at the detector before the green terminates. Added Initial per Actuation. Used only when the initial interval is extended under volume density control, this value (AI) will depend on the number of approach lanes. It should be long enough to ensure that each vehicle crossing the approach detector on the red will add an appropriate increment of time to the initial interval. Minimum Allowable Gap. The minimum allowable gap (MnA) is a user-specified controller parameter, the effect of which will be illustrated later as the analytical model is exercised. It is typically set in the range of 2 to 3 sec and establishes the threshold for the gap length in traffic that will cause the phase to terminate. The value of MnA is usually influenced to some extent by local practice. It is important to distinguish between the time gap and the time headway between vehicles. The time headway indicates the elapsed time between the successive arrival of two consecutive vehicles at a detector. The time gap indicates the elapsed time between the departure of the first vehicle from the detector and the arrival of the second. The time gap is what is left of the headway after the detector occupancy time has been subtracted. A traffic-actuated controller using presence detectors views the passage of traffic in terms of gaps, not headways. Gap Reduction Rate. The gap reduction rate (GR) determines the rate at which the allowable gap is reduced in volume-density controllers as the green display continues. There are subtle differences in the definition of the gap reduction rate among controllers. For the purposes of this procedure, a linear reduction rate (seconds of reduction of gap per second of elapsed green time) will be assumed. Pedestrian Walk plus Don’t Walk Interval. This parameter (WDW) is the minimum time given to each phase when pedestrian demand is registered or pedestrian recall is active. It includes both the pedestrian Walk and flashing Don’t Walk intervals. These are actually entered into the controller as two separate parameters but will be combined for the purposes of this procedure. If the pedestrian timing function is not implemented in a particular phase, the WDW value should be entered as zero. Maximum Green. Maximum green (MxG) is a user-specified parameter the effect of which will be discussed later. Local practice often plays an important part in the determination of maximum green times. Intergreen Time. Another user-specified controller parameter determined in accordance with local practice, the intergreen time (I) consists of a yellow change interval followed by an all-red clearance interval. These two intervals are entered separately into the controller but will be combined here to simplify the analysis. Recall Mode. The recall mode determines how a phase will be treated in the absence of demand on the previous red phase. The options are as follows: None = the phase will not be displayed, Max = the phase will be displayed to its specified maximum length, Updated December 1997
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Min = the phase will always be displayed to its specified minimum length but may be extended up to its specified maximum length by vehicle actuations, Ped = the phase will be given the full Walk plus flashing Don’t Walk interval and may be extended further, up to its specified maximum, by vehicle actuations, and Coord = a coordinated phase on the arterial street; this phase will always be displayed for its nominal design time, which may be increased by reassigning unused green time from actuated phases. The recall mode function will have a significant effect on the operation of the controller. For example, the maximum recall option will have the effect of creating a nonactuated phase. Minimum Phase Time for Vehicles. The minimum vehicle phase time (MnV) is actually a traffic engineering input that specifies the minimum time during which a phase must be displayed unless it is skipped because of lack of demand. It is implemented in a conventional traffic-actuated controller as the sum of three intervals: the initial interval; the minimum allowable gap (MnA), and the intergreen time (I). As a matter of design, it is important that the controller settings be compatible with the minimum phase times determined by traffic engineering considerations. This parameter did not appear earlier in the chapter because the procedure described does not offer the ability to compute timing plans. However, it is impossible to deal realistically with trafficactuated control without recognition of the existence of a minimum phase time. For compatibility with other signal timing programs, the phase times include all intervals, including green, yellow, and all-red. For the purposes of the worksheet, the minimum phase time must be replaced by the maximum phase time (MxG + I) if the ‘‘recall to maximum’’ mode is in effect.
earlier in this appendix. Under this approach, the green time requirement is determined by the slope of the line representing a target v/c of 0.9. If the phase ends when the queue has dissipated under these conditions, the target v/c will be achieved. The second method recognizes the way in which a traffic-actuated controller actually works. It does not deal explicitly with v/c ratios; in fact, it has no way of determining the v/c ratio. Instead it terminates each phase when a gap of a particular length is encountered at the detector. Good practice dictates that the gap threshold must be longer than the gap that would be encountered while the queue is being served. Assuming that gaps large enough to terminate the phase can only occur after the queue service interval (based on v/c = 1.0), the average green time may be estimated as the sum of the queue service time and the green extension time as shown in Figure II.9-4. Each of these components will be discussed separately. Queue Service Time
The queue service time, gs, can be estimated as q rr (s − qg)
gs = f q
(II.9-6)
where qr, qg = red arrival rate and green arrival rate, respectively, veh/ sec; r = effective red time, sec; s = saturation flow rate, veh/sec; and fq = 1.08 − 0.1 (actual green time/maximum green time)2. (II.9-7) The queue calibration factor, fq, was described by Akc¸elik (2) as a factor required to account for randomness in arrivals in determining the average queue service time.
Green Time Estimation Model
Green Extension Time
The discussion of pretimed operation presented earlier in this appendix indicated that the determination of required green time is a relatively straightforward process when the cycle length is given. However, traffic-actuated controllers do not recognize specified cycle lengths. Instead, they determine, by a mechanical analogy, the required green time given the length of the previous red period and the arrival rate. This is accomplished by holding the right-of-way until the accumulated queue has been served. The basic principle underlying all signal timing analysis is the queue accumulation polygon (QAP), which plots the number of vehicles queued at the stop line during the cycle. The QAP for a simple protected movement is illustrated in Figure II.9-4. The queue accumulation and discharge are represented in this very simple case as a triangle. The accumulation takes place on the left side of the triangle (i.e., the effective red) and the discharge takes place on the right side of the triangle (i.e., the effective green). More complex polygons are generated when permitted movements occur and when a movement proceeds on more than one phase. An extensive discussion of this subject may be found earlier in this chapter. Two methods of determining the required green time given the length of the previous red are illustrated in Figure II.9-4. The first employs a ‘‘target v/c’’ approach. This method is the basis for the planning method described earlier in the chapter and for the discussion on timing plan design for pretimed control presented
To estimate the extension time analytically for a particular phase, it is necessary to determine the expected waiting time for a gap of a specific length given the average intervehicular headways and some assumptions about the headway distribution. An analytical model for this purpose was described by Akc¸elik (2,3). This model made use of earlier work by Lin (4,5). The average green extension time, ge, is estimated from the following formula, which is based on the use of a bunched exponential distribution of arrival headways:
Updated December 1997
el(e +t −D) 1 − wq l 0
ge =
0
(II.9-8)
where e0 = unit extension time setting, MnA on Worksheet 1; t0 = time during which the detector is occupied by a passing vehicle; t0 = (Ld + Lv)/v
(II.9-9)
Lv = vehicle length, assumed for the purposes of this discussion to be 18 ft; Ld = detector length, DL on Worksheet 1; v = vehicle approach speed, SP on Worksheet 1; D = minimum arrival (intrabunch) headway, sec; w = proportion of free (unbunched) vehicles; and l = parameter calculated as
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Figure II.9-4. Queue accumulation polygon illustrating two methods of green time computation.
l=
wq 1 − Dq
(II.9-10)
where q is the total arrival flow in vehicles per second for all lane groups that actuate the phase under consideration. The bunched exponential distribution of arrival headways was originally proposed by Cowan (6). A detailed discussion of this model and the results of its calibration using real-life data for single-lane traffic streams and simulation data for multilane streams are given by Akc¸elik and Chung (7). The following relationship can be used for estimating the proportion of free (unbunched) vehicles in the traffic stream (w): w = e−bDq
(II.9-11)
where b is a bunching factor. The recommended parameter values based on the calibration of the bunched exponential model using real-life and simulation data are as follows: Single-lane case: D = 1.5
b = 0.6
(II.9-12a)
Multilane case (number of lanes = 2): D = 0.5
b = 0.5
(II.9-12b)
Multilane case (number of lanes > 2): D = 0.5
b = 0.8
phases. Thus, a circular dependency is established whose solution requires an iterative process. With each iteration, the green time required by each phase, given all the green times required by the other phases, may be determined. The logical starting point for the iterative process is the minimum times specified for each phase. If these times turn out to be adequate for all phases, the cycle length will simply be the sum of the minimum phase times for the critical phases. If a particular phase demands more than its minimum time, more time must be given to that phase. Thus, a longer red time must be imposed on all the other phases. This in turn will increase the green time required for the subject phase.
(II.9-12c)
Simple Two-Phase Example
The circular dependency will converge quite reliably through a series of repeated iterations. The convergence may be demonstrated easily using a trivial example. More complex examples will be introduced later to examine the effects of controller settings and traffic volumes in a practical situation. Consider an intersection of two streets with a single lane in each direction. Each approach has identical characteristics and carries 675 vehicles per hour with no left or right turns. The average headway is 2.0 sec/veh and the lost time per phase is 3.0 sec. Detectors are 30 ft long with no setback from the stop line. The actuated controller settings are as follows:
Computational Structure for Green Time Estimation
This green time estimation model is not difficult to implement, but it does not lead directly to the determination of an average cycle length or green time, because the green time required for each phase is dependent on the green time required by the other
Setting Initial interval Unit extension Maximum green Intergreen
Time (sec) 10 3 46 4 Updated December 1997
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The maximum time for each phase will be (46 + 4) = 50 sec. The minimum phase time will be 10 + 3 + 4 = 17 sec, which will be the starting point for the timing computations. So the first iteration will use a 34-sec cycle with 17 sec of green time on each approach. Allowing for lost time, the effective red time will be 20 sec, and the effective green time will be 14 sec for each phase. The total lost time is the sum of two components, including the startup lost time and the clearance lost time. In this chapter’s procedure for estimation of capacity and delay, all the lost time is assumed to be concentrated at the beginning of the green. This is a valid approximation for delay estimation because the lost time is used only in the computation of effective green time, and its position in the phase is irrelevant. However, for traffic-actuated timing estimation, the distribution of lost time throughout the phase will have a definite influence on the results. The lost time at the beginning of the phase will influence the length of the phase. The lost time at the end of the phase will influence the delay, but it will have no effect on the phase duration. It is recommended by Courage et al. (1) that for a specified lost time of n sec, 1 sec be assigned to the end of the phase and n − 1 sec be assigned to the beginning. Thus, for this example the startup lost time (l1) will be 2.0 sec. The computational process may be described as follows: 1. Compute the arrival throughout the cycle, q: q = 675/3,600 = 0.1875 veh/sec 2. Compute the net departure rate (saturation flow rate minus arrival rate): (s − q) = 0.5 − 0.1875 = 0.3125 veh/sec 3. Compute the queue at the end of 20 sec of effective red time: (qrr) = 20 ∗ 0.1875 = 3.75 veh 4. Compute the queue calibration factor fq from Equation II.9-7: fq = 1.08 − 0.1 (13/46)2 = 1.07 5. Compute the time required to serve the queue, gs: gs = 1.07 (3.75/0.3125) = 12.86 sec Thus, after 12.86 sec of effective green time, the queue will have been served and gaps will start to be observed at the detector. The startup lost time (l1 = 2) must be added to the queue service time for purposes of determining the total phase time requirement. The question now is how long one would expect to wait for a gap of 3.0 sec. 6. Determine the parameters of Equation II.9-8 as follows. D = 1.5 b = 0.6 from Equation II.9-12a w = e−bDq = e−(0.6×1.5×0.1875) = 0.84 wq l= 1 − Dq = (0.84 × 0.1875)/[1 − (1.5 × 0.1875)] = 0.222
el(e + t −D) 1 − wq l 0
ge =
0
= [e 0.222(3.0+1.09−1.5)/(0.84 × 0.1875)] − (1/0.222) = 6.63 sec 9. Compute the total phase time: G = l 1 + gs + ge + Y = 2 + 12.86 + 6.63 + 4 = 25.49 10. Compute the phase time deficiency as the difference between the trial phase time and the computed phase time, or 25.49 − 17.0 = 8.49 sec. This computation indicates that the trial phase time was not adequate to satisfy the rules under which the controller operates. It also suggests a new trial green time of 25.49 sec and a cycle length of 50.98 sec for the next iteration. The next iteration will still produce a green time deficiency, because the red time has been increased. However, this deficiency will be smaller. Successive iterations will produce successively smaller green time deficiencies until eventually the solution will converge. This process is illustrated in Figure II.9-5. The solution converged (i.e., the green time deficiency became negligible) at a phase time of 37.5 sec, producing a cycle length of 75 sec. This was based on a threshold of 0.1 sec difference in the computed cycle length between iterations. In other words, the process terminated when the cycle lengths on two successive iterations fell within 0.1 sec of each other. As a matter of interest, consider the effect of reducing the unit extension time, e0, from 3.0 to 2.0 sec. This would be expected to reduce the green extension time, ge for both phases and to shorten the resulting cycle length. The extent of the reduction may be estimated by repeating all of the steps described above with the new value for ge. In the first iteration, the queue service time will remain the same, but the green extension time will be reduced from the value of 6.63 sec computed above to 4.42 sec. Repeated iterations with this lower unit extension time would converge to a cycle length of 65.3 sec. In this example, the green time for both phases was determined by the sum of the queue service time and the extension time. Phase times will also be constrained by their specified maximum and minimum times. If the maximum phase times had been set at a value less than the 38 sec computed above, the iterative procedure would have terminated before the computed times were reached. Minimum Phase Times
7. Determine the occupancy time of the detector for a vehicle length of 18 ft, a detector length of 30 ft, and an approach speed of 30 mph:
The whole question of minimum phase time requires more attention. The specified minimum green time constraints are valid only for pretimed phases and phases that are set to recall to the minimum time regardless of demand. The real significance of the minimum phase time for an actuated phase is that the phase must be displayed for its specified minimum time unless it is skipped because of lack of demand. This situation may be addressed analytically by determining the probability of zero arrivals on the previous cycle. Assuming a Poisson arrival distribution, this may be computed as
t0 = (30 + 18)/(1.47 × 30) = 1.09 sec
P0v = e−qC
8. Apply Equation II.9-8 to determine the expected green extension time, ge:
where q is the vehicle arrival rate in vehicles per second and C is the cycle length for the current iteration.
Updated December 1997
(II.9-13)
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Figure II.9-5. Convergence of green time computation by elimination of green time deficiency. Thus, assuming that the phase will be displayed for the minimum time except when no vehicles have arrived, the adjusted minimum phase time becomes AVM = MnV(1 − P0v)
(II.9-14)
where AVM is the adjusted vehicle minimum time and MnV is the specified minimum green time from the worksheet in Figure II.93. This relationship also has circular dependencies because, as the adjusted minimums become shorter, the probability of zero arrivals also becomes higher, which further reduces the adjusted minimums. Fortunately, the solution fits well into the iterative scheme just described. The use of adjusted minimum green times offers a practical method for dealing with phases that are not displayed on each cycle but whose minimum durations may be determined by agency policy. The concept applies equally to pedestrian minimum times. Multiphase Operation
Three important concepts have been introduced for estimating the timing plan at traffic-actuated signals: (a) a model for predicting the green time for any phase given the length of the previous red period, (b) an iterative computational structure that converges to a stable value for the average cycle length and green time, and (c) a procedure to account for minimum green times with low volumes. These concepts were illustrated in a trivial example, but fortunately they are robust enough to deal with the practical complexities of traffic-actuated control. These complexities include multiphase operation (both single- and dual-ring), permitted left
turns (from both exclusive and shared lanes), and compound leftturn protection (both leading and lagging). Two extensions to the methodology presented to this point are required to deal with more complex situations. The first is the extension of the QAP from its simple triangular shape to a more complex shape that represents different arrival and departure times at different points in the cycle. The second is a procedure to synthesize a complete single-ring equivalent sequence by combining critical phases in the dual-ring operation. The QAP extensions will be considered first. Figure II.9-4 presents the familiar triangular QAP for a protected movement from an exclusive lane. There are four other cases to be considered, including (a) permitted left turns from an exclusive lane, (b) permitted left turns from a shared lane, (c) protected-pluspermitted left turns, and (d) permitted-plus-protected left turns. The QAP shapes for each of these cases are illustrated in Figures II.96 through II.9-9, all of which conform to a common terminology with respect to labeling. Intervals are illustrated along the horizontal axis as follows: r = effective red time, gq = portion of the permitted green time blocked by a queue of opposing vehicles, gu = portion of the permitted green time not blocked by a queue of opposing vehicles, gs = portion of the protected green time required to serve the queue of vehicles that accumulated on the previous phases, ge = extension to the protected green time that occurs while the controller waits for a gap in the arriving traffic long enough to terminate the phase, and Updated December 1997
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Figure II.9-6. Queue accumulation polygon for permitted left turn from exclusive lane.
Figure II.9-7. Queue accumulation polygon for permitted left turn from shared lane.
gf = portion of the green time in which a through vehicle in a shared lane would not be blocked by a left-turning vehicle waiting for the opposing movement to clear (this condition occurs only at the beginning of the permitted green when one or more through vehicles are at the front of the queue). Note that in each case the phases are arranged so that the protected phase is the last to occur. The length of this phase will be determined by its detector actuations. The actual length will be the sum of the time required to serve the queue that exists at the beginning of the phase plus the extension time. Points in the cycle at which the queue size is important to the computations are also identified as follows: Qr = queue size at the end of the effective red; Updated December 1997
Qq = queue size at the end of the interval gq; Qp = queue size at the end of the permitted green period; Qp′ = queue size at the end of the permitted green period, adjusted for sneakers; Qga = queue size at the beginning of the protected green (green arrow) period; and Qf = queue size at the end of the interval gf. The shape of each of the QAPs is based on termination by a gap that exceeds the unit extension, allowing the full extension time, ge, to be displayed. When a phase terminates on the maximum green time, the extension time may be reduced or eliminated. If a permitted left-turn phase terminates before the queue has been served, a maximum of two sneakers will be dismissed from the queue at that point.
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Figure II.9-8. Queue accumulation polygon for protected-plus-permitted left-turn phasing with exclusive left-turn lane.
Figure II.9-9. Queue accumulation polygon for permitted-plus-protected left-turn phasing with exclusive left-turn lane. These extensions to the QAP analysis will accommodate all of the practical conditions covered by the procedures presented earlier in this chapter. The remaining issue to be dealt with is the synthesis of the complete cycle by combining critical phases in a dual-ring operation. This procedure may be carried out using Worksheet 2 (Figure II.9-10). The structure of this worksheet is compatible with the dual-ring concurrent phasing illustrated in Figure II.9-2. The east-west movements (left side of the barrier) are shown in the first three columns. The first column, labeled A, represents the first phase in each ring (1 or 5). The second, or B, column represents the second phase (2 or 6). The third column will contain the total of the phase times for the movements in the first two columns. The same format is repeated in the second
three columns for the north-south movements (right side of the barrier). There are three rows for each of the two rings. The first row indicates whether the phase pair is swapped. This information was entered on Worksheet 1 in this appendix. The next two rows give the movements and phase times for their respective phases. If the phases are not swapped, the assignments will be as shown in the dual-ring configuration of Figure II.9-2. If they are swapped, the movements and times for the phase pair will be reversed. When a phase pair is reversed, the through movements will appear in Column A and the left turns in Column B. Note that the movements in a given phase pair cannot be swapped if the left turn is not protected. The order of the phases in the pair does not affect the total phase time entered in the last column. Updated December 1997
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Figure II.9-10. Worksheet 2: traffic-actuated timing computations.
The seventh row contains the absolute value of the phase time difference between the two rings. Values are entered in each of the six columns. The components of the cycle time must now be determined and entered in the Cycle Time Components row. The procedure will depend on whether the first phase termination is simultaneous or independent. For simultaneous termination, the maximum value of each phase is entered in the A and B columns (Ring 1 or 2, whichever time is greater). For independent termination, the maximum value of the total time (A + B) from Ring 1 or 2 is entered. For each side of the barrier, either the A and B columns or the Total column will have an entry, but not all three columns. This procedure should be carried out for both sides of the barrier. It should be recalled that the termination treatment may be different on either side. The cycle length may now be determined as the sum of all the entries in the Cycle Time Components row. If the computed cycle length agrees with the cycle length determined on the previous iteration, no further action will be necessary. If it does not, this timing plan will serve as the starting point for the next iteration. COORDINATED SEMIACTUATED OPERATION
It has been pointed out that nonactuated phases under semiactuated control may be coordinated with those in neighboring intersections. In the most common coordination scheme, a background cycle length is imposed. The actuated phases receive their allotment of green time in the usual manner, except that their maximum green times are controlled externally to ensure conformance with the specified cycle length. If the actuated phases require all of their nominal green time allotment, the intersection operates in a more or less pretimed manner. If not, the unused time is reassigned to the coordinated phase. The computational structure developed under NCHRP Project 3-48 is able to approximate this operation quite effectively. The analysis of coordinated operation requires another iterative loop, which executes the procedure described in this appendix, adding Updated December 1997
more green time incrementally to the coordinated phases until the design cycle length has been reached. The result is a timing plan that approximates the operation of the controller in the field. The procedure for timing plan estimation in coordinated systems requires that a design timing plan be established first, with phase splits that add up to the design cycle length. This becomes the starting point for the iterative procedure that involves the following steps: 1. Set up the controller timing parameters for the initial timing plan computations. The coordinated arterial phases (usually 2 and 6) should be set for recall to maximum. The maximum green times for all phases should be determined by their respective splits in the pretimed timing plan. No recall modes should be specified for any of the actuated phases. 2. Perform the timing computations to determine the resulting cycle length. If the maximum green times have been specified correctly in Step 1, the computed cycle length will not exceed the specified cycle length. 3. If the computed cycle length is equal to the specified cycle length, no green time is available for reassignment. In this case the procedure will be complete and the final timing plan will be produced. 4. If the computed cycle length is lower than the specified cycle length, some time should be reassigned to the arterial phases. This is accomplished by increasing the maximum green times for the coordinated phases. The recommended procedure is to assign onehalf of the difference between the computed cycle and the specified cycle to the coordinated phases. This provides a reasonable speed of convergence without overshooting the specified cycle length. 5. Repeat Steps 2 through 4 iteratively until the computed and specified cycle lengths converge. The results of these computations will be illustrated in the following example problem. A MULTI-PHASE EXAMPLE
The complete timing estimation procedure described in this appendix will now be illustrated using the multiphase example pre-
signalized intersections sented as Sample Calculation 3 earlier in this chapter. In the discussion of this example presented previously, observed green times were first used. The green times were then modified by trial and error to arrive at a final design for analysis of capacity, delay, and level of service. The intersection layout for this example is shown in Figure 953. Note that all left turns take place from exclusive lanes. The northbound and southbound left turns have protected-plus-permitted phasing. The eastbound and westbound left turns are permitted, with no protected phases. The final timing plan design was as follows: Phase I: NB and SB left, Phase 2: NB and SB green, Phase 3: EB and WB green, Cycle length,
12.4 sec 49.9 sec 27.7 sec 90 sec
This timing plan was shown to accommodate all movements with no excessive delay. The average delay per vehicle for all approaches was 37.0 sec. The timing estimation methodology for this example will now be exercised using several different values for some of the actuated controller settings to observe their effect on the results. The detector configuration will use loop detectors 30 ft long and positioned at the stop line with no setback. A 30-mph design speed will be assumed for all approaches. Both isolated and coordinated operation will be explored. Different values will be used for the unit extension and maximum green settings. Three different sets of unit extension settings will be used: T Short values of 1.5 sec and 2.0 sec for two-lane approaches and one-lane approaches, respectively. This represents a condition sometimes referred to as ‘‘snappy’’ operation. T Medium values of 2.5 sec and 3.5 sec for two-lane approaches and one-lane approaches, respectively. This will be the standard condition for most scenarios. T Long values of 3.5 sec and 4.5 sec for two-lane approaches and one-lane approaches, respectively. This represents a condition sometimes referred to as ‘‘sluggish’’ operation. These values represent the actual gap between vehicles that will cause a phase to terminate. With the assumed approach speed and detector configuration, each vehicle (assumed length, 18 ft) passing over the loop will occupy the detector for an additional 1.09 sec. Three different values for maximum green times will also be investigated. The first will use very long maximum times (120 sec for each phase) to determine how the intersection would operate if most phases terminated on the unit extension. The second will use maximum times that are proportional to the design times for each phase. Kell and Fullerton (8) proposed that the maximum extensions be set at 125 to 150 percent of the design green times. Lin (9) proposed a more complex scheme that resulted in maximum times in the range of 150 to 200 percent of the design times. For purposes of this exercise, the maximum times will be set at approximately 150 percent of the design times, representing a value somewhere in the middle of the range suggested in the literature. The third will use the actual design green times as maximums to constrain the operation to its original design. In recognition of the fact that much of the benefit of trafficactuated control is derived from the ability of the controller to respond to fluctuations in traffic volumes throughout the day, the operation will also be examined at volume levels of 70 percent of the peak-hour levels reflected in the original data. Coordinated
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operation will also be examined at the reduced volume levels to observe the reassignment of unused green time from the actuated phases to the nonactuated phases to reduce the delay to arterial traffic. The first set of conditions to be analyzed involves 100 percent volume levels, 120 sec maximum green time on each phase, and short unit extensions. The input data worksheet for this example is shown in Figure II.9-11. The resulting cycle length is 238.2 sec. Because of the dual-ring operation, an overlap phase appeared for the north-south approaches in the results. The estimated average phase times were as follows: NB and SB left, SB through and left, NB and SB green, EB and WB green, Cycle length,
17.2 15.0 124.0 82.0 238.2
sec sec sec sec sec
This timing plan, when analyzed by the procedure described earlier in this chapter, produced the results shown on the LOS worksheet in Figure II.9-12. Note that the average delay per vehicle was 69.7 sec. This is considerably higher than the 37.0-sec/veh delay associated with the timing plan developed in Sample Calculation 3. The logical conclusion here is that the peak-hour volumes could not be handled in an optimal manner by a fully actuated controller without some influence being exerted on the timing plan through maximum green constraints. A total of 10 alternatives similar in concept to the one just described were analyzed using combinations of these conditions. For each analysis, the average phase times and cycle length were recorded, along with the average delay per vehicle and any movements that were oversaturated. The results are summarized in Table II.9-1. In the first three alternatives, only the unit extensions (short, medium, and long) were changed. Note that the cycle length increased with the unit extensions from 238.2 sec (short) to 250.9 sec (long). In all cases, the northbound green phase reached its maximum of 124 sec (i.e., 120 sec green plus 4 sec intergreen). Because the northbound phase was already at its maximum length, it lost time proportionally as the other phases increased and therefore became more oversaturated. It is clearly essential that some maximum green times be imposed to control the apportionment of time between the competing phases. The next two analyses used the medium extension times and evaluated both of the strategies for setting the maximum green intervals in proportion to their design values. This reduced the average delay to 41.4 sec per vehicle for the 150 percent strategy and 37.1 sec per vehicle for the 100 percent strategy. The 150 percent strategy produced slightly oversaturated conditions for the southbound approach. Note that the results of the 100 percent strategy were similar to the results reported in the discussion of the design timing plan for Sample Calculation 3. The interpretation here is that when traffic volumes are close to capacity, as they are in this example, maximum green times must be used to apportion the time among the competing phases. The gap termination tactic does not ensure a satisfactory distribution of green times. One of the major benefits of traffic-actuated control is its ability to respond to short-term and daily fluctuations in traffic volumes. To illustrate this principle, the volumes were reduced across the board to 70 percent of their peak values. The analysis using 120-sec maximum green times on all phases was repeated with the three levels of unit extension. The results indicate that Updated December 1997
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Figure II.9-11. Traffic-actuated control data for multiphase example.
Figure II.9-12. LOS results for multiphase example.
the cycle length varied from 62.3 to 76.6 sec throughout the full range of unit extension settings. The average delays were almost identical for these three cases, varying from 16 to 18 sec/veh. This indicates that when traffic volumes drop below their saturation levels, it is no longer necessary to control the distribution of green times using the maximum green settings. An important observation here is that the same controller settings Updated December 1997
would have been able to control both the full- and reducedvolume settings effectively provided that the maximum greens were optimized for the high-volume conditions. The final two cases deal with coordinated operation. Each of the intersecting routes was assumed to be coordinated in separate cases. The design timing plan, based on a 95-sec cycle, was used to establish nominal splits for the coordinated operation. The me-
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Table II.9-1. Comparison of Traffic-Actuated Controller Settings for Multiphase Example estimated phase times (sec) volume level
100 percent
maximum green times (sec) Set to 120 sec for all phases to eliminate maximum green constraints
100 percent
Set to 150 percent of design splits indicated in Chapter 9 example
100 percent
Set to 100 percent of design splits indicated in Chapter 9 example
70 percent
Set to 120 sec for all phases to eliminate maximum green constraints
70 percent
Set to 150 percent of design splits indicated in Chapter 9 example (no overlap phase)
nsg
ewg
average delay cycle (sec/veh)
Short 17.2 15.0
124.0
82.0
238.2
69.7
NB-TH v/c = 1.035
Med.
19.2 16.3
124.0
85.3
244.8
76.0
NB-TH v/c = 1.064
Long
20.8 17.4
124.0
88.7
250.9
81.8
NB-TH v/c = 1.091
Med.
13.4
79.0
43.0
137.0
41.4
SB-LT v/c = 1.072 Similar to Sample Calculation 3 results presented earlier in chapter (different extensions) NB-TH v/c = 1.022
gap (sec)
nsl
sbt +l
1.6
Med.
12.4
—
49.9
27.7
90.0
37.1
Short
6.8
1.8
31.7
22.0
62.3
16.0
Med.
7.5
2.1
35.4
22.0
67.0
16.5
Long
8.4
2.4
41.7
24.1
76.6
18.0
comments
Med.
10.3 —
60.0
25.2
95.5
16.3
North-south arterial phases coordinated
Med.
12.4 —
45.4
36.0
93.8
23.4
East-west arterial phases coordinated
dium unit extensions were used in combination with maximum green times that reflected 150 percent of the design timing plan. Because the design timing plan included no overlap, the input data values were adjusted to require simultaneous termination of the first (i.e., left-turn) phases that accommodate the northbound and southbound traffic as opposed to independent termination. The results indicate that the cycle length established by the iterative computations fell within 1 sec of the design cycle length. In the case involving east-west coordination, the east-west phases received more than their nominal allotment of time at the expense of the north-south movements. The reverse was true when coordination was established for the north-south approaches. The delay was also reduced on the approaches that were coordinated, and increased on those that were not. LIMITATIONS OF TRAFFIC-ACTUATED TIMING ESTIMATION PROCEDURE
The traffic-actuated timing estimation procedure described in this appendix provides a reasonable approximation of the operation of a traffic-actuated controller for nearly all the conditions encountered in practice. As indicated by Courage et al. (1), the results obtained from this method have correlated well with extensive simulation data and with limited field studies. However, the procedure involves a deterministic analytical representation of an extremely complex stochastic process, and therefore has some limitations. Some of the limitations result from unique situations that cannot be modeled analytically in a satisfactory manner, even by the
methodology presented earlier in this chapter. One example is the case of compound left-turn protection with opposing shared lanes for left turns and through movements. The methodology in this chapter treats this as a separate case (Case 6 in Table 9-12) and applies an empirical treatment to determine the saturation flow adjustment factor for left turns. Simulation provides the only effective way to estimate the timing plan parameters for this case. The sample problem presented in this appendix demonstrates the sensitivity of the procedure to the unit extension times set in the controller. As expected, longer unit extension times produce longer average green times except when constrained by the maximum green time settings. Shorter extension times have the opposite effect. There is, however, a lower limit to the range of unit extension times that can be modeled realistically. It is well known in practice that when the unit extension times are too short, premature terminations of a phase may result from anomalies in the departure headways created primarily by lapses in driver attention. The traffic-actuated control model described in this appendix assumes a constant departure headway and does not therefore reflect this phenomenon. Simulation models introduce a stochastic element into the departure headways based on a theoretical distribution. They are therefore able to invoke premature phase terminations to some extent, but they do not deal with anomalous driver behavior. As a practical matter, unit extensions should reflect headways at least 50 percent longer than the expected departure headways. For example, assuming a 2-sec average departure headway, unit extensions should accommodate a 3-sec departure headway without terminating the phase. Assuming a detector occupancy time of 1 sec, this implies a 2-sec gap. So the minimum practical value Updated December 1997
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for the unit extension would be 2 sec. Smaller values may be appropriate in multiple-lane cases in which the average departure headways are shorter. The analysis of permitted left turns from shared lanes always poses special problems. The semiempirical treatment prescribed for shared-lane permitted left turns in this chapter does not lend itself to the iterative timing estimation procedure described in this appendix. An analytical approximation of the shared-lane model was therefore substituted to ensure stable convergence of the solution. This produced timing plans that agreed well with simulation results; however, the analysis of delay resulting from the timing plan did not always agree with the results of the methodology in this chapter. It appears that an iterative method of achieving equilibrium between the shared lane and the adjacent through lanes in this methodology is a prerequisite to the development of a satisfactory timing estimation procedure.
When traffic volumes are extremely low, the timing plan becomes somewhat of an abstraction unless the recall function is used for each phase. In the absence of any demand, the green indication rests on the phase that received the last demand, and may do so for several minutes. This implies that very long red times will be displayed on some phases; however, no delay will be associated with these red times, because no vehicles will be affected. The procedure described in this appendix will compute very short equivalent red times for these phases in an attempt to provide a signal timing plan that will produce realistic delays. Although the procedure produces a reasonable approximation, design decisions based on comparison of delays in the LOS A range should be avoided.
REFERENCES 1. Courage, K.G., Fambro, D.F., Akc¸ elik, R., Lin, P.S., and Anwar, M., Capacity Analysis for Actuated Intersections. NCHRP Project 3-48 Final Report. University of Florida, Texas Transportation Institute, and ARRB Transport Research, Ltd. (1996). 2. Akc¸ elik, R., Analysis of Vehicle-Actuated Signal Operations. Working Paper WD TE 93/007, Australian Road Research Board (1993). 3. Akc¸ elik, R., ‘‘Estimation of Green Times and Cycle Time for Vehicle-Actuated Signals.’’ Transportation Research Record 1457, TRB, Washington, D.C. (1994). 4. Lin, F.B., ‘‘Estimation of Average Phase Durations for FullActuated Signals.’’ Transportation Research Record 881, TRB, Washington, D.C. (1982), pp. 65–72.
Updated December 1997
5. Lin, F.B., ‘‘Predictive Models of Traffic-Actuated Cycle Splits.’’ Transportation Research, Vol. 16B, No. 5 (1982), pp. 65–72. 6. Cowan, R.J., ‘‘Useful Headway Models.’’ Transportation Research, Vol. 9, No. 6 (1975), pp. 371–375. 7. Akc¸ elik, R., and Chung, E., ‘‘Calibration of the Bunched Exponential Distribution of Arrival Headways.’’ Road and Transport Research, Vol. 3, No. 1 (1994) pp. 42–59. 8. Kell, J.H., and Fullerton, I.J., Manual of Traffic Signal Design. Institute of Transportation Engineers, Prentice-Hall, Inc., Englewood Cliffs, N.J. (1982). 9. Lin, F.B., ‘‘Optimal Timing Setting and Detector Lengths of Presence Mode Full-Actuated Control.’’ Transportation Research Record 1010, TRB, Washington, D.C. (1985), pp. 37–45.
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APPENDIX III MEASUREMENT OF INTERSECTION CONTROL DELAY IN THE FIELD As an alternative to estimation of average control delay per vehicle using Equation 9-22 and the progression adjustment factor, delay at existing locations may be measured directly. There are a number of measurement methods, including the use of test-car observations, path tracing of individual vehicles, and recording of arrival and departure volumes on a cycle-by-cycle basis. The method summarized here is based on direct observation of vehiclein-queue counts at the intersection and, unless the volume is very light, requires two field personnel per lane group surveyed. Also needed is a multifunction digital watch with a timer that counts an interval of, for example, 17 sec and then repeats the countdown for another 17-sec interval, plus a volume count board that has at least two tally counters. Alternatively, a laptop computer can be programmed to emit audio count markers at user-selected intervals, take volume counts, and execute real-time delay computations, thus simplifying data reduction. In general, this method is applicable to all signalized intersections operating from low, undersaturated conditions to conditions in which the lane group demand-to-capacity ratio approaches 1.0. For oversaturated conditions, queue buildup normally makes the method impractical. Under those circumstances, more personnel will be required to complete the field study, and other methods may be considered, such as an input-output technique or a zoned survey technique. In the input-output technique, different observers count arrivals separately from departures and vehicles in queue are calculated as the accumulated difference, subject to in-process checks for vehicles leaving the queue before they reach the stop line. The zoned survey technique requires subdividing the approach into manageable segments to which the observers are assigned; they then count queued vehicles in their assigned zone. Both of these techniques require more personnel and are more complicated in setup and execution. The method described here is applicable to situations in which the average maximum queue per cycle is no more than about 20 to 25 vehicles per lane. When queues are long or the demand-tocapacity ratio is near 1.0, care must be taken to continue the vehicle-in-queue count past the end of the arrival count period, as detailed below. This requirement is for consistency with the analytic delay equation used earlier in the chapter. The method does not directly measure delay during deceleration and a portion of acceleration delay, which are very difficult to measure without sophisticated tracking equipment. However, this method has been shown to yield a reasonable estimate of control delay. It includes an adjustment for errors that may occur when this type of sampling technique is used, as well as an accelerationdeceleration delay correction factor, which is a function of the typical number of vehicles in queue during each cycle and the normal free-flow speed when vehicles are unimpeded by the signal. Figure III.9-1 is an intersection control delay worksheet that may be used for recording observations and computation of average time-in-queue delay. Before beginning the detailed survey, the observers should estimate the average free-flow speed during the study period—in other words, the speed at which vehicles would pass through the intersection if the signal were green for a long time. Accuracy to within 3 to 5 mph is sufficient. This estimate
may be obtained by driving through the intersection a few times when the light is green and no queue is present and recording the speed at a location least affected by signal control. Typically, the recording location should be upstream and about midblock. This value and the number of lanes in the lane group should be recorded on the worksheet. The survey should begin at the start of the red phase of the study lane group, ideally when there are no cycle failures (no overflow queue) from the previous green period. The reason for this is the need for consistency with the analytic delay equation, which is based on delay to vehicles that arrive during the study period, not before. If the survey does start with an overflow queue, the overflow vehicles need to be excluded from subsequent queue counts; that is, only vehicles arriving during the study period are included in the queue and arrival volume counts. It should not be difficult to do this as long as the number of overflow vehicles is small. PROCEDURE
Observer 1
1. Keep track of the end of standing queues for each cycle in the survey period, that is, the last vehicle in each lane that stops because of the signal. This includes vehicles that arrive when the signal is actually green but stop because vehicles in front have not yet started moving. For purposes of the survey, a vehicle is considered as having joined the queue when it approaches within one car length of a stopped vehicle and is itself about to stop. This definition is used because of the difficulty of keeping precise track of the moment when a vehicle comes to a stop. All vehicles that join a queue are then included in the vehicle-in-queue counts until they cross the stop line. 2. At regular intervals of between 10 and 20 sec, record the number of vehicles in the queue (e.g., using the countdown-andrepeat timer on a digital watch to control the count intervals). The regular intervals should not be an integral divisor of the cycle length (e.g., if the cycle is 120 sec, use 14-sec or 16-sec count intervals, not 15-sec intervals). Vehicles in queue are those that (a) are included in the queue of stopping vehicles as defined in Step 1 and (b) have not yet exited the intersection. A through vehicle can be considered as having exited the intersection when its rear axle crosses the stop line. A turning vehicle can be considered as having exited the intersection the instant it clears the opposing through traffic or the pedestrians to which it must yield and begins accelerating back to free-flow speed. Note that the vehiclein-queue count often includes some vehicles that have regained cruise speed but have not yet exited the intersection. 3. Enter the vehicle-in-queue counts in the appropriate box on the worksheet. Cycles in the survey period are listed in the second column on the worksheet, next to the column for clock time, which is recorded every five cycles, and interval count identifiers are given as column headings. For ease in conducting the study, the survey period is most conveniently defined as an integer number Updated December 1997
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Figure III.9-1. Field intersection control delay worksheet.
Updated December 1997
signalized intersections of cycles, though a precisely defined time length for the survey period (e.g., 15 min) could be used. The key point is that the end of the survey period must be clearly defined in advance, since the last arriving vehicle or vehicles in the period that stop must be identified and counted until they have exited the intersection (see Step 4). This method is necessary for consistency with the delay definition included in the procedure in this chapter. 4. At the end of the survey period, continue taking vehicle-inqueue counts for all vehicles that arrived during the survey period until all of them have exited the intersection. This requires noting the last stopping vehicle that arrived during the survey period in each lane of the lane group and continuing the vehicle-in-queue counts until the last stopping vehicle or vehicles, plus all vehicles in front of the last stopping vehicles, have exited the intersection. Stopping vehicles that arrive after the end of the survey period are not included in the final vehicle-in-queue counts.
Observer 2
During the entire survey period, maintain separate volume counts of (a) total vehicles arriving during the survey period and (b) total vehicles arriving during the survey period that stop one or more times; that is, a vehicle stopping multiple times is counted only once as a stopping vehicle. Enter these volumes in the appropriate cells on the worksheet.
DATA REDUCTION
1. Each column of the vehicle-in-queue counts is summed; then the column totals for the entire survey period are summed. 2. A vehicle recorded as part of a vehicle-in-queue count is in queue, on average, for the time interval between counts. The average time in queue per vehicle arriving in the survey period is estimated as Time in queue per vehicle = (I ×
ov
iq
/Vtot) × 0.9
where I = interval between vehicle-in-queue counts, sec; S viq = sum of vehicle-in-queue counts; Vtot = total number of vehicles arriving during the survey period; and
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Table III.9-1. Acceleration-Deceleration Delay Correction Factor free-flow speed (mph) ≤37 38–44 ≥45
correction factor (sec) by avg no. of vehicles stopping per lane in each cycle ≤7
8–19
20–301
+5 +7 +9
+2 +4 +7
−1 +2 +5
1
Vehicle-in-queue counts in excess of about 25 vehicles per lane are typically unreliable.
0.9 = empirical adjustment factor. The 0.9 adjustment factor accounts for the errors that may occur when this type of sampling technique is used to derive actual delay values, which normally results in an overestimate of delay. Research has shown the correction required to be fairly consistent over a variety of conditions. 3. The fraction of vehicles stopping and the average number of vehicles stopping per lane in each signal cycle, as indicated on the worksheet, are computed. 4. Table III.9-1 is used to look up a correction factor appropriate to the lane group cruise speed and the average number of vehicles stopping per lane in each cycle. This factor adds an adjustment for deceleration and acceleration delay, which cannot be measured directly with manual techniques. 5. The correction factor is multiplied by the fraction of vehicles stopping; then this product is added to the time-in-queue value of Step 2 to derive the final estimate of control delay per vehicle. Figure III.9-2 presents a sample application for a study site over a 15-min period, operating with a 115-sec cycle over almost 8 cycles. Annotations have been added to clarify the procedure. The 15-sec count interval is not an integral divisor of the cycle length, to eliminate potential survey bias caused by queue buildup in a regular, cyclic pattern. Figure III.9-3 shows how the field survey would have been finished if a queue still remained at the end of the 15 minute survey period. Only the vehicles that arrived during the 15-min period would be counted, even though other vehicles continued to arrive after the 15-min period. If the study site has an actuated signal with varying cycle and phase lengths, the count interval may be chosen as the most convenient value for conducting the field survey on the basis of volume and vantage point considerations.
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Figure III.9-2. Sample application of intersection control delay worksheet.
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Figure III.9-3. Sample application with residual queue at end.
APPENDIX IV DIRECT MEASUREMENT OF PREVAILING SATURATION FLOW RATES GENERAL NOTES
The default ideal saturation flow rate used in the methodology of this chapter is 1,900 pcphgpl. This value must be adjusted for prevailing traffic conditions such as lane width, left turns, right turns, heavy vehicles, grades, parking, parking blockage, area type, bus blockage, and left-turn blockage. These computations are made in the Saturation Flow Rate Module. As an alternative to these computations, the prevailing saturation flow rate may be measured directly in the field. Saturation flows have been measured and researched in recent years by various groups, including the City of Edmonton in conjunction with the University of Alberta, the University of Kentucky, Texas Transportation Institute, JHK & Associates, and the Australian Road Research Board. Results of these studies have demonstrated that saturation flow rate can be used as the starting design and analysis variable. Measured saturation flow rates are always preferable to estimated values. Saturation flow rate is the maximum discharge rate during the green time. It is usually achieved after the fourth to seventh vehicle has entered the intersection from a standing queue. The ideal saturation flow rate is defined as the discharge rate from a standing queue in a 12-ft (3.6-m) wide lane that carries only through passenger cars and is otherwise unaffected by conditions such as grade, parking, and so forth. Vehicles are recorded
when their rear axles cross the stop line. The measurement starts with the passage of the fourth vehicle. Other reference points may yield different saturation flow rates. In order to maintain consistency with the method described in this chapter and to allow for information exchange, maintaining the roadway and vehicle reference points identified here is essential. The ideal saturation flow rate is usually stable over a period of time for similar traffic conditions in a given community. Values measured in the same lane during repetitive weekday traffic conditions (e.g., a.m. or p.m. peak patterns) normally exhibit relatively narrow distributions. On the other hand, saturation flow rates for different communities or different traffic conditions and compositions, even at the same location, may vary significantly. For practical purposes, prevailing saturation flow rates are usually expressed in vehicles per hour of green per lane. As a result, their values also depend on traffic flow composition. The default value used in the methodology of this chapter is expressed in pecphgpl (i.e., passenger cars only). Preferably, local prevailing saturation flow rates should be observed directly. Alternatively the computation module can be used, with the measured regional ideal saturation flow rates as the starting values. The default value should be used only as an approximate substitute. Severe weather conditions, unusual traffic mixes, or other special local conditions can yield saturation flow rates Updated December 1997
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that differ markedly from those estimated using the computation procedures. The procedure for measuring prevailing saturation flow rates is summarized below. A sample field worksheet for recording observations is included as Figure IV.9-1.
MEASUREMENT TECHNIQUE
The following example describes a single-lane saturation flow survey. A two-person field crew is recommended. One person with a tape recorder, pushbutton event recorder, or a notebook computer with appropriate software will suffice. The field notes and tasks identified in the following section must be adjusted accordingly. 1. General tasks a. Measure and record the area type and width and grade of the lane being studied. b. Fill out the survey identification data shown in Figure IV.9-1 completely. c. Select an observation point where the stop line for the surveyed lane and the corresponding signal heads are clearly visible. d. The reference point is normally the stop line. Vehicles should consistently stop behind this line. When a vehicle crosses it unimpeded, it has entered the intersection conflict space for the purpose of saturation flow measurement. Left- or right-turning vehicles yielding to opposing through traffic or yielding to pedestrians are not recorded until they proceed through the opposing traffic. 2. Recorder tasks a. Note the last vehicle in the stopped queue when the signal turns green. b. Describe the last vehicle to the timer. c. Note on the worksheet which vehicles are heavy vehicles and which vehicles turn left or right. d. Record the time called out by the timer. 3. Timer tasks
Updated December 1997
a. Start stop watch at beginning of green and notify the recorder. b. Count aloud each vehicle in the queue as its rear axle crosses the stop line. c. Call out the time of the fourth, tenth, and last vehicle in the queue. d. If queued vehicles are still entering the intersection at the end of the green, call out ‘‘saturation through the end of green—last vehicle was number XX.’’ Note any unusual events that may have influenced the saturation flow rate, such as buses, stalled vehicles, and unloading trucks. The period of saturation flow rate begins when the rear axle of the fourth vehicle in the queue crosses the stop line or reference point and ends when the rear axle of the last queued vehicle at the beginning of the green time crosses the stop line. Measurements are taken cycle by cycle. To reduce the data for each cycle, the time recorded for the fourth vehicle is subtracted from the time recorded for the last vehicle in the queue. This value is total headway for (n − 4) vehicles, where n is the number of the last vehicle surveyed (this may not be the last vehicle in the queue). The total headway is divided by (n − 4) to obtain the average headway per vehicle under saturation flow. The saturation flow rate is 3,600 divided by this value. For example, if the time for the fourth vehicle was observed as 10.2 sec and the time for the 14th and last vehicle surveyed was 36.5 sec, the average saturation headway per vehicle would be (36.5 − 10.2)/(14 − 4) = 26.3/10 = 2.63 sec/veh and the prevailing saturation flow rate in that cycle would be 3,600/2.63 = 1,369 vphgpl In order to obtain a statistically significant value, a minimum of 15 signal cycles with more than 8 vehicles in the initial queue is usually needed. An average of the saturation flow rate values in individual cycles represents then the prevailing local saturation flow rate for the surveyed lane. The percentage of heavy vehicles and turning vehicles in the sample used in the computations should be determined and noted for reference.
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Figure IV.9-1. Field Saturation Flow Rate Study Worksheet.
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APPENDIX V WORKSHEETS FOR USE IN ANALYSIS WORKSHEET
PAGE
Input Module Worksheet ......................................................................................................................................................................... 9-125 Volume Adjustment Module Worksheet................................................................................................................................................. 9-126 Saturation Flow Rate Module Worksheet ............................................................................................................................................... 9-127 Supplemental Worksheet for Permitted Left Turns: Multilane Approach............................................................................................. 9-128 Supplemental Worksheet for Permitted Left Turns: Single-Lane Approach......................................................................................... 9-129 Capacity Analysis Module Worksheet .................................................................................................................................................... 9-130 LOS Module Worksheet .......................................................................................................................................................................... 9-131 Supplemental Uniform Delay Worksheet for Left Turns from Exclusive Lanes with Primary and Secondary Phases...................... 9-132 Planning Method Input Worksheet.......................................................................................................................................................... 9-133 Planning Method Lane Volume Worksheet ............................................................................................................................................ 9-134 Planning Method Signal Operations Worksheet ..................................................................................................................................... 9-135 Intersection Control Delay Worksheet .................................................................................................................................................... 9-136 Field Saturation Flow Rate Study Worksheet......................................................................................................................................... 9-137 Delay/LOS Worksheet with Initial Queue .............................................................................................................................................. 9-138
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APPENDIX VI EXTENSION OF SIGNAL DELAY MODELS TO INCORPORATE EFFECT OF INITIAL QUEUE INTRODUCTION
The delay model represented by Equations 9-22 through 9-25 in this chapter is based on the assumption that there are no initial queues at the start of an analysis period of length T. In some cases, the analysis period starts with a residual demand that was unmet from a previous time period. This unmet demand will be designated Qb in vehicles. Qb is observed at the start of the red period and excludes any vehicles in the queue present because of random, cycle-by-cycle fluctuations in demand (overflow queue due to cycle failures). When Qb ≠ 0, vehicles arriving in period T will experience an additional delay due to the presence of an initial queue. The magnitude of this supplemental delay depends on several factors, namely, the size of the initial queue, the length of the analysis period, and the prevailing (adjusted) volume-to-capacity ratio in T. Hereafter, the supplemental delay term is referred to as d3. Five scenarios emerge when control delay is estimated. These are labeled Cases I through V. Cases I and II occur when there is no initial queue and the period is either undersaturated (Case I) or oversaturated (Case II). In both these cases, d3 = 0, and the delay model in Equation 9-22 applies. Cases III through V are shown in Figures VI.9-1 through VI.9-3. Case III occurs when unmet demand Qb can be fully served in time period T. For this to happen, the sum of Qb and the total demand in T, qT, must be less than the available capacity, cT. Case IV occurs when there is still unmet demand at the end of T but the size of the unmet demand is decreasing. For this to happen, the demand in T, qT, should be less than the capacity, cT. Finally, Case V occurs when the demand in T, qT, exceeds the capacity, cT. Here, the unmet demand will increase at the end of period T. The total supplemental delay due to an initial queue that is incurred in the average cycle is depicted as the shaded area in Figures VI.9-1 through VI.9-3, which is labeled D. It represents the entire delay experienced by all vehicles arriving in T, including delay that is experienced in subsequent time periods (Figures VI.9-
Figure VI.9-2. Case IV: supplemental delay with initial oversaturation demand decreasing in T. [Supplemental delay per vehicle (d3) in seconds = 3,600Qb/c − 1,800T [1 − Min (1,X)].]
Figure VI.9-3. Case V: supplemental delay with initial oversaturation demand increasing in T. [Supplemental delay per vehicle (d3) in seconds = 3,600Qb /c.] 2 and VI.9-3). Excluded from this delay are two components: the delay incurred for vehicles in the initial queue (labeled Di) and the oversaturation delay corresponding to a zero initial queue (labeled Dso in Figure VI.9-3). This last term is already accounted for in the d2 term component of the delay model in Equation 9-25. ESTIMATION OF d3
A generalized form of d3, defined as the average supplemental control delay per vehicle (in seconds) when an initial queue of size Qb is present at the start of the analysis period T, was developed in a recent FHWA-sponsored project. It is an additive term in the delay model given in Equation 9-22 and is expressed as follows: Figure VI.9-1. Case III: supplemental delay with initial oversaturation demand clearing in T. [Supplemental delay per vehicle (d3) in seconds = 1,800Qbt/cT.].
d3 =
1,800Qb(1 + u)t cT
(VI.9-1)
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Table VI.9-1. Selection of Delay Model Variables by Case Case I II III IV V
≤ > ≤ ≤ >
X
Qb
d1
1.0 1.0 1.0 1.0 1.0
0 0 >0 >0 >0
Eq. 9-23 Eq. 9-23 Eq. VI.9-5 Eq. VI.9-5 Eq. VI.9-5
d2 Eq. Eq. Eq. Eq. Eq.
9-25 9-25 9-25 9-25 9-25
where Qb = initial unmet demand at the start of period T, veh; c = adjusted lane group capacity, veh/hr; T = duration of analysis period, hr; t = duration of unmet demand in T, hr; and u = delay parameter. The parameters t and u are determined according to the prevailing case (III, IV, or V). The following two equations may be used to estimate their values: Qb (VI.9-2) t = 0 if Qb = 0, else t = Min T, c[1 − Min(1,X)] cT [1 − Min(1,X)] (VI.9-3) u = 0 if t < T, else u = 1 − Qb
5
6
where X is lane group degree of saturation (v/c). In addition to the supplemental delay term, the analyst may be interested in computing the time that the last vehicle arriving in T clears the intersection (measured from the start of the time period T), as affected by the presence of an initial queue of length Qb. This time will be referred to as the supplemental clearing time Tc. In Cases I–III, it is evident that all vehicles will clear at the end of period T (in addition to the normal delays d1 + d2). For Cases IV and V, the last vehicle arriving in T will clear the intersection at time Tc > T (again in addition to d1 + d2). Therefore, a general formula for the supplemental clearing time in the case of an initial queue, measured from the start of the analysis period T, is Tc = Max (T,
Qb + TX) c
(VI.9-4)
To summarize the procedure for estimating control delays, Table VI.9-1 gives a comparison of the model parameters for Cases I– V. Note that in order to decide whether Case III (t < T) or IV (t = T) applies, the value of t must first be computed from Equation VI.9-2. For Cases III, IV, and V, the uniform control delay component (d1) must be evaluated using X=1.0 for the period when an oversaturation queue exists (t) and using the actual X value for the remainder of the analysis period (T-t). Therefore, in these cases, a timeweighted value of d1 is to be used, as follows: d1 = ds∗t/ T + du∗PF∗(T-t)/T
(VI.9-5)
where ds = is the saturated delay (d1 evaluated for X=1.0), and du = is the undersaturated delay (d1 evaluated for the actual X value). In equation VI.9-5 for Cases IV and V, the du term drops out because t=T and need not be calculated. Equation 9-23 can be used to evaluate the ds and du components in all cases except for left turns with compound left turn protection (protected-permitted Updated December 1997
t
u
d3
Tc
0 0 Eq. VI.9-2 T T
0 0 0 Eq. VI.9-3 1
0 0 Eq. VI.9-1 Eq. VI.9-1 Eq. VI.9-1
T TX T Eq. VI.9-4 Eq. VI.9-4
and permitted-protected), using X=1.0 in the equation to compute ds and using the actual X value to compute du. For compound left turn protection, the Supplemental Uniform Delay Worksheet in Figure 9-21 must be used as a means to approximate the ds and du compounds, again using X=1.0 for ds and the actual X value for du. When using X=1.0 for the ds component in Figure 9-21, the left turn volume used (v) must also be adjusted by the actual X value (use v′=v/X) in order to meet the basic assumptions of the Supplemental Uniform Delay Worksheet. Note that the only place where PF is used in an initial queue analysis of Appendix VI is for the undersaturated du portion of a Case III condition. This is because the existence of the initial queue defeats the value of the progression under all other conditions. Analysts are advised to be wary of a similar concern in the use of PF in a Case II analysis (oversaturated) using Equation 9-22 because all but the first cycle will be blocked by initial queues due to the oversaturated condition. NUMERICAL EXAMPLE OF DELAYS WITH INITIAL QUEUE
To illustrate the application of the delay model extension, an analysis of the EB lane group in Sample Calculation 1 in Section IV is carried out with and without an initial queue. The following input values are taken directly from Figure 9-31, the Capacity Analysis Module Worksheet: Lane group capacity (c) = 787 veh/hr, Lane group v/c ratio (X) = 1.017, Analysis period length (T) = 0.25 hr, and Initial queue = 20 vehicles (across the two-lane lane group). Scenario I: No Initial Queue
In Scenario I, d3 = 0 as given in Table VI.9-1, Case II. The average control delay per vehicle is d1PF + d2 + d3 = 22.0 ∗ .923 + 36.3 + 0.0 = 56.6 sec, as given in Figure 9-32. The corresponding LOS for a control delay of 56.6 sec is E. Finally, the supplemental clearing time Tc = 15.3 min for Case II. Scenario II: Initial Queue of 20 Vehicles
Since X > 1.0 and Qb = 20, Case V in Table VI.9-1 applies. Here, t = 0.25 and u = 1. Substituting in Equation VI.9-1 gives the following: d3 =
1800 ∗ 20 ∗ (1 + 1) ∗ 0.25 = 91.5 sec/veh 787 ∗ 0.25
Therefore, the average control delay is computed as d = 22.0 + 36.3 + 91.5 = 149.8 sec/veh (LOS F) which is more than twice the delay calculated assuming a zero
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time in a 100-sec cycle. Arrivals are considered to be random (Arrival Type 3). Calculate the delay and level of service for vehicles arriving in each 15-min time period and for the overall analysis period of 1 hr.
Period 1
Period 1 is undersaturated, with a degree of saturation X = 800/ 1,000 = 0.80. Therefore, from Equation VI.9-6, there is no unmet demand at the start of Period 2, Qb,2 = 0, assuming no initial queue at the start of Period 1, Qb,1 = 0. The average control delay for vehicles arriving in Period 1 will be labeled dc,1 and is estimated as follows: Figure VI.9-4. Demand profile for multiple-period analysis (15min periods). initial queue. Note that PF is not applied for Case V. Thus the impact of an initial queue can be substantial and must be accounted for in delay and LOS estimation. Finally, the supplemental clearing time, Tc, is estimated from Equation VI.9-4 as
1
Tc = Max 0.25,
2
20 + 0.25 ∗ 1.017 = 0.28 hr 787
!
3
4
Period 2
or 16.8 min from the start of the peak period. Therefore, the last vehicle entering in the peak 15-min period will experience an additional 1.8 min delay because of the presence of the initial queue of 20 vehicles.
Period 2 is oversaturated, with a degree of saturation X = 1,200/ 1,000 = 1.20. There is no unmet demand at the start of the period, so again the two-component delay formula can be used as follows: dc,2 =
EXTENSION TO MULTIPLE TIME PERIODS
The procedure just described can be extended to analyze multiple time periods, each of duration T and each having a fixed demand during T. The analysis is performed sequentially, carrying over the final unmet demand Qb (if any) from one time period to the beginning of the next. In general, for time period i, the final unmet demand Qb,i+1 at the start of the next time period T can be estimated as follows: Qb,i+1 = Max[0, Qb,i + cT(Xi − 1)] for i = 1,2, . . ., n
0.50 ∗ 100 ∗ (1 − 40/100)2 ∗ 1.0 + 900 ∗ 0.25 ∗ 40 Min(1, 0.80) 1− 100 8 ∗ 0.50 ∗ 0.80 (0.80 − 1) + (0.80 − 1)2 + = 33.2 sec 1,000 ∗ 0.25
dc,1 =
0.50 ∗ 100 ∗ (1 − 40/100)2 ∗ 1.0 + 900 ∗ 0.25 ∗ 40 Min(1, 120) 1− 100 8 ∗ 0.50 ∗ 1.20 (1.20 − 1) + (1.20 − 1)2 + = 129.7 sec 1,000 ∗ 0.25
!
3
4
Period 3
(VI.9-6)
where Qb,i and Xi are the unmet demand and the degree of saturation for the time period i, respectively. Typically, a multiple-time-period analysis would start with an undersaturated time period, particularly one for which Qb,1 = 0. Once the unmet demand is calculated, delays are estimated according to the method described in the previous section. An important feature of multiple-period analysis is that the actual counts taken during each time period should be used in the procedure; that is, the PHF is unity. Counts are then converted into hourly flow rates by dividing each count by T (in hours). The procedure is best described using a numerical example. NUMERICAL EXAMPLE FOR MULTIPLE-PERIOD ANALYSIS
In this example, consider a signalized lane group with no initial queue that has a fixed capacity of 1,000 vph. The demand profile based on 15-min counts (factored to hourly rates) is shown in Figure VI.9-4. The lane group receives 40 sec of effective green
Period 3 is fully saturated, with a degree of saturation X = 1,000/1,000=1.00. The unmet demand from the previous period is calculated from Equation VI.9-6 as follows: Qb,3 = Max[0, 0 + 1,000 ∗ 0.25 ∗ (1.2 − 1)] = 50 veh Here, the supplemental delay term (d3) must be added. First the values of t and u are determined from Equations VI.9-2 and VI.93, respectively:
3
t = Min 0.25, u=1−
4
50 = 0.25 1,000(1 − 1)
1,000 ∗ 0.25[1 − Min(1.0, 1.0)] = 1.0 50
Substituting in Equation VI.9-1 gives d3 =
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9-142 Thus, the average control delay in Period 3 is
0.50 ∗ 100 ∗ (1 − 40/100) 0.25 + 900 ∗ 0.25 ∗ ∗ 0.25 40 1− 1.0 100 8 ∗ 0.50 ∗ 1.0 (1.0 − 1) + (1.0 − 1)2 + + 180 = 238.5 sec 1,000 ∗ 0.25 2
dc,3 =
!
3
4
be carried out over subsequent time intervals to ensure that the most severe LOS period has been captured. PROCEDURES FOR MAKING CALCULATIONS
Figure VI.9-6 provides a worksheet that can be used to make the calculations of delay with initial queue. The following steps should be used with this worksheet.
Period 4 Step 1: Enter Time Period and Duration
Period 4 is undersaturated, with a degree of saturation X = 600/ 1,000 = 0.60. The unmet demand from the previous period is calculated from Equation VI.9-6 as follows: Qb,4 = Max[0, 50 + 1,000 ∗ 0.25 ∗ (1.0 − 1)] = 50 veh In essence, since the previous period was at capacity, the residual demand at the end of the period is equivalent to that at the start of the period. Again, the computation of d3 requires the values of t and u, which are calculated as follows:
3
t = Min 0.25,
Step 2: Identify Lane Groups for Analysis
4
50 = 0.125 1,000(1 − 0.60)
In Column 1, label each of the lane groups to be analyzed according to those used in the LOS Module Worksheet (Figure 9-20). Lane groups that do not have an initial queue may appear on this worksheet so that their delay values can be averaged with those of oversaturated lane groups. In this case, their d1 and d2 values will be unchanged and d3 will be zero on the worksheet.
Since t < 0.25, u = 0 from Equation VI.9-3. Substituting in Equation VI.9-1 gives d3 =
Each time period will need a separate worksheet to calculate the delay when any of the movements at the intersection start with an initial queue during that time period. Each time period should be numbered and the period number and time entered in the upper left corner of the worksheet. The duration of the time period, in hours, should also be entered. Note that in a multiperiod analysis the length of all time periods should be the same.
1,800 ∗ 50 ∗ (1 + 0.0) ∗ 0.125 = 45 sec 1,000 ∗ 0.25
Since t < T, the uniform delay component is calculated using Equation VI.9-5: 0.50 ∗ 100 ∗ (1 − 40/100) 0.125 ∗ 1 − 40/100 ∗ 1.0 0.25 0.50 ∗ 100 ∗ (1 − 40/100)2 0.25 − 0.125 + ∗ 1.0 ∗ = 26.8 sec/veh 1 − 40/100 ∗ Min(1,0.60) 0.25
Step 3: Enter First- and Second-Term Delay Information
2
d1 =
Thus, the average control delay in Period 4 is dc,4 = 26.8 + 900 ∗ 0.25 ∗
3(0.60 − 1.0) + !(0.60 − 1.0)
2
+
8 ∗ 0.50 ∗ 0.60 1,000 ∗ 0.25
4
+ 45 = 74.5 sec/veh The contribution of each of the delay terms in each period is illustrated in Figure VI.9-5, which displays the general delay component trends. The impact of the initial queue delay term is evident, particularly for Periods 3 and 4. Finally, the average overall control delay to all vehicles arriving in the hour is calculated as a volume-weighted delay of the individual period delays as follows: dc,t = (800 ∗ 33.2 + 1,200 ∗ 129.7 + 1,000 ∗ 238.5 + 600 ∗ 74.5)/(800 + 1,200 + 1,000 + 600) = 129.3 sec/veh It is interesting to note that although the average overall signal delay in the entire period is virtually identical to the delay for vehicles arriving in peak Period 2, it is much smaller than the worse delay (and level of service) that is experienced in Period 3, which immediately follows the peak. Thus, a single-period analysis may not be sufficient to determine the worst level of service in an oversaturated time period. When residual queues do occur at the end of a peak period, it is recommended that a delay analysis Updated December 1997
In Columns 2, 3, 6, and 8, enter the v/c ratio, lane group capacity, unadjusted uniform delay, and incremental delay values from Columns 2, 6, 4x5, and 8 of the LOS Module Worksheet, respectively. To get unadjusted uniform delay, enter the product of the uniform delay (LOS Module Worksheet, Column 4) and the progression adjustment factor (column 5). Step 4: Enter Initial Unmet Demand
In Column 4, enter the initial unmet demand for each lane group. This entry may be the initial queue observed at the start of the red period (excluding any vehicles in queue because of random, cycleby-cycle fluctuations in demand), or it may be the final unmet demand for the lane group estimated in Column 10 from the previous analysis period. Step 5: Calculate Duration of Unmet Demand
In Column 5, calculate the duration of unmet demand, t, using Equation VI.9-2. If there is no initial queue (Qb = 0), then t = 0, and the value of t is limited to be no larger than the length of the time period, T. Step 6: Calculate Adjusted Uniform Delay
In Column 7, calculate the adjusted uniform delay term, d1, using Equation VI.9-5. When t = 0, the result is the same as the unad-
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Figure VI.9-5. Delay model components for multiple-period analysis. justed value of d1. Progression effects are included, as appropriate, in this adjusted uniform delay result. The values of g and C for the lane group from the LOS Module Worksheet must be used to make this calculation. Note that the unadjusted value of d2 will be used from the LOS Module Worksheet in the final delay calculation and that this delay value includes the oversaturation delay when v/c > 1.
Step 7: Calculate Initial Queue Parameter
In Column 9, calculate the initial queue parameter, u, using Equation VI.9-3. When t < T, u = 0 (Cases I-III); otherwise Equation VI.9-3 is used (Case IV) or u = 1 (Case V).
Step 8: Calculate Final Unmet Demand
In Column 10, calculate the final unmet demand using Equation VI.9-6. This is the estimate of the number of vehicles in queue at the end of the analysis period. If its value is nonzero, this indicates that the subsequent analysis period should be analyzed to determine the average delay per vehicle that results because of this initial queue for that time period.
Step 9: Calculate Supplemental Delay
In Column 11, calculate the supplemental (initial queue) delay, d3, using Equation VI.9-1. This is the additional delay that results
from the existence of the initial queue. Note that this value does not include any of the oversaturation delay accounted for in d2. Step 10: Find Delay and Level of Service for Each Lane Group
Delay and level of service are found by adding the three delay terms in Columns 7, 8, and 11 for each lane group. Note that the d1 value in Column 7 includes any appropriate effects of PF on the d1 term. The result is entered in Column 12. The level of service corresponding to this delay, taken from Table 9-1, is entered in Column 13. Step 11: Find Delay and Level of Service for Each Approach
The average delay per vehicle is found for each approach by adding the product of the lane group flow rate and the delay for each lane group on the approach and dividing the sum by the total approach flow rate. The weighted-average delay is entered in Column 14 for each approach. Level of service is determined from Table 9-1 and entered in Column 15. Step 12: Find Delay and Level of Service for Intersection
The average delay per vehicle for the intersection as a whole is found by adding the product of the approach flow rate and the approach delay for all approaches and dividing the sum by the total intersection flow rate. This weighted-average delay is entered at the bottom of the worksheet. The overall intersection level of service is found from Table 9-1 and entered at the bottom of the worksheet.
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chapter 10
UNSIGNALIZED INTERSECTIONS
PREFACE Procedures for the capacity and level-of-service (LOS) analysis of three types of unsignalized intersections are described in this chapter: two-way stop-controlled (TWSC) intersections, all-way stop-controlled (AWSC) intersections, and roundabouts. These procedures are not intended for use in the analysis of totally uncontrolled intersections or for yield-controlled intersections. Research sponsored by the National Cooperative Highway Research Program (NCHRP) provided the basis for the analysis methodologies for TWSC and AWSC intersections. The methodologies are based on data from the first comprehensive data base established for traffic flow characteristics at unsignalized intersections in the United States, including information from 79 TWSC intersections and 41 AWSC intersections. A separate study of four intersections sponsored by the Federal Highway Administration provided the data to calibrate the procedures for roundabouts.
CONTENTS
PART A. TWO-WAY STOP-CONTROLLED INTERSECTIONS ...................................................................................................... 10-3 i.
introduction .......................................................................................................................................................................... 10-3 Variables Used in Analysis of TWSC Intersections ............................................................................................................ 10-3 Overview of Procedures ........................................................................................................................................................ 10-4
ii.
methodology.......................................................................................................................................................................... Conceptual Approach ............................................................................................................................................................ Capacity Formula .................................................................................................................................................................. Structure of the Methodology ............................................................................................................................................... Input Data Requirements ................................................................................................................................................. Conflicting Traffic............................................................................................................................................................ Critical Gap and Follow-Up Time .................................................................................................................................. Potential Capacity for Movement.................................................................................................................................... Impedance Effects ............................................................................................................................................................ Shared-Lane Capacity ...................................................................................................................................................... Upstream Signals.............................................................................................................................................................. Two-Stage Gap Acceptance............................................................................................................................................. Flared Minor-Street Approaches...................................................................................................................................... Queue Lengths.................................................................................................................................................................. Control Delay ................................................................................................................................................................... Delay to Major-Street Through Vehicles ........................................................................................................................ Other Relevant Delay Estimates...................................................................................................................................... Level-of-Service Criteria....................................................................................................................................................... Interpretation of Results ........................................................................................................................................................ Shared Lanes on Minor Approach .................................................................................................................................. Consideration of Queue Lengths ..................................................................................................................................... Determination of Intersection Control Type ........................................................................................................................
10-5 10-5 10-6 10-6 10-7 10-7 10-10 10-11 10-11 10-15 10-16 10-20 10-21 10-21 10-22 10-23 10-23 10-25 10-25 10-25 10-25 10-27
iii.
procedures for application ................................................................................................................................................ Field Data Requirements....................................................................................................................................................... Sequence of Computations for Capacity .............................................................................................................................. Capacity Adjustments ...................................................................................................................................................... Geometric Features and Movement Definitions ............................................................................................................. Volume Adjustment .........................................................................................................................................................
10-27 10-29 10-29 10-29 10-29 10-29
10-1
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10-2
Site Characteristics........................................................................................................................................................... Critical Gap and Follow-Up Time .................................................................................................................................. Effect of Upstream Signals.............................................................................................................................................. Computations of Impedance and Movement Capacities ................................................................................................ Two-Stage Gap Acceptance............................................................................................................................................. Shared-Lane Capacity ...................................................................................................................................................... Effect of Flared Minor-Street Approaches...................................................................................................................... Average Control Delay, Queue Length, and Level of Service ...................................................................................... Planning and Design Applications........................................................................................................................................
10-29 10-30 10-30 10-30 10-31 10-31 10-31 10-31 10-32
iv.
sample calculations ............................................................................................................................................................ Sample Calculation A1.......................................................................................................................................................... Sample Calculation A2.......................................................................................................................................................... Sample Calculation A3.......................................................................................................................................................... Sample Calculation A4.......................................................................................................................................................... Sample Calculation A5.......................................................................................................................................................... Sample Calculation A6..........................................................................................................................................................
10-46 10-46 10-49 10-50 10-52 10-53 10-55
v.
references .............................................................................................................................................................................. 10-58
PART B. ALL-WAY STOP-CONTROLLED INTERSECTIONS........................................................................................................ 10-59 i.
introduction .......................................................................................................................................................................... 10-59 Variables Used in Analysis of AWSC Intersections............................................................................................................ 10-59 Overview of Procedures ........................................................................................................................................................ 10-59
ii.
methodology.......................................................................................................................................................................... Conceptual Approach ............................................................................................................................................................ Capacity Concept................................................................................................................................................................... Capacity Model...................................................................................................................................................................... Intersection of Two One-Way Streets............................................................................................................................. Intersection of Two Two-Way Streets ............................................................................................................................ Generalized Model for Single-Lane Sites ....................................................................................................................... Generalized Model for Multilane Sites ........................................................................................................................... Control Delay ........................................................................................................................................................................ Level-of-Service Criteria.......................................................................................................................................................
10-61 10-61 10-62 10-62 10-62 10-63 10-63 10-64 10-64 10-67
iii.
procedures for application ................................................................................................................................................ Field Data Requirements....................................................................................................................................................... Geometric Features and Movement Definitions................................................................................................................... Volume Adjustment and Lane Assignment.......................................................................................................................... Saturation Headway Adjustment Factor ............................................................................................................................... Departure Headway and Service Time................................................................................................................................. Worksheet B4................................................................................................................................................................... Worksheet B4 Supplemental............................................................................................................................................ Capacity ................................................................................................................................................................................. Delay and Level of Service .................................................................................................................................................. Planning and Design Applications........................................................................................................................................
10-67 10-67 10-67 10-67 10-67 10-68 10-68 10-69 10-69 10-69 10-75
iv.
sample calculations ............................................................................................................................................................ Sample Calculation B1.......................................................................................................................................................... Sample Calculation B2.......................................................................................................................................................... Sample Calculation B3.......................................................................................................................................................... Sample Calculation B4..........................................................................................................................................................
10-75 10-75 10-77 10-77 10-78
v.
references .............................................................................................................................................................................. 10-81
PART C. ROUNDABOUTS ................................................................................................................................................................... 10-81 i.
introduction .......................................................................................................................................................................... Variables Used in Analysis of Roundabouts........................................................................................................................ Characteristics of Roundabouts............................................................................................................................................. Overview of Procedures ........................................................................................................................................................
ii.
methodology.......................................................................................................................................................................... 10-83
Updated December 1997
10-81 10-81 10-81 10-82
unsignalized intersections
10-3
Conceptual Approach ............................................................................................................................................................ 10-83 Capacity ................................................................................................................................................................................. 10-84 iii.
procedures for application ................................................................................................................................................ 10-84
iv.
sample calculations ............................................................................................................................................................ 10-87
v.
references .............................................................................................................................................................................. 10-89
PART A. TWO-WAY STOP-CONTROLLED INTERSECTIONS
I. INTRODUCTION In Part A, procedures for analysis of two-way stop-controlled (TWSC) intersections based on research sponsored by NCHRP (1) are discussed. A variety of terminology is introduced applying to the unique characteristics of TWSC intersection capacity and LOS analyses. For ease of reference, these terms are defined in the following section and are more fully described as they are used in the succeeding sections. VARIABLES USED IN ANALYSIS OF TWSC INTERSECTIONS
Capacity and Delay Parameters
cm,x = movement capacity of minor Movement x (veh/hr); cp,x = potential capacity of minor Movement x (veh/hr); cSH = capacity of shared lane (veh/hr); cT,x = total capacity for Movement x considering two-stage gap acceptance process; cI = capacity for Stage I of two-stage gap acceptance process; cII = capacity for Stage II of two-stage gap acceptance process; d = average control delay (sec/veh); dSH = average control delay for shared-lane case; dsep = average control delay for separate-lane case; dRank 1 = average control delay to Rank 1 vehicles; X = degree of saturation, or volume-to-capacity ratio; and T = length of study period (hr).
Critical Gap and Follow-Up Time Parameters
tc = critical gap, or minimum time interval in major-street traffic stream that allows intersection entry to one minorstream vehicle (sec); tf = follow-up time, or headway between departure of one vehicle from minor street and departure of next vehicle, using same major-stream gap during periods of continuous queueing on minor-street traffic stream (sec); tc,base = base critical gap; tc,HV = critical gap adjustment factor for heavy vehicles; tc,G = critical gap adjustment factor for grade; tc,T = critical gap adjustment factor for each part of two-stage gap acceptance process;
t3,LT = critical gap adjustment factor for intersection geometry (T-intersection); tf,base = base follow-up time (sec); and tf,HV = follow-up time adjustment factor for heavy vehicles.
Impedance Parameters
fp = pedestrian blockage factor; fx = capacity adjustment factor for Movement x that accounts for impeding effects of higher-ranked movements; p0,x = probability that conflicting Movement x will operate in queue-free state; p′ = adjustment to major-street left turn, minor-street through movement impedance factor; p″ = product of probabilities of queue-free states of Rank 1 and Rank 2 vehicles; and p*0,x = factor indicating probability that there will be no queue in shared lane for major-street Movements 1 and 4, where x is the particular movement being considered; this factor is used in lieu of p0,x where shared lanes for left-turn and through movements exist on major street; and sp = pedestrian walking speed (ft/sec).
Miscellaneous Intersection Characteristics
PHV = proportion of heavy vehicles; G = percent grade divided by 100; and w = lane width.
Movement Definitions
i = vehicle j = vehicle k = vehicle l = vehicle
movements movements movements movements
of of of of
Rank Rank Rank Rank
1; 2; 3; and 4.
Platoon Dispersion Model Parameters
g = effective green time of upstream signalized intersection; Updated December 1997
10-4
urban streets
gq = time required for queue to clear from upstream signal at beginning of green phase; F = (1 + abta)−1; a = platoon dispersion factor; b = dispersion factor, or (1 + a)−1; P = proportion of vehicles at upstream signalized intersection arriving during green; s = saturation flow rate for upstream signalized intersection; C = cycle length for upstream signalized intersection; ta = travel time from signalized intersection to subject TWSC intersection; vc,max = maximum platooned flow rate in conflicting stream; vc,u,x = conflicting flow for Movement x during unblocked period; tp,i = duration of blocked period for Movement i; px = proportion of time blocked for Movement x; cplat,x = capacity of subject Movement x accounting for effect of platooning; and N = number of major-street through lanes per direction.
Two-Stage Gap Acceptance and Flared Right-Turn Approach Parameters
m = number of vehicles that can be stored in median of intersection during two-stage gap acceptance process; n = number of vehicles that can be stored in flared right-turn approach; nmax = maximum value of n, number of vehicles that can be stored in flared right-turn approach above which it will operate like a separate-lane condition; a = adjustment factor for two-stage gap acceptance process; QSH = average queue length for shared-lane case for flared rightturn calculations; and Qsep = average queue length for separate-lane case for flared right-turn calculations.
Volume Parameters
Vx = volume for Movement x expressed in vehicles per hour for vehicular flows and pedestrians per hour for pedestrian flows; Vc,x = conflicting volume for Movement x, that is, total volume that conflicts with Movement x expressed in vehicles per hour or pedestrians per hour; vL = major left-turn flow rate; vr = shared-lane right-turn flow rate; vt = shared-lane through flow rate; vl = shared-lane left-turn flow rate; vSH = flow rate in shared lanes; used to compute capacity for flared right-turn approach; vsep = flow rate in separate lanes on minor-street approach; used to compute capacity for flared right-turn approach; and vprog = progressed flow rate from upstream signalized intersection to compute effect of upstream signals. OVERVIEW OF PROCEDURES
The procedures described in this chapter for the analysis of capacity and level of service of TWSC intersections represent a revision of the methodology published in the 1994 update of the Updated December 1997
1985 manual (2). The current procedures are based on a study of traffic operations at 79 TWSC intersections in the United States (1). New critical gaps and follow-up times are presented, and new weighting factors for conflicting flows are given. Adjustments are included in the procedures to take into account the effects of nonrandom flows (platoons from upstream signals), two-stage gap acceptance, flared minor-street approaches, pedestrians, and delay to major through movements. TWSC intersections, in which stop signs are used to assign the right-of-way, are the most prevalent type of intersection within the United States and abroad. At TWSC intersections, the stopcontrolled approaches are referred to as the minor-street approaches and can be either public streets or private driveways. The intersection approaches that are not controlled by stop signs are referred to as the major-street approaches. A three-leg intersection is considered to be a standard type of TWSC intersection as long as the single minor-street approach (i.e., the stem of the T-configuration) is controlled by a stop sign. Three-leg intersections in which two of the three approaches are controlled by stop signs represent a special form of unsignalized intersection control that is not addressed by the procedures described in this chapter. Some TWSC intersections have unusual operating characteristics. For example, there are situations in which one or more leftturning movements are allowed to travel unimpeded through the intersection and are given the right-of-way over opposing through movements. Although it is recognized that such operating conditions may legitimately and appropriately exist under special circumstances, they are relatively rare in practice, and are not addressed in this chapter. TWSC intersections as defined herein assign the right-of-way among conflicting traffic streams according to the following hierarchy: Rank 1. All conflicting movements yield the right-of-way to any through or right-turning vehicle on the major-street approaches. These major-street through and right-turning movements are hereafter referred to as the highest-priority movements at a TWSC intersection. Rank 2. (a) Vehicles turning left from the major street onto the minor street yield only to conflicting major-street through and right-turning vehicles. All other conflicting movements at a TWSC intersection yield to these major-street left-turning movements. (b) Vehicles turning right from the minor street onto the major street yield only to conflicting major-street through movements. Rank 3. Minor-street through vehicles yield to all conflicting major-street through, right, and left-turning movements. Rank 4. Minor-street left-turning vehicles yield to all conflicting major-street through, right, and left-turning vehicles, and also to all conflicting minor-street through and right-turning vehicles. Even though the hierarchy just described suggests that the highest-priority movements experience no delay as they travel through a TWSC intersection, experience shows that their right-of-way is sometimes preempted by other conflicting movements. Such preemptions most often occur during periods of congestion when vehicles in the conflicting movements are experiencing long delays and queues. The procedures described in this chapter include calculations to account for such preemptions. At TWSC intersections, drivers on the controlled approaches are required to use judgment in selecting gaps in the major-street flow through which to execute crossing or turning maneuvers. In the presence of a queue, each driver on the controlled approach must also use some measurable amount of time to move into the
unsignalized intersections front-of-queue position and get ready to evaluate gaps in the majorstreet flow. Thus, the capacity of the controlled legs is based on three factors: 1. 2. their 3.
The distribution of gaps in the major-street traffic stream, Driver judgment in selecting gaps through which to execute desired maneuvers, and The follow-up time required by each driver in a queue.
In the basic capacity model presented here it is assumed that gaps in the conflicting stream are randomly distributed. When traffic signals are within 0.25 mi upstream of the subject intersection on
10-5
the major street, flows may not be random but will likely have some platoon structure. A procedure is included in this chapter to account for this effect. Often the minor-street approaches to a TWSC intersection will be flared or there will be storage space in the median for vehicles crossing or merging with the major-street traffic streams. Procedures to account for the increase in capacity resulting from these conditions are included. Pedestrians may impede the flow of both major- and minorstream vehicles. Impedance equations are included to adjust for this effect.
II. METHODOLOGY CONCEPTUAL APPROACH
Capacity analysis at TWSC intersections depends upon a clear description and understanding of the interaction between drivers on the minor, stop-controlled approach and drivers or vehicles on the major street. Both gap acceptance and empirical models have been developed as a means to describe this interaction. The procedures described in this chapter rely upon a gap acceptance model developed and refined in Germany (3). Gap acceptance models begin with the recognition that TWSC intersections give no positive indication or control to the driver on the minor street as to when it is safe to leave the stop line and enter the major traffic stream. The driver must determine both when a gap in the major stream is large enough to permit safe entry and when it is his or her turn to do so on the basis of the relative priority of the competing traffic streams. This decisionmaking process has been formalized into what is commonly known as gap acceptance theory. Gap acceptance theory includes three basic elements: the size and distribution (availability) of gaps in the major traffic stream, the usefulness of these gaps to the minor-stream drivers, and the relative priority of the various traffic streams at the intersection. Availability of Gaps
The first element to consider in gap acceptance theory is the proportion of gaps of a particular size in the major traffic stream offered to the driver entering from the minor stream, as well as the pattern of interarrival times of vehicles. The distribution of gaps between vehicles in the different streams has a major effect on the performance of the intersection. Errors associated with the assumption of exponential interarrival times have been found to be compensated for by offsetting errors caused by the variations in actual critical gaps and follow-up times of individual drivers (3). Usefulness of Gaps
The second element is the extent to which drivers find gaps of a particular size useful when they are attempting to enter the intersection. It is generally assumed in gap acceptance theory that drivers are both consistent and homogeneous. In reality, this assumption is not entirely correct: past studies have demonstrated
that different drivers have different gap acceptance thresholds and even that the gap acceptance threshold of an individual driver changes over time (4). Therefore, it is appropriate for the purposes of this methodology to consider the critical gap and follow-up times as representative of a statistical average of the driver population. Under this assumption, the statistically representative driver is expected to behave in the same way every time under all similar situations.
Priority of Traffic Streams
The third element is the priority of right-of-way given to each traffic stream. Some streams have absolute priority, whereas others have to give way or yield to higher-order streams. Figure 10-1 illustrates the relative priority of streams at both T- and four-leg intersections. T Movements of Rank r = 1 (the ordinal rank, denoted by the subscript i in the remainder of this chapter) — Through traffic on the major street (Movements 2, 5) — Right-turning traffic from the major street (Movements 3, 6) — Pedestrians crossing the minor street (Movements 15, 16) T Movements of Rank r = 2 (subordinate to 1 and denoted by the subscript j in the remainder of this chapter) — Left-turning traffic from the major street (Movements 1, 4) — Right-turning traffic onto the major street (Movements 9, 12) — Pedestrians crossing the major street (Movements 13, 14) T Movements of Rank r = 3 (subordinate to 1 and 2 and denoted by the subscript k in the remainder of this chapter) — Through traffic on the minor street (in the case of a fourleg intersection) (Movements 8, 11) — Left-turning traffic from the minor street (in the case of a T-intersection) (Movement 7) T Movements of Rank r = 4 (subordinate to all and denoted by the subscript l in the remainder of this chapter; four-leg intersection only) — Left-turning traffic from the minor street (Movements 7, 10) For example, if a left-turning vehicle on the major street and a through vehicle from the minor street are waiting to cross the Updated December 1997
urban streets
10-6
Figure 10-1. Traffic streams at TWSC intersection: (a) four-leg intersection; (b) T-intersection.
major traffic stream, the first available gap (of acceptable size) would be taken by the major street’s left-turning vehicle. The minor-street through vehicle must wait for the second available gap. In aggregate terms, a large number of such left-turning vehicles could use up so many of the available gaps that minor-street through vehicles would be severely impeded or unable to make safe crossing movements. Right-turning vehicles from the minor street are not assumed to use up available gaps. Because such vehicles merely merge into gaps in the right-hand lane of the stream into which they turn, they require only a gap in that lane, not in the entire major-street traffic flow (this may not be true for some trucks and vans with long wheelbases, which encroach on more than one lane in making their turn). Further, a gap in the overall major-street traffic could be used simultaneously by a vehicle in an adjacent lane. For this reason, the methodology does not assume that right turns from the minor street impede any of the other flows using major-street gaps. Pedestrian movements also have priorities with respect to vehicular movements. Although this may be a policy issue that varies by jurisdiction, in both the Policy on Geometric Design of Highways and Streets (5) and the Manual on Uniform Traffic Control Devices (6), it is implied that pedestrians must use acceptable gaps in major-street (Rank 1) traffic streams and that pedestrians have priority over all minor-street traffic at a TWSC intersection. Specific rankings for pedestrian movements are shown in Figure 101 and are discussed later in this chapter (section on Conflicting Traffic). Updated December 1997
CAPACITY FORMULA
The gap acceptance method employed in these procedures was originally developed in Germany (7,8). The method computes the potential capacity of each minor traffic stream in accordance with the following equation: cp,x = vc,x
exp(−vc,xtc /3,600 ) 1 − exp(−vc,xtf /3,600)
(10-1)
where cp,x = potential capacity of minor Movement x (veh/hr); vc,x = conflicting flow rate for Movement x; tc = critical gap, or minimum time interval that allows intersection entry to one minor-stream vehicle (sec) for minor Movement x; and tf = follow-up time, or headway between departure of one vehicle from minor street and departure of next vehicle under continuous-queue conditions (sec) for minor Movement x.
STRUCTURE OF THE METHODOLOGY
The basic structure of the methodology is as follows: 1. Define existing geometric and traffic conditions for the intersection under study;
unsignalized intersections 2. Determine the conflicting traffic through which each minorstreet movement and the major-street left-turn movement must cross; 3. Determine the size of the gap in the conflicting traffic stream needed by vehicles in each movement crossing or merging into a conflicting traffic stream; 4. Determine the capacity of the gaps in the major traffic stream or the ability of these gaps to accommodate each of the subject movements that attempt to utilize these gaps; 5. Adjust the calculated capacities to account for impedance and the use of shared lanes; 6. Adjust the calculated capacities to account for the effect of upstream signals (platooning) on the major-street traffic flow headway distribution; 7. Adjust the calculated capacities to account for a two-stage gap acceptance process at intersections with raised or striped medians or two-way left-turn lanes; 8. Adjust the calculated capacities to account for flared minorstreet approaches; and 9. Estimate the average control delay and queue length for each of the subject movements and determine the level of service for each movement and for the intersection. Each of these analysis steps is discussed in detail in the sections that follow.
Input Data Requirements
Data requirements for the TWSC intersection methodology are similar to those for other capacity analysis techniques. Detailed descriptions of the geometrics, volumes, and control at the intersection are needed. Key geometric factors include 1. Number and use of lanes; 2. Channelization; 3. Two-way left-turn lane, raised or striped median storage, or both; 4. Approach grade; and 5. Flared approaches on the minor street. Each of these factors has a substantial effect on the basic capacity of each minor movement under any given conflicting volume level. The number and use of lanes are critical factors. Vehicles in adjacent lanes can use the same gap in the traffic stream simultaneously (unless impeded by a conflicting user of the gap). When movements share lanes, only one vehicle from those movements may use each gap. Channelization is also important because it can be used to reduce impedance by separating conflicting flows from each other. A two-way left-turn center lane, raised or stripped median, or both allow a minor-stream vehicle to cross one major traffic stream at a time. The approach grade has a direct and measurable effect on the capacity of each minor movement: relative to a level approach, downgrades increase capacity and upgrades decrease capacity. A flared approach on the minor street increases capacity by allowing more vehicles to be served simultaneously. Volumes must be specified by movement. For the analysis to reflect conditions during the peak 15 min, the analyst must divide the full-hour volumes by the peak-hour factor (PHF) before beginning computations. If the analyst has peak 15-min flow rates, these
10-7
flow rates can be entered directly with the PHF set to 1. The adjusted flow rate for Movement x is designated vx in this chapter. By convention, subscripts 1 to 6 are used to define vehicle movements on the major street and subscripts 7 to 12 to define movements on the minor street. Pedestrian flows impede all minorstreet traffic streams. Pedestrian volumes must be specified by movement, defined by subscripts 13 to 16. The presence of traffic signals upstream from the intersection on the major street will produce nonrandom flows and has an effect on the capacity of the minor-street approaches if the signal is within 0.25 mi of the intersection. The basic capacity model (Equation 10-1) assumes that the headways on the major street are exponentially distributed. To assess the effect of signals on capacity, a separate analysis is provided that requires the use of signalized-intersection data (cycle length, green time, saturation flow rate, and platooned flow from the signals).
Conflicting Traffic
The nature of conflicting movements for a TWSC intersection is relatively complex. Each subject movement faces a different set of conflicts directly related to the nature of the movement. These conflicts are shown in Figure 10-2, which illustrates the computation of the parameter vc,x, the conflicting flow for Movement x, that is, the total flow that conflicts with Movement x, expressed in vehicles per hour. The right-turn movement from the minor street, for example, is in conflict with the major-street through movement only in the right-hand lane into which right-turners will merge. Figure 10-2 includes half of the right-turn movement from the major street, because this flow has been found to have a somewhat inhibiting effect on the subject movement. This effect may be caused by major-street right-turning vehicles approaching without using their turn indicator, which causes the driver of a waiting vehicle to believe that the turning vehicle will travel straight through the intersection, or by side frictions created as they turn into a lane adjacent to waiting vehicles. Left turns from the major street are in absolute conflict with the total opposing through and right-turn flows, because they must cross the through flow and merge with the right-turn flow. The method does not differentiate between crossing and merging conflicts. Left turns from the major street and the opposing right turns from the major street are considered to merge regardless of the number of lanes provided in the exit leg of the intersection. Minor-street through movements have a direct crossing or merging conflict with all movements on the major street, as indicated in Figure 10-2, except the right turn into the subject approach. Only half of this movement is included in the computation, for the same reasons as those discussed above. In addition, field research (1) has shown that the effect of left-turning vehicles is twice their actual number; this is reflected in Figure 10-2. The left turn from the minor street is the most difficult maneuver to execute from a TWSC intersection, and it faces the most complex set of conflicting flows. Conflicting flows include all majorstreet flows, in addition to the opposing right-turn and through movement on the minor roadway. Only half of the opposing rightturn and through movement flow rate is included as conflicting because both movements are stop-controlled and thus their effect on the subject left-turn movement is diminished. The additional capacity impedance effects of the opposing right-turn and through Updated December 1997
10-8
urban streets
Figure 10-2. Definition and computation of conflicting volumes.
Updated December 1997
unsignalized intersections
10-9
Figure 10-2. (continued) Updated December 1997
10-10
urban streets
movement flow rates are taken into account elsewhere within the procedure. When Figure 10-2 is used to compute conflicting flow rates, the analyst should carefully consult the footnotes to the figure, which allow modifications to the equations shown in special cases. Note that in the equations in Figure 10-2, the conflicting traffic flow for Movement x, which is denoted vc,x, is computed in terms of an hourly flow rate of mixed vehicles per hour. Pedestrians may also conflict with vehicular traffic streams. Pedestrian movements should be included as part of the conflicting flow rates, since they, like vehicular flows, define the beginning or end of a gap that may be used by a minor-stream vehicle. Although this methodology recognizes some peculiarities associated with pedestrian flows, it takes a uniform approach to both vehicular and pedestrian movements at an intersection. Pedestrian flow rates are also defined as vx, with x denoting the leg of the intersection being crossed (Figure 10-1): T x = 15 denotes crossing of the minor-street approach serving Movements 7, 8, and 9; T x = 16 denotes crossing of the opposite minor-street approach serving Movements 10, 11, and 12; T x = 13 denotes crossing of the major-street approach serving Movements 1, 2, and 3; and T x = 14 denotes crossing of the major-street approach serving Movements 4, 5, and 6. Although regulations or practices may vary between jurisdictions, this methodology assumes that pedestrians crossing the subject approach or opposing approaches have Rank 1 status, whereas pedestrians crossing the two conflicting approaches to the left or right of the subject minor-street approach have Rank 2 status. The conflicting pedestrian flow rates are included in the equations shown in Figure 10-2. Figure 10-2 also identifies the conflicting flow rates for each stage of the two-stage gap acceptance process that takes place at some intersections. When a two-stage gap acceptance process is not present, the conflicting volumes shown for Stages I and II should be added and considered as one conflicting volume for the movement in question. Two-stage gap acceptance is discussed later in this chapter. Critical Gap and Follow-Up Time
The critical gap, tc, is defined as the minimum time interval in the major-street traffic stream that allows intersection entry to one minor-stream vehicle (9). Thus, the driver’s critical gap is the minimum gap that the driver finds acceptable. A particular driver would therefore reject any gaps less than this critical gap and would accept any gaps greater than or equal to this critical gap. This definition, although true, makes the critical gap difficult to estimate. In particular, it is impossible to measure the critical gap through simple field observations. However, estimates of the critical gap can be made on the basis of observations of the largest rejected gap and the accepted gap sizes for a given intersection. In most cases, the driver’s largest rejected gap must be less than the critical gap, and the driver’s accepted gap must be greater than or equal to the critical gap. That is, Largest rejected gap < driver’s critical gap ≤ accepted gap Even this relationship may not always be entirely true, because Updated December 1997
drivers may not always act consistently and may occasionally reject gaps of greater length than their accepted gap. The time span between the departure of one vehicle from the minor street and the departure of the next vehicle using the same major-street gap, under a condition of continuous queueing on the minor street, is called the follow-up time, tf. Put another way, tf is the headway that defines the saturation flow rate for the approach if there are no conflicting vehicles with movements of higher rank. Values of tc and tf for passenger cars are given in Table 10-1. These values are based on studies of 79 intersections throughout the United States and are believed to be representative of a broad range of conditions. Adjustments are made to account for the presence of heavy vehicles, approach grade, T-intersections, and two-stage gap acceptance. The critical gap is computed separately for each minor movement. tc = tc,base + tc,HVPHV + tc,GG − tc,T − t3,LT
(10-2)
where tc = critical gap tc,base = base critical gap from Table 10-1; tc,HV = adjustment factor for heavy vehicles: 1.0 for two-lane major streets and 2.0 for four-lane major streets; PHV = proportion of heavy vehicles for minor movement; tc,G = adjustment factor for grade: 0.1 for Movements 9 and 12 and 0.2 for Movements 7, 8, 10, and 11; G = percent grade divided by 100; tc,T = adjustment factor for each part of two-stage gap acceptance process: +1.0 for first or second stage, zero when only one-stage gap acceptance process; and t3,LT = adjustment factor for intersection geometry: 0.7 for minorstreet left-turn movement at three-leg intersection, 0 otherwise. The follow-up time is computed for each minor movement. Adjustments are made for the presence of heavy vehicles: tf = tf,base + tf,HVPHV
(10-3)
where tf = follow-up time; tf,base = base follow-up time from Table 10-1; tf,HV = adjustment factor for heavy vehicles: 0.9 for two-lane major streets and 1.0 for four-lane major streets; and PHV = proportion of heavy vehicles for minor movement. Values from Table 10-1 should apply for most typical intersections. It is conceivable that the actual values will differ from these representative figures at different sites. If smaller values for tc and tf are observed, they will lead to an increase in capacity in comparison with those values shown in Table 10-1. If larger values for tc and tf are used, the result will be a decrease in capacity. Empirical observations of maximum capacity (i.e., discharge rates from a minor approach with continuous queueing) as well as measurements of critical gaps and follow-up times should be used in such cases to calibrate the methodology to local conditions. In all cases, more accurate capacity estimates will be produced if field estimates can be made of the critical gap and follow-up time for the intersection under study. Although some previous studies have shown that factors relating to major-street speed and minor-stream sight distance may affect the critical gap, the findings by Kyte et al. (1) did not show these
unsignalized intersections
10-11
Table 10-1. Critical Gaps tc and Follow-Up Times tf for Passenger Cars at TWSC Intersections Critical Gap tc Vehicle Maneuver
Two-Lane Major Road
Four-Lane Major Road
Follow-Up Time tf
Left turn, major street Right turn, minor street Through traffic, minor street Left turn, minor street
4.1 6.2 6.5 7.1
4.1 6.9 6.5 7.5
2.2 3.3 4.0 3.5
effects. The effect on major-street speed is primarily one of distance. Drivers make their gap acceptance decisions based on distance, and this results in a time gap that is independent of speed. It should also be noted that the critical-gap data for multilane sites account for the actual lane distribution of traffic flows measured at each site. This distribution accounts for the higher value of critical gap for the minor-street right turn (6.9 sec) compared with the value for the minor-street through movement (6.5 sec), a result that at first glance may seem counterintuitive. Potential Capacity for Movement
The potential capacity of a movement is denoted cp,x (for Movement x) and is defined as the capacity under ideal conditions for a specific subject movement, assuming the following conditions: 1. Traffic from nearby intersections does not back up into the intersection under consideration; 2. A separate lane is provided for the exclusive use of each minor-street movement under consideration; 3. An upstream signal does not affect the arrival pattern of the major-street traffic; that is, the headways are exponentially distributed; and 4. No other movements of Rank 2, 3, or 4 impede the subject movement. Applying Equation 10-1 and using the values presented in Table 10-1, Figure 10-3 gives the potential capacity, cp,x, in vehicles per hour of the individual minor traffic streams for a two-lane major road and Figure 10-4 gives the potential capacity for a four-lane major road. It can be seen from Figures 10-3 and 10-4 that potential capacity is a function of conflicting flow vc,x expressed as an hourly rate, as well as a function of the particular minor-street movement being analyzed. Impedance Effects
Vehicle Impedance
It has been noted that vehicles use gaps at a TWSC intersection in a priority-ranked manner. When traffic becomes congested in a high-priority movement, it can impede lower-priority movements (i.e., streams of Ranks 3 and 4) from using gaps in the traffic stream and reduce the potential capacity of these movements. It should be noted that major-street traffic is not assumed to be impeded at any time by minor-street flows and that impedance effects apply only to minor-street vehicles. Major traffic streams of Rank 1 are assumed to be unimpeded by any of the minor traffic stream movements; this rank also implies that vehicles in the major traffic streams are not expected to incur any delay or slowing as they travel through the TWSC
intersection. Although empirical observations have shown that such delays do occasionally occur, it is important for the analyst to keep in mind that although these delays and slowing effects are not taken into account by the basic methodology, adjustments to estimate the extent of this effect are now included in the procedures (see the section Delay to Major-Street Through Vehicles). Minor traffic streams of Rank 2 (including left turns from the major road and right turns from the minor road) must yield only to the major-road through and right-turning traffic streams of Rank 1. There are no additional impedances from other minor traffic streams, and thus the movement capacity of each Rank 2 traffic stream is equal to its potential capacity: cm, j = cp, j
(10-4)
where j is movements of Rank 2 priority. Minor traffic streams of Rank 3 must yield not only to the major traffic streams, but also to the conflicting major-street left-turn movements, which are of Rank 2. Thus, not all gaps of acceptable length that pass through the intersection will normally be available for use by Rank 3 traffic streams, because some of these gaps are likely to be used by the major-street left-turning traffic instead. Rank 3 traffic streams are therefore impeded by major-street leftturning traffic. The magnitude of this impedance depends, of course, on the probability that major-street left-turning vehicles will be waiting for an acceptable gap at the same time as vehicles of Rank 3. A higher probability that this situation will occur means greater capacity-reducing effects of the major-street left-turning traffic on all Rank 3 movements. What is of interest to the analyst, therefore, is the probability that the major-street left-turning traffic will operate in a queuefree state. This probability can be expressed as vj p0, j = 1 − c m, j
(10-5)
where p0, j is the probability that conflicting Rank 2 movement j will operate in a queue-free state and j is 1, 4 (major-street leftturn movements of Rank 2). The movement capacity cm,k for all Rank 3 movements depends on calculation of a capacity adjustment factor that accounts for the impeding effects of higher-ranked movements. This capacity adjustment factor is denoted fk for all Movements k and for all Rank 3 movements can be expressed as fk =
pp
0, j
(10-6)
j
where k is the Rank 3 movement. The movement capacity for Rank 3 movements can then be computed as cm,k = (cp,k)fk
(10-7)
Rank 4 movements (i.e., minor-street left turns at a four-leg Updated December 1997
Figure 10-3. Potential capacity, two-lane roadway.
10-12
Updated December 1997
urban streets
10-13
Figure 10-4. Potential capacity, four-lane roadway.
unsignalized intersections
Updated December 1997
urban streets
10-14
intersection) have the potential to be impeded by the queues of three higher-ranked traffic streams: T Major-street left-turning traffic (Rank 2), T Minor-street through movements (Rank 3), and T Minor-street right-turning movements (Rank 2). As before, the probability that each of these higher-ranked traffic streams will operate in a queue-free state is central to determining their overall impeding effects on the minor-street left-turn movement. At the same time, it must be recognized that not all of these probabilities are independent of each other. Specifically, queueing in the major-street left-turning movement affects the probability of a queue-free state in the minor-street through movement. Applying the simple product of these two probabilities would likely overestimate the impeding effects of these two movements on the minor-street left-turning traffic. The curve in Figure 10-5, based on empirical and theoretical work conducted in Germany (3), can be used to adjust for the overestimate caused by the statistical dependence between queues in streams of Ranks 2 and 3. The mathematical representation of this curve, the validity of which was ascertained through simulation, is given by
p′ = 0.65p″ −
p″ + 0.6√p″ p″ + 3
where p′ = adjustment to major-street left, minor-street through movement impedance factor; p″ = (p0,j)(p0,k); p0,j = probability of queue-free state for conflicting major-street left-turning traffic; and p0,k = probability of queue-free state for conflicting minor-street crossing traffic. Figure 10-5 is entered on the horizontal axis with the value of p″ as defined in Equation 10-8. A vertical line is drawn to the curve, and a horizontal line is then drawn from the intersection with the curve to the vertical axis, where the result, p′, is read. The capacity adjustment factor for the Rank 4 minor-street leftturn movements can then be computed as follows: fl = ( p′)( p0,j)
(10-9)
where l is the minor-street left-turn movement of Rank 4 [i.e., Movement 7 or 10 in Figure 10-1 (a)] and j is the conflicting Rank
Figure 10-5. Adjustment to major left-turn, minor-through impedance factor (3). Updated December 1997
(10-8)
unsignalized intersections 2 minor-street right-turn movement [i.e., Movement 9 or 12 in Figure 10-1(a)]. Finally, the movement capacity for Rank 4 minor-street leftturn movements can be determined from the following equation: cm,l = cp,l fl
Table 10-3. Pedestrian Impedance Factors Vehicle Stream
Pedestrian Impedance Factor, pp,x
v1 v4 v7 v8 v9 v10 v11 v12
pp,16 pp,15 pp,15 · pp,13 pp,15 · pp,16 pp,15 · pp,14 pp,16 · pp,14 pp,15 · pp,16 pp,16 · pp,13
(10-10)
Pedestrian Impedance
Minor-street traffic streams must yield to pedestrian streams. Table 10-2 shows the relative hiearchy between pedestrian and vehicular streams that is assumed in this procedure. Pedestrian groups crossing an intersection thus impede lowerranked minor-street vehicles, but only one lane at a time because drivers performing a given through or turning movement tend to pass in front of or behind pedestrians once a target lane is clear. Pedestrian flows are counted somewhat differently than vehicle flows. If the typical pattern is for pedestrians to cross individually, each pedestrian should be counted individually in the pedestrian flow. However, if pedestrians tend to cross in groups, the number of groups should be counted in the pedestrian flow. The important factor is to determine the number of blockages that occur. In most cases, this number will be a combination of individual pedestrians and groups of pedestrians. Thus, as defined for the purposes of determining the pedestrian impedance, the pedestrian volume is the sum of individual pedestrians crossing individually and groups of pedestrians crossing together during the time period of study. A factor accounting for pedestrian blockage is computed on the basis of the pedestrian volume, the pedestrian walking speed, and the lane width: (vx)(w/sp) 3,600
fp =
(10-11)
where
10-15
Equation 10-9 becomes fl = p′p0, j pp, x
(10-14)
where pp,x takes on the value pp,13 · pp,15 for v7 and pp,14 · pp,16 for v10. Shared-Lane Capacity
Up to this point, the methodology has assumed that each minorstreet movement has the exclusive use of a lane. This geometric scenario is often not the case, and frequently two or three movements share a single lane on the minor approach. When this geometric scenario occurs, vehicles from different movements do not have simultaneous access to gaps, nor can more than one vehicle from the sharing movements use the same gap. Occasionally, an intersection with wide corner radii or a flared approach will allow vehicles approaching in the same lane to stop side by side. This geometric effect, which acts to reduce or eliminate the adverse impact of the shared lane, is considered in a later section (see Flared Minor-Street Approaches). Minor-Street Approaches
fp = pedestrian blockage factor, or proportion of time that one lane on an approach is blocked during 1 hr; vx = pedestrian flow rate, where x is 13, 14, 15, or 16; w = lane width; and sp = pedestrian walking speed, assumed to be 4 ft/sec.
When several movements share the same lane and cannot stop side by side at the stop line of the intersection, the following equation is used to compute the capacity of the shared lane: cSH =
The pedestrian impedance factor for pedestrian movement x, pp,x, is pp,x = 1 − fp
(10-12)
If pedestrians are present to a significant degree, pp,x is included as a factor in Equations 10-6 and 10-9. Equation 10-6 becomes fk =
p (p
)pp,x
(10-13)
0, j
j
where pp,x takes on the values shown in Table 10-3.
Table 10-2. Relative Pedestrian-Vehicle Hierarchy Vehicle Stream
Must Yield to Pedestrian Stream
v1 v4 v7 v8 v9 v10 v11 v12
v16 v15 v15, v13 v15, v16 v15, v14 v16, v14 v15, v16 v16, v13
vl + v t + v r vl vt vr cm,l + cm,t + cm,r
1 2 1 2 1 2
(10-15)
where cSH = capacity of shared lane (veh/hr), vl = volume or flow rate of left-turn movement in shared lane (veh/hr), vt = volume or flow rate of through movement in shared lane (veh/hr), vr = volume or flow rate of right-turn movement in shared lane (veh/hr), cm,l = movement capacity of left-turn movement in shared lane (veh/hr), cm,t = movement capacity of through movement in shared lane (veh/hr), and cm,r = movement capacity of right-turn movement in shared lane (veh/hr). Only those movements included in the shared lane are included in the equation. For example, if the shared lane includes only rightturn and through movements, both numerator and denominator terms for left-turners are deleted in the equation. Updated December 1997
urban streets
10-16 Major-Street Approaches
It is important to remember that the methodology implicitly assumes that an exclusive lane is provided for all left-turning traffic from the major street. In situations where a left-turn lane is not provided, it is possible for major-street through (and possibly rightturning) traffic to be delayed by left-turning vehicles waiting for an acceptable gap. To account for this possibility, the factors p*0,1 and p*0,4 may be computed as an indication of the probability that there will be no queue in the respective major-street shared lanes: p*0, j = 1 −
1 − p0, j v v 1 − i1 + i2 si1 si2
1
2
(10-16)
where p0, j = probability of queue-free state for movement j assuming exclusive left-turn lane on major street; j = 1,4 (major-street left-turning traffic streams); i1 = 2,5 (major-street through traffic streams); i2 = 3,6 (major-street right-turning traffic streams); si1 = saturation flow rate for major-street through traffic streams (veh/hr), which is a parameter that can be measured in the field; si2 = saturation flow rate for major-street right-turning traffic (veh/hr), which can be measured in the field; vi1 = major-street through flow rate in shared lane; and vi2 = major-street right-turning flow rate in shared lane, or 0 if exclusive right-turn lane is provided. By using p*0,1 and p*0,4 in lieu of p0,1 and p0,4 (as computed from Equation 10-5), the additional influence of the potential for queues on a major street with shared left-turn lanes may be properly taken into account.
Upstream Signals
The existence of nearby upstream signalized intersections (i.e., traffic signals on the major street within 0.25 mi of the subject intersection) usually causes vehicles to arrive at the subject intersection in platoons. Major-street vehicles arriving at a TWSC intersection in platoons from a single direction may cause an increase in the minor-street capacity compared with the case of random arrivals. The greater the number of vehicles traveling in platoons, the higher the minor-street capacity for a given opposing flow because there is a greater proportion of large gap sizes that can be used by more than one minor-street vehicle. When signalized intersections exist upstream of the subject TWSC intersection in both directions, the effect is much more complex. When a traffic signal is more than 0.25 mi from the subject intersection, the effect on capacity is greatly diminished, since the major-street gaps are once again negative-exponentially distributed as the platoons disperse. The method described here considers the flow patterns that result from traffic signals located upstream of the subject TWSC intersection and the headway distribution that results from the platooned flow. The method is based on a platoon dispersion algorithm (10– 12). Figure 10-6 shows a generalized case of a TWSC intersection located on an arterial between two signalized intersections. The queues that form during the respective red phases at each signalized Updated December 1997
intersection will disperse as the vehicles travel downstream away from the signalized intersection. Four flow regimes, and thus four headway distributions, result as the platoons arrive at the subject intersection: T T T T
Regime Regime Regime Regime
1: 2: 3: 4:
no platoons, platoon from the left only, platoon from the right only, and platoons from both directions.
During Regime 1, minor-stream vehicles enter the subject TWSC intersection as described by the traditional gap acceptance process. When platoons are present from both directions, during Regime 4, no minor-stream vehicles are able to enter the subject intersection since the mean headways of the platoon are assumed to be less than the critical gap. Some of the minor-stream movements are blocked by the platoon during Regimes 2 and 3, and are unable to enter the subject intersection. A minor stream is considered to be blocked if a conflicting platoon is traveling through the TWSC intersection; the stream is considered to be unblocked if no conflicting platoons are traveling through the TWSC intersection. If the traffic signals at the two upstream intersections are coordinated, these patterns are predictable and occur at regular intervals during the hour. On the basis of the flow pattern that exists during each regime, the capacity can be estimated. If one or both of the signals are actuated, or if the signal cycle lengths are different, the patterns are less predictable. The analyst needs the following data for each upstream signal: T Cycle length (sec); T Effective green time (sec) for the major-street through movement and, if applicable, for the exclusive left-turn phase from the minor street; T Saturation flow rate in vehicles per hour of green (veh/hrg); T Distance from the signalized intersection to the subject TWSC intersection; T Speed of the platoon as it progresses from the signalized intersection to the TWSC intersection; T Through flow rate arriving at the signalized intersection on the major-street approach and, if applicable and significant, the left-turn flow rate from the side street during an exclusive leftturn phase; and T Arrival type of vehicles at the signalized intersection. The method includes five sets of computations: 1. Time for the queue to clear at each upstream signalized intersection, 2. Proportion of time that the subject TWSC intersection is blocked as a result of platoons from each upstream intersection, 3. Duration of the defining platoon events for each of the four flow regimes, 4. Conflicting flows during each unblocked period, and 5. Weighted capacity for each movement. Computation 1: Time for Queue To Clear at Each Upstream Signalized Intersection
In a typical four-leg signalized intersection, three movements combine to constitute the exit-leg flow toward the subject TWSC intersection: the through movement on the major street and the right- and left-turn movements from the minor street. In addition, the exit-leg flow consists of two components: (a) a stable platoon discharging at the saturation flow rate when the
unsignalized intersections
10-17
Figure 10-6. Platoon dispersion from upstream signalized intersections.
The proportion of vehicles arriving on the green is computed as follows: P = Rp(g/C)
P ≤ 1.0
(10-17)
where Rp is the platoon ratio, a function of the arrival type (Table 9-2). The time to discharge the vehicles that arrive during the red is given by gq1 =
vprogC(1 − P) s
(10-18)
where vprog is either vT or vL,prot. The time to discharge the vehicles that arrive on the green and join the back of the queue is given by Figure 10-7. Upstream signalized intersection.
signal changes from red to green, and (b) more or less random arrivals and departures of a platoon from another upstream signal passing through on the green. The first component includes both the portion of vT that arrives during the red and the portion that arrives during the green when the standing queue is clearing. It also includes vL for the same periods if vL has an exclusive leftturn lane and a protected green phase (see Figure 10-7). The second component includes vR and the portion of vT (and vL, if applicable) that arrives after the queue has cleared. The time that it takes for a standing queue to clear is dependent on the pattern of vehicles arriving at the upstream signalized intersection. The arrival pattern, designated ‘‘arrival type’’ in Chapter 9 of this manual, is determined by the proportion of vehicles arriving during the green phase. For vT, the arrival type ranges from 1 (very poor progression; few vehicles arrive on the green) to 6 (exceptional progression; most vehicles arrive on the green in a structured platoon). For vL,prot it is assumed to be 3 (random arrivals).
gq2 =
vprogCPgq1 sg − vprogCP
(10-19)
where vprog is either vT or vL,prot. The total time to discharge the queue is gq = gq1 + gq2
(10-20)
where gq is less than or equal to g. Computation 2: Time Subject TWSC Intersection Blocked Because of Upstream Platoons
The discharging queue from the upstream signal will disperse as it travels downstream toward the subject TWSC intersection. A platoon dispersion model is used to determine the time duration during which the TWSC intersection is blocked by the densest part of the platoon. The platoon headways are smaller than the critical gap, and thus no minor movement at the TWSC intersection can enter the intersection during passage of the platoon (see Figure 10-8). The basic platoon dispersion model parameters are as follows: a = platoon dispersion factor obtained from Table 10-4; Updated December 1997
urban streets
10-18
Figure 10-8. Platoon dispersion model [adapted from Bonneson and Fitts (12)].
Table 10-4. Platoon Dispersion Factor, a (12, 1) No. of Through Traffic Lanes Median Type
N=1
N=2
N=3
Undivided Raised curb TWLTL
0.55 0.45 0.40
0.50 0.40 0.35
0.40 0.35 0.30
The duration of the blocked period for either the through movement or the protected left-turn movement is computed using the following equation, where ‘‘ln’’ indicates the natural logarithm:
5
tp,i = gq − 0
b = (1 + a) ; ta = D/Sprog, travel time from signalized intersection to subject TWSC intersection, where D is distance from upstream signal to subject movement and Sprog is average platoon running speed; F = (1 + abta)−1; and f = vprog/vc ≥ 0 and ≤ 1, proportion of conflicting flow that originated at upstream signal, where vprog is either vT when the platoon generated by the through movement is considered or vL,prot when the platoon generated by the protected leftturn movement from the minor street is considered.
ln
311 −
21
vc,min vc,max − vprog Rp f sf vc,min − vprog Rp f ln(1 − F)
24
vc,max > vc (10-22)
vc,max ≤ vc,min
−1
The maximum platooned flow rate in the conflicting stream is given by g
vc,max = sf[1 − (1 − F) q]
(10-21)
The minimum platooned flow rate, vc,min, is at least larger than 3,600N/tc, where N is the number of through lanes per direction on the major street. By default, it is assumed to be equal to 1,000N veh/hr on the basis of simulation data (12). Updated December 1997
with all variables defined earlier. Note that the variables vc,min, vc,max, s, and vprog must be in the same units, either vehicles per hour or vehicles per hour per lane. The subscript i is set to T when the blocked period caused by the through-movement platoon is computed; the subscript is set to L when the blocked period caused by the protected left-movement platoon is computed. The proportion of time blocked is computed using the following equation, considering both the through movement and the protected left-turn movement platoons: p=
tp,T + tp,L C
(10-23)
Computation 3: Platoon Event Periods
The purpose of the third computation is to determine the proportion of the study period during which each of the four flow regimes exists. In particular, it is important to determine, for each minor movement, the proportion of the study period that is unblocked.
unsignalized intersections The existence of a traffic signal on both upstream approaches will result in an overlapping platoon structure at the subject TWSC intersection. Depending on the signal timing parameters, a range of cases may present themselves, from a best case of simultaneous platoons from both directions to a worst case of alternating platoons from each direction. An average case results in a partial overlap of the platoons (Figure 10-9). Figure 10-9 can also be interpreted to represent the expected pattern averaged over the analysis period. The method described here is based on the average case. If p2 and p5 represent the proportion of the study period during which Movements 2 and 5, respectively (and their corresponding turning movements), are blocking the TWSC intersection, the proportion of the study period during which blockages exist can be computed. The dominant and subordinate platoons are determined: pdom = max(p2, p5)
(10-24)
psubo = min(p2, p5)
(10-25)
Two conditions exist. In the unconstrained condition, there is some period of time during which neither platoon is present: pdom + (psubo /2) ≤ 1
(10-26)
for each minor movement. The results for each minor movement for the average case are shown in Table 10-6. Computation 4: Conflicting Flows During Each Unblocked Period
The flow for the unblocked period (that is, the time periods when no platoons are present) is determined. This flow becomes the conflicting flow for the subject movement and is used to compute the capacity for this movement. The conflicting flow for Movement x during the unblocked period is given by vc,u,x =
vc,x − s(1 − px) px
(10-28)
where vc,x > s (1 − px); vc,u,x is zero otherwise; and vc,x = total conflicting flow for Movement x as determined from Figure 10-2;
Table 10-6. Proportion of Study Period Unblocked for Each Minor Movement for Average Case Proportion Unblocked for Movement, px
The constrained condition exists when one or both platoons are always present: pdom + (psubo /2) > 1
10-19
(10-27)
Table 10-5shows the proportion of the study period for each of the four flow regimes for the average case. It is used to determine the proportion of the study period that is blocked and unblocked
p1 p4 p7 p8 p9 p10 p11 p12
Unconstrained Condition
1− 1− 1− 1−
1 − p5 1 − p2 (pdom + psubo /2) (pdom + psubo /2) 1 − p2 (pdom + psubo /2) (pdom + psubo /2) 1 − p5
Constrained Condition 1 − p5 1 − p2 0 0 1 − p2 0 0 1 − p5
Figure 10-9. Various platoon overlap cases: best case—platoons completely overlap so unplatooned period is maximum; worst case— platoons alternate so unplatooned period is minimum; average case—one-half of subordinate platoon is subsumed by dominant platoon.
Table 10-5. Proportion of Study Period for Each Flow Regime for Average Case Flow Regime 1, 2, 3, 4,
no platoons dominant platoon only subordinate platoon only both platoons
Unconstrained Condition
Constrained Condition
1 − (pdom + psubo /2) pdom − psubo /2 psubo /2 psubo /2
0 1 − psubo 1 − pdom pdom + psubo − 1 Updated December 1997
urban streets
10-20
s = total saturation flow rate for that movement, which is conflicting flow for Movement x during blocked period; and px = proportion of time that subject Movement x is unblocked by major-street platoon, determined from Table 10-6. Computation 5: Capacity for Subject Movement During Unblocked Period
The capacity of subject Movement x, accounting for the effect of platooning, is given by cplat,x = pxcr,x
(10-29)
where px is the proportion of time that Movement x is unblocked by a platoon and cr,x is the capacity of Movement x assuming random flow during the unblocked period, using the conflicting flow vc,u,x computed for this unblocked period and Equation 10-1.
Two-Stage Gap Acceptance
The existence of a raised or striped median or a two-way leftturn lane (TWLTL) on the major street often causes some degree of a special gap acceptance phenomenon known as two-stage gap acceptance. For example, the existence of a raised or striped median allows a significant proportion of the minor-street drivers to cross part of the major-street approach first and then to pause in the middle of the road to wait for a gap on the other approach. When a TWLTL exists on the major street, the minor-street leftturning vehicle usually merges into the TWLTL first and then seeks a usable gap on the other approach while slowly moving for some distance along the TWLTL. Both of these behaviors can contribute to increased capacity. In this procedure, the intersection is assumed to consist of two parts with the minor-street traffic crossing the major street in two stages. Between partial intersections I and II there is storage space for m vehicles. This area has to be passed by the left-turner from the major street (Movement V1 or V4) and the minor through or left-turn traffic. It is assumed that the usual rules for TWSC intersections are applied by drivers at the intersections. Thus the major through traffic has priority over all other movements. For example, Movement 1 (or Movement 4) vehicles must give way to priority Movement 5 (or Movement 2), whereas Movement 7 or 8 (or Movements 10 and 11) has to give the right-of-way to all other movements (see Figure 10-10). The conflicting volumes are defined for each minor-stream movement that uses the two-stage gap acceptance process using Figure 10-2 for both the first-stage and second-stage movements. For the first stage, the conflicting flows consist of the major-street flows from the left. For the second stage, the conflicting flows consist of the major-street flows from the right. The specific streams that are included in each conflicting flow are shown in Figure10-2. First, the capacity for the subject movement is computed assuming a single-stage gap acceptance process through the entire intersection. Next the capacity for Stage I, cI, and the capacity for Stage II, cII, are computed using the appropriate values of critical gap and follow-up time for the two-stage gap acceptance process using Equations 10-2 and 10-3: c1 is the capacity considering conflicting flows vc,I, and cII is the capacity considering conflicting flows vc,II (Figure 10-2). Updated December 1997
Figure 10-10. Intersection with two-stage gap acceptance process. The capacity for the subject movement considering the twostage gap acceptance process is computed as follows. An adjustment factor a and an intermediate variable y are computed: a = 1 − 0.32 exp(−1.3√m) y=
cI − cm,x cII − vL − cm,x
for m > 0
(10-30) (10-31)
where m = number of storage spaces in the median; cI = capacity for Stage I process, Equation 10-1; cII = capacity for Stage II process, Equation 10-1; vL = major left-turn flow rate, either v1 when considering Movement 1, 2, or 3 or v4 when considering Movement 4, 5, or 6; and cm,x = capacity of subject movement considering total conflicting volume for both stages of two-stage gap acceptance process, Equation 10-1. The total capacity cT of the intersection for the subject movement considering the two-stage gap acceptance process is computed. For y ≠ 1: cT =
a [y(y m − 1)(cII − vL) + (y − 1)cm,x] (10-32) ym+1 − 1
unsignalized intersections For y = 1: cT =
a [m(cII − vL) + cm,x] m+1
(10-33)
Flared Minor-Street Approaches
Geometric elements near the stop line on stop-controlled approaches of many intersections may result in a greater capacity than may be predicted by the shared-lane capacity formula because at such approaches two vehicles may occupy or depart from the stop line simultaneously as a result of a large curb radius, a tapered curb, or a parking prohibition. The magnitude of this effect will depend in part on the turning-movement flow rates and the resultant probability of there being two vehicles simultaneously at the stop line and in part on the storage length available to feed the second position at the stop line. If n is defined as the number of spaces for passenger cars belonging to one movement that can queue at the stop line without obstructing the access to the stop line for other movements, it is clear that with n > 0, the capacity of the minor-street approach is increased compared with that in the shared-lane condition. With an increase in n, the total capacity approaches the case in which each movement has its own individual lane of infinite length. Figure 10-11 shows a situation in which the curb lane provides space for
10-21
two vehicles to proceed, one beside the other, to the stop line. In this case, the storage can be defined as n = 1, since one additional vehicle is able to use the stop line. The actual capacity resulting from this configuration will be greater than that in the case in which the right-turning vehicles must share the lane and less than that in the case in which the vehicles have separate lanes. The analyst must compute the average queue length for each movement considering the separate-lane case and the actual storage available in the flared-lane area for the intersection approach under study. Figure 10-11 shows how the actual capacity can be interpolated using this information. First, the average queue length for each movement sharing the right lane of the approach is computed, assuming that each movement operates as a separate lane. The movement with the maximum average queue length is identified: Qsep =
dsepvsep 3,600
(10-34)
where Qsep = average queue length for movement considered as a separate lane, dsep = average control delay for movement considered as a separate lane, and vsep = flow rate for movement. Next, the required length of the storage area is computed such that the approach would operate effectively as separate lanes. This length is the maximum value of the queue lengths computed for each separate movement plus one vehicle length: nmax = max round(Qsep,i + 1)
(10-35)
i
where Qsep,i = average queue length for Movement i in the shared lane considered as separate lane; round = round-off operator, rounding quantity in parentheses to nearest integer; max = operator determining maximum value of various values of Qsep,i; and nmax = length of storage area such that approach would operate as separate lanes. Finally, the capacity of the approach is computed, taking the flare into account. The capacity is interpolated, as shown in Figure 10-11. A straight line is established using values of two points: (csep, nmax) and (cSH, 0). The interpolated value of cact is computed using the following equation: cact = =
1o c i
oc i
sep
sep
2
n − cSH n + cSH max
when n ≤ nmax (10-36) when n > nmax
where cact = actual capacity of flared approach, csep = capacity for separate-lane case, and cSH = capacity of shared-lane case. Queue Lengths
Figure 10-11. Capacity approximation at intersections with flared minor-street approach.
Queue length estimation is an important consideration at unsignalized intersections. Theoretical studies and empirical observaUpdated December 1997
10-22
urban streets
Figure 10-12. Estimation of 95th-percentile queue length.
tions have demonstrated that the probability distribution function for queue lengths for any minor movement at an unsignalized intersection is a function of the capacity of the movement and the volume of traffic being served during the analysis period. Figure 10-12 can be used to estimate the 95th-percentile queue length for any minor movement at an unsignalized intersection during the peak 15-min period on the basis of these two parameters (13). The mean queue length is computed as the product of the average delay per vehicle and the flow rate for the movement of interest. The expected total delay (in vehicle hours per hour) equals the expected number of vehicles in the average queue; that is, the total hourly delay and the average queue are numerically identical. For example, 4 vehicle-hr/hr of delay can be used interchangeably with an average queue length of 4 during the hour. Updated December 1997
Control Delay
The delay experienced by a motorist is made up of a number of factors that relate to control, geometrics, traffic, and incidents. Total delay is the difference between the travel time actually experienced and the reference travel time that would result during conditions with ideal geometrics and in the absence of incidents, control, and traffic. Chapters 9 and 10 of this manual quantify only that portion of total delay attributed to traffic control measures, either traffic signals or stop signs. This delay is called control delay and its use is consistent in Chapters 9, 10, and 11. Control delay includes initial deceleration delay, queue move-up time, stopped delay, and final acceleration delay. Although the methodology here results in an estimate of average control delay, it is recommended that, where possible under ex-
unsignalized intersections isting conditions, estimates of average control delay also be obtained through field measurements. Average control delay for any particular minor movement is a function of the capacity of the approach and the degree of saturation. The analytical model used to estimate control delay (Equation 10-37) assumes that demand is less than capacity for the period of analysis. In situations where the degree of saturation is greater than about 0.9, average control delay is significantly affected by the length of the analysis period. In most cases, the recommended analysis period is 15 min, or 0.25 hr. If demand exceeds capacity during a 15-min period, the delay results calculated by the procedure may not be accurate. In this case, the period of analysis should be lengthened to equal the period of oversaturation. d=
3,600 + 900T cm,x
3 !
vx −1+ × cm,x
1
2
4
1 c 21c 2 3,600
2 vx −1 + cm,x
m,x
450T
vx
m,x
10-23
In the simplest procedure, the proportion of major-street Rank 1 vehicles not being blocked (i.e., in a queue-free state) is given by p*0,j in Equation 10-16 (p*0, j should be substituted for the major left-turn factor p0, j in Equation 10-6 when the capacity of lowerranked conflicting movements is calculated). Therefore, the proportion of Rank 1 vehicles being blocked is 1 − p*0, j. The average delay to Rank 1 vehicles on this approach is given by
dRank 1 =
5
(1 − p*0, j) (dM,LT) v j,1 + vi,2
(1 − p*0, j)(dM,LT)
1N2 vi,1
N>1 (10-38) N=1
where dRank 1 = delay to Rank 1 vehicles; +5 (10-37)
where d = average control delay (sec/veh); vx = volume for Movement x, expressed as hourly flow rate; cm,x = capacity of Movement x, expressed as hourly flow rate; and T = analysis time period (hr) (for 15-min analysis period, use T = 0.25). The final term, a constant value of 5 sec/veh, is included in Equation 10-37 to account for the deceleration of the vehicle from cruise speed to the speed of the vehicles in the queue and the acceleration of the vehicle from the stop line to cruise speed. Equation 10-37 is depicted graphically in Figure 10-13 for a discrete range of capacities and a 15-min analysis period.
Delay to Major-Street Through Vehicles
Traffic engineers are also interested in knowing the effect of a shared lane on the major-street approach where left-turning vehicles may block Rank 1 through or right-turning vehicles. If no exclusive left-turn pocket is provided on the major street, a delayed left-turning vehicle may block the Rank 1 vehicles behind it and cause them some delay. This effect delays not only Rank 1 vehicles, but also lower-ranked streams. When the delayed Rank 1 vehicles are discharged from the queue formed behind a major left-turning vehicle, they impede lower-ranked movements with which they conflict. In this section the impedance for major-street left-turning vehicles in a shared lane is used to estimate delay to Rank 1 vehicles. Field observations have shown that the effect of such a blockage is usually very small because the major street provides enough space for the blocked Rank 1 vehicle to sneak around the leftturning vehicle. Models could be developed from a theoretical point of view when the major-street width does not allow a through vehicle to bypass the left-turning vehicle. At a minimum, incorporating this effect requires the following information: 1. The proportion of Rank 1 vehicles being blocked, and 2. The average delay to the major-street left-turning vehicles that are blocking through vehicles.
p*0, j = proportion of Rank 1 vehicles not blocked (Equation 10-16); dM,LT = delay to major-street left-turning vehicles; vi,1 = flow rate of major-street through vehicles in shared lane; and vi,2 = flow rate of major-street right-turning vehicles in shared lane. Note that on a multilane road, only the major-street volumes in the lane that may be blocked should be used in the calculation as vi1 and vi2. On multilane roads if it is assumed that blocked Rank 1 vehicles do not bypass the blockage by moving into other through lanes (a reasonable assumption under conditions of high majorstreet flows), then vi1 = v1/N. Because of the unique characteristics associated with each site, the decision whether to account for this effect should be left to the analyst. Geometric design features such as an adjacent exclusive right-turn lane, a large curb radius, or a wide shared left and through travel lane may enable Rank 1 vehicles to bypass the blockage caused by major left-turning vehicles. Also, conflicting traffic volumes in such adjacent bypass lanes must provide sufficient gaps to accept bypassing vehicles.
Other Relevant Delay Estimates
Frequently it is also useful for the analyst to be aware of the average control delay per vehicle for an entire approach and for the entire intersection. These parameters are important to consider when estimates of delay under various types of traffic control are compared. The average approach delay for all vehicles on a particular approach can be computed as the weighted average of the control delay estimates for each individual movement on the approach: dA =
dRTvRT + dTHvTH + dLTvLT vRT + vTH + vLT
(10-39)
where dA = average approach control delay (sec/veh); dRT, dTH, dLT = computed average control delay for right-turn, through, and left-turn movements, respectively (sec/veh); and vRT, vTH, vLT = volume or flow rate of right-turn, through, and left-turn approach traffic, respectively (veh/hr). Updated December 1997
urban streets
Figure 10-13. Average control delay.
10-24
Updated December 1997
unsignalized intersections Similarly, the average intersection control delay can be computed: dintx =
dA,1vA,1 + dA,2vA,2 + dA,3vA,3 + dA,4vA,4 vA,1 + vA,2 + vA,3 + vA,4
(10-40)
where dA,x is the average approach control delay on Approach x (sec/veh), and vA,x is the volume or flow rate on Approach x (veh/ hr). If the effects of delay to major-street through vehicles, as calculated using Equation 10-38, are not be included in the analysis, the delay for all major-street movements of Rank 1 is assumed to be zero seconds per vehicle. LEVEL-OF-SERVICE CRITERIA
The level of service for a TWSC intersection is determined by the computed or measured control delay and is defined for each minor movement. Level of service is not defined for the intersection as a whole. LOS criteria are given in Table 10-7. Average control delay less than 10 sec/veh is defined as LOS A. Follow-up times of less than 5 sec/veh have been measured when there is no conflicting traffic for a minor-street movement, so control delays of less than 10 sec/veh are appropriate for low flow conditions. The proposed LOS criteria for TWSC intersections are somewhat different than the criteria used in Chapter 9 of this manual for signalized intersections. The primary reason for this difference is that drivers expect different levels of performance from different kinds of transportation facilities. The expectation is that a signalized intersection would be designed to carry higher traffic volumes than an unsignalized intersection. In addition, a number of driver behavior considerations combine to make delays at signalized intersections less onerous than delays at unsignalized intersections. For example, drivers at signalized intersections are able to relax during the red interval, whereas drivers on the minor approaches to unsignalized intersections must remain attentive to the task of identifying acceptable gaps and vehicle conflicts. Also, there is often much more variability in the amount of delay experienced by individual drivers at an unsignalized intersection versus that at signalized intersections. For these reasons, it is considered that the control delay threshold for any given level of service would be less for an unsignalized intersection than it would be for a signalized intersection. INTERPRETATION OF RESULTS
Shared Lanes on Minor Approach
A movement, most often a left-turn movement, can sometimes have a poorer level of service if it is given a separate lane than if it shares a lane with another movement (usually a through move-
Table 10-7. Level-of-Service Criteria Level of Service A B C D E F
Delay Range >10 >15 >25 >35
≤10 and ≤15 and ≤25 and ≤35 and ≤50 >50
10-25
ment). This is not inconsistent in terms of the stated criteria. Leftturn movements will generally experience longer control delays than other movements because of the nature and priority of the movement. If left turns are placed in a shared lane, the average control delay to vehicles in that lane may indeed be less than the average control delay to left turns in a separate lane. However, all vehicles in the shared lane experience increased control delay over the condition in which left turns have a separate lane. Consider the following: 1. Ten left-turners will experience an average control delay of 10 sec if they have a separate lane and 15 sec if they share a lane with a through movement. 2. Fifty through vehicles will experience an average control delay of 5 sec if they have a separate lane and 6 sec if they share a lane with the 10 left-turners. If the vehicles are forced to share a lane, the average control delay to a vehicle in the shared lane will be [(10 × 15) + (50 × 6)] 450 = = 7.5 sec/veh (10 + 50) 60
(10-41)
Table 10-8 illustrates this comparison. Although each vehicle experiences increased control delay when placed in a shared lane, the average control delay in the shared lane is less than the average control delay to left-turners in an exclusive lane and more than the average control delay to through vehicles in an exclusive lane. Thus, the level of service in the exclusive left-turn lane may be poorer than that for the shared lane. The analyst, however, may wish to carefully consider the aggregate impact on control delay. In general, expanding a one-lane stop-controlled approach to include an exclusive left-turn or right-turn lane will decrease the approach control delay, regardless of LOS designations. Consideration of Queue Lengths
LOS F exists when there are insufficient gaps of suitable size to allow side-street demand to safely cross through a major-street traffic stream. This level of service is generally evident from extremely long control delays experienced by side-street traffic and by queueing on the minor-street approaches. The method, however, is based on a constant critical gap size; that is, the critical gap remains constant no matter how long the side-street motorist waits. LOS F may also appear in the form of side-street vehicles selecting smaller-than-usual gaps. In such cases, safety may be a problem, and some disruption to the major traffic stream may result. It is important to note that LOS F may not always result in long queues but may result in adjustments to normal gap acceptance behavior, which are more difficult to observe in the field than queueing. In most cases at TWSC intersections the critical movement is the minor-street left-turn movement. As such, the minor-street leftturn movement can generally be considered the primary factor affecting overall intersection performance. The lower threshold for LOS F is set at 50 sec of delay per vehicle. There are many instances, particularly in urban areas, in which the delay equations will predict delays of 50 sec (LOS F) or more for minor-street movements under very low volume conditions on the minor street (less than 25 veh/hr). Since the first term of the equation is a function only of the capacity, the LOS F threshold of 50 sec/veh is reached with a movement capacity of approximately 85 veh/hr or less. Updated December 1997
urban streets
10-26
Table 10-8. Example Left-Turn Delay Calculation Separate-Lane Case
Shared-Lane Case
Movement
Volume (veh)
Control Delay/Vehicle (sec/veh)
Cumulative Control Delay (sec)
Control Delay/Vehicle (sec/veh)
Cumulative Control Delay (sec)
LT
10
10
100
15
150
TH
50
5
250
6
Total
350
Total
6 7.5
300 450
Figure 10-14. Queue-versus-delay relationship.
This procedure assumes random arrivals on the major street. For a typical four-lane arterial with average daily traffic volumes in the range of 15,000 to 20,000 vehicles per day (peak hour, 1,500 to 2,000 veh/hr), the delay equation used in the TWSC capacity analysis procedure will predict 50 sec of delay or more (LOS F) for many urban TWSC intersections that allow minorstreet left-turn movements. The LOS F threshold will be reached regardless of the volume of minor-street left-turning traffic. Notwithstanding this fact, most low-volume minor-street approaches would not meet any of the volume or delay warrants for signalization of the Manual on Uniform Traffic Control Devices (MUTCD) since the warrants define an asymptote at 100 veh/hr on the minor approach. As a result, many public agencies that use the HCM level of service thresholds to determine the design adequacy of TWSC intersections may be forced to eliminate the minor-street left-turn movement, even when the movement may not present any operational problem, such as the formation of long queues on the minor street or driveway approach. This point is illustrated more clearly in Figure 10-14, which presents plots of average delay and average queue lengths for an individual movement with volume-to-capacity ratios varying from 0.2 to 1.4. The points on each of the v/c lines are for volumes Updated December 1997
ranging from a low of 10 veh/hr to a high of 700 veh/hr. As can be seen from Figure 10-14, the current LOS F threshold of 50 sec/ veh based solely on average delay can be exceeded under many low-volume, low-v/c, and low-queue conditions. Of concern is the region (denoted Region 2) that includes v/c ratios less than 1.0 and average delays greater than 50 sec. In this region, the average queue length is typically fewer than one vehicle, which indicates that, although drivers would likely experience relatively long delays, it is unlikely that long queues would form because of the low demand volumes. There are also conditions in which average delays will be less than 50 sec/veh but drivers will be faced with very long queues, as can be seen on the far right of Region 1 in Figure 10-14. This would represent conditions in which there is a long queue that is being served relatively fast. Region 3 includes volume-to-capacity ratios greater than 1.0. In this region drivers would be faced with extremely long queues, extremely long delays, or both. In the performance evaluation of TWSC intersections, it is important to consider other measures of effectiveness (MOEs) in addition to delay, such as v/c ratios for individual movements, average queue lengths, and 95th-percentile queue lengths. By focusing on a single MOE for the worst movement only, such as
unsignalized intersections delay for the minor-street left turn, users may make inappropriate traffic control decisions. The potential for making such inappropriate decisions is likely to be particularly pronounced when the HCM level of service thresholds are adopted as legal standards, as is the case in many public agencies. A number of important implications result from the use of average delay as the sole basis for determining level of service, particularly when only the worst movement at the intersection is considered. One of the primary motivations for using average delay as the primary MOE as opposed to reserve capacity (as was done in the 1985 HCM) was to provide the user community with a more direct and consistent way to compare unsignalized and signalized intersection operations. In doing so, however, it is important for users to understand that there are other operational indicators that must be considered as well as average delay.
DETERMINATION OF INTERSECTION CONTROL TYPE
Determination of an appropriate control for an intersection, either signal control or some form of stop control, is now made by integrating information from several sources. Traffic signal warrants, LOS analyses, accident data, and public complaints form the basis for a decision to signalize an intersection or to change to stop control. Three documents, among others, are available to assist the traffic engineer in this assessment: the MUTCD, the ITE Traffic Engineering Handbook (TEH) (14), and the HCM. The MUTCD provides a set of warrants to help determine the appropriate conditions for signalization, two-way stop control, or all-way stop control. The following 11 signal warrants are provided in the MUTCD: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
Minimum vehicular volume, Interruption of continuous traffic, Minimum pedestrian volume, School crossings, Progressive movement, Accident experience, Systems, Combination of warrants, Four-hour volumes, Peak-hour delay, and Peak-hour volume.
Although only one of these warrants is required to be met before a signal is recommended, traffic engineers should ideally consider all these aspects when making a decision regarding an intersection
10-27
control type. This set of warrants represents guidance based on collective professional consensus accumulated over many decades. Practicing traffic engineers can refer to these warrants whenever issues arise regarding decisions on intersection control types. The TEH points out that traffic signals do not always increase safety and reduce delay. Therefore, it is not appropriate to install signals regardless of the traffic volume conditions. The TEH cites the following warrants for all-way stop control (from the MUTCD): 1. As an interim measure that can be installed quickly while arrangements are being made for a warranted traffic signal; 2. When an accident problem, as indicated by five or more reported accidents in a 12-month period, is of a type that can be corrected using a multiway stop and less restrictive controls have not been successful; and 3. For the following minimum traffic volumes: (a) the total vehicle volume entering the intersection from all approaches averages at least 500 veh/hr for any 8 hr of an average day, and (b) the combined vehicular and pedestrian volume from minor streets averages at least 200 units/hr for the same 8 hr with an average delay to minor-street traffic of at least 30 sec/veh during the maximum hour [but when the 85th-percentile approach speed of the major-street traffic exceeds 40 mph, minimum volume warrants are 70 percent of the requirement in (a)]. Regarding traffic signal warrants, the TEH states: ‘‘Traffic signals that are appropriately justified, properly designed, and effectively operated can be expected to achieve one or more of the following: 1. To effect orderly traffic movement through an appropriate assignment of right-of-way, 2. To provide for the progressive flow of a platoon of traffic along a given route, 3. To interrupt heavy traffic at intervals to allow pedestrians and cross-street traffic to cross or to enter the main street flow, 4. To increase the traffic handling ability of an intersection, or 5. To reduce the frequency of occurrence of certain types of accidents.’’ The HCM provides methodologies to compute delay and level of service based on certain traffic volume and intersection conditions given both stop control and signal control. With the development of new models and procedures of estimating capacity and delay at stop-controlled intersections, it is now possible to compare different intersection control types from an operational perspective.
III. PROCEDURES FOR APPLICATION The analysis of TWSC intersections is generally applied to existing locations either to evaluate existing operational conditions under present demands or to estimate the impacts of anticipated new demands. The methodology is specifically structured to yield a level of service and an estimate of average control delay for an existing or planned TWSC intersection. Thus, operational analysis is the mode in which it is used. Design applications are treated as trial-and-error computations based on anticipated improvements
to an existing intersection or on the projected design of a new intersection. The procedures, however, are easily manipulated to investigate the impact of key design features on probable operations. Figure 10-15 shows the procedures, which are divided into three separate modules. In the first module, Initial Calculations, the analyst uses Worksheets A1 through A4 to record input conditions and to compute the critical gap and follow-up time. Worksheets Updated December 1997
10-28
urban streets
Figure 10-15. TWSC intersection capacity and LOS computational procedures.
Updated December 1997
unsignalized intersections A5 through A9 form the second module, Capacity Calculations, to compute the capacity of each movement and make adjustments for the effects of upstream signals, two-stage gap acceptance, shared lanes, or flared minor-street approaches. The third module, Delay and LOS Calculations, includes worksheets to compute the delay, queue length, and level of service for the intersection. FIELD DATA REQUIREMENTS
As noted previously, computations require several types of data as inputs to the methodology, including 1. Vehicle volumes by movement for the period of interest; 2. Vehicle classification for the period of interest; 3. Peak-hour factor (if peak flow rates are being used as the basis for analysis); 4. Number and use of lanes on the major-street approaches; 5. Number and use of lanes on the minor-street approaches; 6. Grade of all approaches; and 7. Other geometric features of interest, such as channelization, two-way left-turn lane, raised or striped median, and flared approach. To determine the effects of pedestrians, two-way left-turn lanes, raised or striped medians, upstream signals, and flared approaches on capacity and level of service, the following data are also required: 1. Pedestrian volumes by movement for the period of interest; 2. Number of vehicles that can be stored in the median; 3. Number of vehicles that can be stored in the flared minorstreet approaches; 4. Distance to upstream signals on the major street; and 5. Other data relating to upstream signals that are within 0.25 mi of the subject intersection: cycle length, green time, saturation flow rate, and platooned flow.
SEQUENCE OF COMPUTATIONS FOR CAPACITY
Since the methodology is based on prioritized use of gaps by vehicles at a TWSC intersection, it is important that computations be made in a precise order. The computational sequence is the same as the priority of gap use, and movements are considered in the following order: 1. 2. 3. 4.
Right turns from the minor street; Left turns from the major street; Through movements from the minor street; and Left turns from the minor street.
To assist in maintaining the proper order of computations, worksheets are provided. The use of each of these worksheets in the computations is described in the following sections. Capacity Adjustments
The standard gap acceptance capacity model makes several key assumptions regarding the geometry and flow characteristics of the intersection, including a negative exponential distribution of headways for the major-street traffic flow (‘‘random arrivals’’), single-stage gap acceptance process, and no impedance from pe-
10-29
destrians. The procedure includes computations that account for the effects of these factors.
Geometric Features and Movement Definitions
Worksheet A1 shows the basic features of the intersection and the movements of interest. The intersection name, analyst’s name, count date, and time period are entered on this form. A north orientation arrow is also entered on this form. The major-street vehicle flows are denoted v1 through v6, minorstreet vehicle flows are denoted v7 through v12, and pedestrian flows are denoted v13 through v16. The two upstream signals are denoted S2 and S5, corresponding to the through vehicle streams that arrive at the subject intersection from the direction of these two signalized intersections. Median storage may be present in the center of the intersection; flared approaches may also be present on the two minor-stream approaches.
Volume Adjustment
Vehicle and pedestrian flows are entered in Worksheet A2. Measured or forecast vehicle volumes (in vehicles per hour) are entered on Line 1 of the worksheet. The flows should be carefully entered because subsequent worksheets refer to these flows by their movement number to ease computations. The peak-hour factor is entered on Line 2 for each movement. The equivalent hourly flow rate is computed for each movement by dividing the volume by the peak-hour factor and entering the result on Line 3. The proportion of heavy vehicles (PHV) for the minor movement is entered on Line 4. Pedestrian flows are entered on Line 5 for each movement. The average lane width for each approach is entered on Line 6. The average walking speed for pedestrians in the area is entered on Line 7; a suggested default value is 4.0 ft/sec. The percent blockage for each approach is computed using Equation 10-11 and is entered on Line 8.
Site Characteristics
Lane designation data for each approach are entered into the first section of Worksheet A3. For example, if Movements 1, 2, and 3 all share a single lane and there are no other lanes on the approach, the string ‘‘1,2,3’’ would be entered in the ‘‘Lane 1’’ column on Line 1. The grade for each approach is also entered here. If the right turn is channelized, this is noted. If the minor-street approaches have flared lanes that can store right-turning vehicles, this should be noted on Lines 5 and 6. The number of storage spaces should also be entered. If there is storage in the median, this should be noted on Lines 7 and 8. The number of storage spaces should also be entered. If there is an upstream signalized intersection within 0.25 mi of the intersection on the major street, this should be noted on Lines 9 and 10. The effective green time (in seconds), the cycle length (in seconds), the progression speed, and the distance to the signal (in feet) should be entered on Lines 9 and 10. The saturation flow rate (in vehicles per hour of green) and the through flow rate arriving at the upstream signalized intersection on the major-street Updated December 1997
urban streets
10-30
approach and the protected left-turn movement from the side street should also be entered on Lines 9 and 10. If the analyst needs to compute the delay to major-street vehicles resulting from sharing a lane with major-street left-turning vehicles, relevant data are entered on Lines 11 through 15. The length of the study period is entered on Line 16. Critical Gap and Follow-up Time
Table 10-1 and Equations 10-2 and 10-3 are used to compute the critical gap and follow-up time. The base values of the critical gap are entered on Line 1 of Worksheet A4 for each movement. The adjustment factors for heavy vehicles (1.0 sec for two-lane major streets and 2.0 sec for four-lane major streets) are entered on Line 2. The proportion of heavy vehicles for each movement (from Line 4 of Worksheet A2) is entered on Line 3. The adjustment factor for approach grade (0.1 for Movements 9 and 12 and 0.2 for Movements 7, 8, 10, and 11) is entered on Line 4. The grade in percent/100 (from Lines 1 through 4, Worksheet A3) is entered on Line 5. The adjustment factor for minor-street left turns at T-intersections is entered on Line 6. For single-stage gap acceptance computations, tc,T is zero. For two-stage gap acceptance computations, tc,T is 1 sec. This is entered on Line 7. The critical gap for each movement, entered on Lines 8 or 9, is computed from Line 1 + (Line 2 × Line 3) + (Line 4 × Line 5) − Line 6 − Line 7 The base value of the follow-up time is entered on Line 10 of Worksheet A4 for each movement. The heavy-vehicle adjustment factor (0.9 sec for two-lane major streets and 1.0 sec for four-lane major streets) is entered on Line 11. The proportion of heavy vehicles for each movement is entered on Line 12. The follow-up time, entered on Line 13, is computed as the sum of Line 10 and the product of Lines 11 and 12: (Line 10) + (Line 11 × Line 12)
Effect of Upstream Signals
Worksheets A5a through 5e are used to compute the flow patterns that result from upstream signalized intersections that are within 0.25 mi of the subject TWSC intersection. Worksheet A5a is used to determine the length of time required for the queue to clear from the upstream signalized intersection for both the through movement and the protected left-turn movement. Signalized intersection parameters (progressed volume, total saturation flow rate, arrival type, effective green time, cycle length) are entered on Lines 1 through 5. The platoon ratio, Rp, is determined from Table 9-2 and entered on Line 6. The proportion of vehicles arriving on the green, P, is computed using Equation 1017 and entered on Line 7. The length of time for the queue to clear is computed using Equations 10-18 through 10-20 and entered on Lines 8, 9, and 10. Worksheet A5b is used to determine the proportion of the time that the subject TWSC intersection is blocked by the passing platoon from the upstream signalized intersection. The platoon disperUpdated December 1997
sion parameters are entered on Lines 1 through 5. The maximum flow during the platooned period is computed using Equation 1021 and entered on Line 6. The minimum flow during the platooned period (default = 1,000N) is entered on Line 7. Note that tpi = 0 if vc,max is less than 1,000N. The duration of the blocked period, tp, is computed using Equation 10-22 and is entered on Line 8. The proportion of time blocked, p, considering both the through movement and the protected left-turn movement, is computed using Equation 10-23 and is entered on Line 9. Worksheet A5c is used to determine the platoon event periods and the proportion of time that is unblocked for each minor-stream movement. The proportion of time blocked as a result of each platoon, p2 and p5, is entered on Lines 1 and 2, respectively. The dominant and subordinate platoons are computed using Equations 10-24 and 10-25, and are entered on Lines 3 and 4, respectively. Equations 10-26 and 10-27 are used to determine if the condition is unconstrained (i.e., there is some time during which no platoons are present) or constrained (i.e., one or more platoons are always present). The proportion of time that is unblocked is determined for each minor movement, px, using Table 10-6 and is entered on Lines 6 through 13 in Column 1. Note that if the subject intersection includes a two-stage gap acceptance process, the computations for Stages I and II are entered separately on Lines 6 through 13 in Columns 2 and 3. Worksheet A5d is used to compute the conflicting flows during the unblocked period for each minor movement. The first panel in Worksheet A5d is used for a single-stage gap acceptance process; the second panel is used for a two-stage gap acceptance process. The conflicting flow, vc,x, is entered on Line 1. The total saturation flow s is entered on Line 2. The proportion of time that is unblocked is determined from Lines 6 through 13 of Worksheet A5c for each minor movement, px, and entered on Line 3. The conflicting flow for Movement x during the unblocked period, vc,u,x, is computed using Equation 10-28 and is entered on Line 4. Worksheet A5e is used to determine the capacity for the subject movement during the unblocked period. The first panel in Worksheet A5e is used for a single-stage gap acceptance process; the second panel is used for a two-stage gap acceptance process. The proportion of time that is unblocked is determined from Lines 6 through 13 of Worksheet A5c for each minor movement, px, and is entered on Line 1. The capacity for Movement x during the unplatooned period (assuming random flow), cr,x, is computed using Equation 10-1 and is entered on Line 2. The capacity of the subject Movement x accounting for the effect of platooning is computed using Equation 10-29 and is entered on Line 3. The capacity computed here is the potential capacity for the movement. It is used in Worksheet A6 (and Worksheet A7, if twostage gap acceptance is present).
Computations of Impedance and Movement Capacities
The capacity for each movement is computed using Worksheet A6. Volumes are keyed to the diagram in Worksheet A1. Computations proceed in the prescribed order, considering first the right turns from the minor street, followed by left turns from the major street, through movements from the minor street, and left turns from the minor street. The user should solve parts of movements before proceeding to the next step; that is, both right turns in Step 1 should be computed before the user proceeds to Step 2.
unsignalized intersections For each movement, the following sequence of computations is used: 1. Compute conflicting flows, vc,i, in vehicles per hour. Figure 10-2 may be consulted if a further explanation of this computation is desired. 2. Use Equation 10-1 to find the potential capacity, cp,i, in vehicles per hour if there is no upstream signal. Use Worksheet A5e to find the potential capacity if there is an upstream signal. 3. Compute the pedestrian impedance factor using Equation 10-12. 4. Compute the probability of a queue-free state for the majorstreet left-turn movements and minor-street through and right-turn movements using Equation 10-5. 5. Compute the capacity adjustment factor due to impeding movements, fi, for the minor-street through and left-turn movements using Equation 10-9 or 10-14 and Figure 10-5. 6. The movement capacity, cm,i, is computed as the product of the potential capacity, cp,i, and the capacity adjustment factor due to impeding movements, fi. Note that if the problem involves a two-stage gap acceptance process, Worksheets A7a and A7b must be used for Steps 3 and 4 in place of Steps 3 and 4 from Worksheet A6. Two-Stage Gap Acceptance
Worksheets A7a and 7b are used to compute the capacity for a two-stage gap acceptance process for the through and left-turn movements from the minor street. The procedure requires that the analyst compute parameters both for each stage of the two-stage gap acceptance case and for the single-stage case (as if no median were present). The results from both cases are combined to yield the increase in capacity that results from the two-stage gap acceptance process. Steps 3 and 4 from Worksheets A7a and A7b are used in place of Steps 3 and 4 from Worksheet A6. For the minor through movement (Step 3), Worksheet A7a is used. The analyst computes the conflicting flows, the potential capacity, the pedestrian impedance factor, the capacity adjustment factor, the movement capacity, and the probability of a queue-free state and enters the results on Lines 1 through 6 for the first stage of the gap acceptance process and on Lines 7 through 11 for the second stage. The same computations are completed for the singlestage process (as if there were no median storage) and the results are entered on Lines 12 through 16. Parameters a and y are computed using Equations 10-30 and 10-31 and are entered on Lines 17 and 18. Either Equation 10-32 or 10-33 is used to compute the movement capacity for the two-stage process. The result is entered on Line 19. For the minor left-turn movement (Step 4), Worksheet A7b is used. The analyst computes the conflicting flows, the potential capacity, the pedestrian impedance factor, the capacity adjustment factor, and the movement capacity and enters the results on Lines 1 through 5 for the first stage of the gap acceptance process. For the second stage, the analyst computes the conflicting flows, the potential capacity, the pedestrian impedance factor, the capacity adjustment factor, and the movement capacity and enters the results on Lines 6 through 10. These same parameters are computed for the single-stage process; the results are entered on Lines 11 through 17. Parameters a and y are computed using Equations 10-30 and 10-31 and are entered on Lines 18 and 19. Either Equation 10-32
10-31
or Equation 10-33 is used to compute the movement capacity for the two-stage process. The result is entered on Line 20. Note that if upstream signals are present, the results from Worksheet A5e are used as the potential capacities for Steps 3 and 4.
Shared-Lane Capacity
Worksheet A8 is used to compute the shared-lane capacity. The equation for this computation (Equation 10-15) is given on Worksheet A8.
Effect of Flared Minor-Street Approaches
Worksheet A9 is used to compute the effect of flared minorstreet approaches. Although three columns are provided on the worksheet (for either Movements 7, 8, and 9 or Movements 10, 11, and 12), only those movements that share the right lane on the subject approach are included in the computation. The movement capacity, or the capacity for the separate-lane case, csep, is entered on Line 1 for each of the movements that occupy the right lane. The flow rate and delay for each of these movements are entered on Lines 2 and 3, respectively. The average queue length for each movement is computed using Equation 1034 and entered on Line 4. The value on Line 4 is increased by 1 and entered on Line 5. The value on Line 5 is rounded to the nearest integer and entered on Line 6. The value of nmax is computed using Equation 10-35 and entered on Line 7. The shared-lane capacity for the movements that share the right lane is computed using Worksheet A8 and entered on Line 8. The sum of the separate lane capacities (Line 1) is computed and entered on Line 9. The number of storage spaces in the flare is entered on Line 10. The actual capacity of the flared approach is computed using Equation 10-36 and entered on Line 11.
Average Control Delay, Queue Length, and Level of Service
Worksheet A10 is used to compute average control delay, average queue length, and level of service. The flow rate and the capacity for each minor movement are entered on Lines 1 and 2. The v/c ratio is entered on Line 3. The queue length is computed from Figure 10-12 and entered on Line 4. The control delay for the movement is computed using Equation 10-37 and entered on Line 5. The level of service is determined from Table 10-7 and entered on Line 6. The approach delay and level of service are entered on Lines 7 and 8. Worksheet A11 is used to compute the delay to Rank 1 vehicles. The probability of a queue-free state for Movement j is computed using Equation 10-5 and entered on Line 1. The major-street through and right-turn volumes in the lane shared with the leftturn movement are entered on Lines 2 and 3, respectively. The saturation flow rates for the major-street through and right-turn movements are entered on Lines 4 and 5. The probability of a queue-free state in the major-street shared lane is computed using Equation 10-16 and entered on Line 6. The computed delay for the major-street left-turn movement is entered on Line 7. The number of major-street through lanes is entered on Line 8. The delay to Rank 1 vehicles is computed using Equation 10-38 and entered on Line 9. Updated December 1997
10-32
urban streets
PLANNING AND DESIGN APPLICATIONS
The operational analysis method described earlier in this chapter provides a detailed procedure to evaluate the performance of a TWSC intersection. Sometimes, however, an analyst may wish to estimate the level of service for a long-term time horizon. This kind of analysis is called a planning-level analysis. It is expected that for such an analysis only a limited amount of input data is available. The planning analysis method described here is based on the operational analysis method and requires geometric data and traffic flow data. The base values of critical gap and follow-up time from Table 10-1 are used. The effects of upstream signals, two-stage gap acceptance, and flared right-turn approaches are normally not accounted for in a planning analysis. However, if these data are available and the project under study includes these elements, their effects can be included. The planning analysis uses the same worksheets as does the operational analysis, with some exceptions: T Worksheet A1 is used to describe basic conditions. T Worksheet A2 is used to summarize vehicle volumes. Pedestrian volumes are not generally used in a planning analysis. If estimates of the pedestrian volumes are available, these data can also be used in Worksheet A2. T Worksheet A3 is used to note the lane designation for each movement. Generally, the corrections for flared minor-street ap-
Updated December 1997
proach, median storage, and upstream signals are not included in a planning analysis. T Worksheet A4 is generally not used, since the base values from Table 10-1 are used without adjustment. T Worksheets A5a–A5e are not used, since the effect of upstream signals is generally not included in a planning analysis. T Worksheet A6 is used to compute the movement capacities. T Worksheets A7a and A7b may be used to include the effects of two-stage gap acceptance when the effects of a divided roadway or the addition of two-way left-turn lanes are to be considered on the major street. T Worksheet A8 is used to compute shared-lane capacities if more than one movement shares the same minor-street approach. T Worksheet A9 is not used, since the effect of flared minorstreet approaches is generally not included in a planning analysis. T Worksheet A10 is used to compute control delay, queue length, and level of service. T Worksheet A11 is not used, since the impedance and delay for the major through movements are not accounted for in a planning analysis. The operational analysis procedure described earlier in this chapter is not normally used for design purposes. However, through iteration, the analyst can use a given set of traffic flow data and determine the number of lanes that would be required to produce a given level of service.
unsignalized intersections
10-33
WORKSHEET A1: BASIC INTERSECTION INFORMATION
Updated December 1997
10-34
urban streets
WORKSHEET A2: VOLUME ADJUSTMENT
Updated December 1997
unsignalized intersections
10-35
WORKSHEET A3: SITE CHARACTERISTICS
Updated December 1997
10-36
urban streets
WORKSHEET A4: CRITICAL GAP AND FOLLOW-UP TIME CALCULATION
Updated December 1997
unsignalized intersections
10-37
WORKSHEET A5a: EFFECT OF UPSTREAM SIGNALS (COMPUTATION 1)
WORKSHEET A5b: EFFECT OF UPSTREAM SIGNALS (COMPUTATION 2)
Updated December 1997
10-38
urban streets
WORKSHEET A5c: EFFECT OF UPSTREAM SIGNALS (COMPUTATION 3)
Updated December 1997
unsignalized intersections
10-39
WORKSHEET A5d: EFFECT OF UPSTREAM SIGNALS (COMPUTATION 4)
Updated December 1997
10-40
urban streets
WORKSHEET A5e: EFFECT OF UPSTREAM SIGNALS (COMPUTATION 5)
Updated December 1997
unsignalized intersections
10-41
WORKSHEET A6: IMPEDANCE AND CAPACITY CALCULATIONS
Updated December 1997
urban streets
10-42
WORKSHEET A7a: COMPUTATION OF EFFECT OF TWO-STAGE GAP ACCEPTANCE (STEP 3)
Updated December 1997
unsignalized intersections
10-43
WORKSHEET A7b: COMPUTATION OF EFFECT OF TWO-STAGE GAP ACCEPTANCE (STEP 4)
Updated December 1997
10-44
urban streets
WORKSHEET A8: SHARED-LANE CALCULATIONS
Updated December 1997
unsignalized intersections
10-45
WORKSHEET A9: COMPUTATION OF EFFECT OF FLARED MINOR-STREET APPROACHES
Updated December 1997
10-46
urban streets
WORKSHEET A10: DELAY, QUEUE LENGTH, AND LEVEL OF SERVICE
WORKSHEET A11: SHARED MAJOR LT IMPEDANCE AND DELAY
IV. SAMPLE CALCULATIONS Six sample calculations that illustrate the application of the TWSC methodology are given in this section. The first example is a three-leg intersection with stop control on the minor leg. It illustrates the basic steps involved in applying the methodology. The second example extends this analysis to include an examination of the effects of combining the westbound through and leftturn lanes. The third example focuses on a four-leg intersection with multiple-lane approaches on the major street. This situation is further examined in Sample Calculations A4 through A6, in which the effects of upstream signals, variations in geometric configuration, right-turn flaring on the minor approaches, and twostage gap acceptance are explored. Updated December 1997
SAMPLE CALCULATION A1
Sample Calculation A1 illustrates the TWSC capacity analysis methodology for a three-leg (T-) intersection.
Description
Sample Calculation A1 concerns the intersection of Market and Jones streets in an urban area with a population of 100,000 (Figure 10-16). Market Street is a two-lane collector with an exclusive left-turn lane on the westbound approach to the intersection,
unsignalized intersections
10-47
Figure 10-16. Traffic volumes for Sample Calculation A1. whereas Jones Street is a two-lane, stop-controlled local street serving a residential development. There is no widening in the vicinity of the intersection, so adjustments for right-turn flaring are not appropriate. Area residents have complained that there is substantial total delay for drivers turning right onto Market Street in the late afternoon. Residents claim that this is due to the need for right- and left-turners to share a lane and have requested that a right-turn-only lane be provided. The following discussion illustrates the capacity analysis of this example problem. Solution
Steps 1 and 2: Use Worksheets A1 and A2 to enter basic data and traffic flow volumes. The diagram in Worksheet A1 contains the volumes and turning movements by approach. This information for Sample Calculation A1 is presented in Figure 10-16. Line 1 on Worksheet A2 again requires the vehicle volumes by movement, and entries are made on Line 2 for PHF. In this example, PHF = 1.00, which means that the hourly flow rates on Line 3 are identical to the volumes on Line 1. The proportion of heavy vehicles is entered on Line 4, which in this case is 10 percent. Lines 5–8 pertain to pedestrian volumes and adjustments; however, such data were not recorded in this sample calculation. Step 3: Use Worksheet A3 for site characteristics. Lines 1–4 of Worksheet A3 are used to describe the geometry of the intersection. In this example, since both the eastbound and northbound approaches have only one lane each, Movements 2 and 3 and Movements 7 and 9 appear in the column labeled ‘‘Lane 1’’ on Lines 1 and 3, respectively. However, since the westbound approach has an exclusive left-turn lane, Movement 4 is entered under ‘‘Lane 1’’ and Movement 5 is entered under ‘‘Lane 2’’ on Line 2. The grade is 0 percent, and there are no channelized right turns. There are no flared minor-street approaches or median storage areas, so an N for No is entered on Lines 5 and 7 in the ‘‘Yes or No?’’ column. There are no upstream signals either, so the third panel of the worksheet is left blank. The fourth panel is left empty as well; however, 0.25 is entered on Line 16 for T. Step 4a: Use Worksheet A4 to calculate critical gap. Since the example intersection is a T, the only columns in Worksheet A4 that contain entries are those that correspond to Movements 4, 7, and 9. The base critical gap times, taken from Table 10-1, are entered on Line 1 of Worksheet A4. The values in this case are those that pertain to a two-lane major road: 4.1, 6.2, and 7.1
sec, respectively. Line 2 contains the adjustment factor for heavy vehicles (1.0 sec), Line 3 gives the proportion of heavy vehicles for each movement (0.10 in this case), and Line 4 gives the adjustment factor for approach grade (0.1 and 0.2 for Movements 9 and 7, respectively). Lines 5 and 6 contain the percent grade and the critical gap adjustment factor for minor-street left turns at T-intersections, respectively. As mentioned before, the percent grade for this sample problem is 0, and because the intersection is a T, an adjustment factor of −0.7 is entered into the column pertaining to Movement 7. Line 7 is left blank since there is no two-stage gap acceptance. The critical gap for each movement, based on the first equation at the bottom of Worksheet A4, is then calculated and entered on Line 8. The calculation for Movement 7 is as follows: tc = 7.1 + 1.0 ∗ 0.10 + 0.2 ∗ 0 − 0.7 = 6.5
(10-42)
Step 4b: Use Worksheet A4 to calculate follow-up time. The base follow-up time values for each movement are entered on Line 10. According to Table 10-1, they are 2.2, 3.3, and 3.5 for Movements 4, 9, and 7, respectively. The heavy-vehicle adjustment factor is entered on Line 11 (0.9 sec), and the proportion of heavy vehicles for each movement is entered on Line 12 (again, 0.10). The results of the follow-up time calculations, based on the second equation given at the bottom of Worksheet A4, are entered on Line 13. The calculation for Movement 7 is as follows: tf = 3.5 + 0.9 ∗ 0.10 = 3.6
(10-43)
Step 5: Use Worksheets A5a–A5e to determine effect of upstream signals. Since no signals are present within 0.25 mi of the intersection, these worksheets are not used. Step 6: Use Worksheet A6 to calculate impedance and capacity. Worksheet A6 is divided into four different steps, each corresponding to two movements. However, given the geometry of this example, only the calculations associated with Movements 9, 4, and 7 in Steps 1, 2, and 4, respectively, pertain. The first line of Step 1 refers to Figure 10-2 for the computation of conflicting flows; the second line refers to Equation 10-1 or 10-29 for potential capacity; the third line refers to Equation 10-12 for the pedestrian impedance factor, which in this case is 1.00; and the fifth line refers to Equation 10-5 for the probability of a queue-free state. The fourth line is for the calculation of movement capacity, which in this step equals potential capacity since there are no conflicting pedestrian flows. Equations 10-44 through 10-46 calculate the conflicting Updated December 1997
urban streets
10-48
flow, potential capacity, and probability of a queue-free state, respectively, for Movement 9, as follows: vc,9 = 250 + 20 + 0 = 270 cp,9 = 270 ∗
e−(270*6.3)/3,600 = 750 1 − e−(270*3.4)/3,600
p0,9 = 1 −
120 = 0.84 750
(10-44) (10-45)
(10-46)
In calculating the conflicting flows, the user must always be careful to read the notes to Figure 10-2. In the case of Movement 9 above, no adjustments to the formula referred to on Worksheet A6 are necessary. The first five lines in Step 2 are identical to those in Step 1. The equation for conflicting flows is provided for convenience, and again no adjustments are necessary. The equations for potential capacity, movement capacity, and probability of a queue-free state are the same as those referred to in Step 1. The sixth line of Step 2 is left blank since the example intersection has a left-turn bay on the main street. The values corresponding to the first five lines under Movement 4 are 290 veh/hr, 1,227 veh/hr, 1.00, 1,227 veh/ hr, and 0.88, respectively. As in Steps 1 and 2, the first line of Step 4 is used to compute conflicting flows, and the second is used to calculate potential capacity. The corresponding values for Movement 7 of this example problem are 870 veh/hr and 312 veh/hr, respectively. No adjustments are made to the equation for conflicting flow. Line 3 contains the pedestrian impedance factor, which again is 1.00. The fourth line of Step 4 is used to compute the major-left, minor-through impedance factor. The fifth line uses the number generated by Line 3 to calculate the major-left, minor-through adjusted impedance factor, the sixth line is used to compute the capacity adjustment factor due to impeding movements, and the seventh line is used to determine movement capacity. Equations 10-47 through 10-50 demonstrate the calculations for Lines 4–6, respectively, corresponding to Movement 7. The variables p0,1, p0,11, and p0,12 and are set to be 1.00, since in this instance Movements 1, 11, and 12 are not defined. p″7 = 1.00 ∗ 0.88 = 0.88 p′7 = 0.65 ∗ 0.88 −
(10-47)
0.88 + 0.6√0.88 = 0.91 (10-48) 0.88 + 3
f7 = 0.91 ∗ 1.00 = 0.91
(10-49)
cm,7 = 0.91 ∗ 312 = 283
(10-50)
The remaining values for Worksheet A6 are shown in Table 10-9. Step 7: Use Worksheets A7a and A7b to compute effect of twostage gap acceptance. Since there is no two-stage gap acceptance process, Worksheets A7a and A7b are not used. Step 8: Use Worksheet A8 to calculate shared-lane capacity. Lines 1–3 of Worksheet A8 are used to calculate the shared-lane capacity of Movements 7, 8, and 9. In this case, the last three columns of Worksheet A8 are left blank, since Movements 10, 11, and 12 are not defined. The volumes for Movements 7 and 9 and their capacities from Worksheet A6 are entered in the second and fourth columns of the top row, respectively. The shared-lane capacity is computed using the first equation given on Worksheet A8: Updated December 1997
Table 10-9. Impedance and Capacity Calculations Step 1—Minor Right Turn
v9
v12
Conflicting flows Potential capacity Pedestrian impedance factor Movement capacity Probability of queue-free state
270 750 1.00 750 0.84
— — — — 1.00
v4
v1
290 1,227 1.00 1,227 0.88
— — — — —
v7
v10
870 312 1.00
— — —
0.88
—
0.91 0.91 283
— — —
Step 2—Major Left Turn Conflicting flows Potential capacity Pedestrian impedance factor Movement capacity Probability of queue-free state Step 4—Minor Left Turn Part III—Single stage (no storage) Conflicting flows Potential capacity Pedestrian impedance factor Major left turn, minor through impedance factor Major left turn, minor through adjustment impedance Capacity adjustment factor Movement capacity
cSH =
40 + 120 = 531 (40/283) + (120/750)
(10-51)
Step 9: Use Worksheet A9 to compute effect of flared minorstreet approaches. Since the northbound approach is not flared, Worksheet A9 is not used in this calculation. Step 10: Use Worksheet A10 to calculate delay, queue length, and level of service. In this instance, only the top columns for Movement 4 and Movements 7 and 9 are relevant. Since Movements 7 and 9 share one lane, the third column contains one value. The combined volume of Movements 7 and 9, 160 veh/hr, is entered in the first row, third column. The approach capacity, 531 veh/hr, is entered in the second row, third column. The v/c ratio, 0.30, is simply the ratio of these two numbers. The queue length, 1.4 cars, is determined by referring to Figure 10-12. The control delay is computed using Equation 10-37 and is demonstrated as follows: d=5+
3,600 + 900 ∗ 0.25 531
3 !
160 −1+ ∗ 531
1
2
4
1 531 2 ∗ 15312 3,600
2 160 −1 + 531
160
450 ∗ 0.25
= 14.7 (10-52)
According to Table 10-7, 14.7 sec of delay corresponds to LOS B. The approach delay is the same as the control delay in this instance, since there is only one lane. The values for Movement 4 are presented in Table 10-10. Step 11. Use Worksheet A11 to calculate shared major left-turn impedance and delay. The presence of the left-turn bay on the major street precludes the use of Worksheet A11.
unsignalized intersections Table 10-10. Delay, Queue Length, and Level of Service Movement v (veh/hr) c (veh/hr) v/c Queue length Control delay Level of service
4
7, 9
150 1,227 0.12 10 >15 >25 >35
≤10 and ≤15 and ≤25 and ≤35 and ≤50 >50
the 5-sec acceleration-deceleration term in the delay equation, implies that a LOS range up to 10 sec is appropriate for LOS A. The LOS breakpoints for AWSC intersections are somewhat different than the criteria used in Chapter 9 of this manual for signalized intersections. The primary reason for this difference is that drivers expect different levels of performance from different kinds of transportation facilities. The expectation is that a signalized intersection is designed to carry higher traffic volumes than an AWSC intersection. Thus a higher level of control delay is acceptable at a signalized intersection for the same level of service.
III. PROCEDURES FOR APPLICATION Documented in this section are the steps that make up the computational procedures for capacity and level of service for AWSC intersections. Five worksheets are required to complete the computations defined in these procedures. Four primary sections make up the procedures: T T T T
Initial conditions and adjustments, Headway and service time, Capacity, and Delay and level of service.
4 so that the equivalent hourly flow rate can be computed. The hourly flow rates are entered on Lines 5, 6, and 7. The total flow rate for the lane (the sum of Lines 5, 6, and 7) is entered on Line 8. PHV is entered for each movement on Line 9. The number of lanes on the subject and opposing approaches is entered on Lines 10 and 11. The maximum number of lanes on the conflicting approaches, from either the left or the right, is entered on Line 12. The geometry group, from Table 10-39, is entered on Line 13. The length of the analysis period is entered on Line 14.
Figure 10-32 shows the steps in the computational procedures. SATURATION HEADWAY ADJUSTMENT FACTOR FIELD DATA REQUIREMENTS
The following field data are needed for this procedure: 1. Number and configuration of lanes on each approach, 2. Volume (V) by turning movement for each approach, 3. Proportion of heavy vehicles (PHV) on each approach, 4. Peak-hour factor (PHF), and 5. Length of study period or length of oversaturated period (T) in hours.
Worksheet B3 is used to compute the saturation headway adjustment factor for each lane. The total lane flow rate, the left-turn flow rate, and the right-turn flow rate as computed on Worksheet B2 are entered on Lines 1 through 3 of Worksheet B3. The proportion of left turns, right turns, and heavy vehicles is computed and entered on Lines 4 through 6. The geometry group, from Worksheet B2, is entered on Line 7. The saturation headway adjustments for turning movements and heavy vehicles are made using Table 10-40. Equation 10-98 defines this computation:
GEOMETRIC FEATURES AND MOVEMENT DEFINITIONS
hadj = hLT−adjPLT + hRT−adjPRT + hHV−adjPHV Worksheet B1 shows the basic features of the intersection and the movements of interest. The intersection name, the analyst’s name, the count date, and the time period are entered on this form. A north orientation arrow is also entered. VOLUME ADJUSTMENT AND LANE ASSIGNMENT
The volumes for each movement are entered on Worksheet B2, Lines 1, 2, and 3 for Lanes 1 and 2. The PHF is entered on Line
(10-98)
where hadj = headway adjustment, hLT-adj = headway adjustment for left turns (either 0.2 or 0.5, depending on geometry case), hRT-adj = headway adjustment for right turns (either −0.6 or −0.7), hHV-adj = headway adjustment for heavy vehicles (1.7), PLT = proportion of left-turning vehicles on the approach, PRT = proportion of right-turning vehicles on the approach, and PHV = proportion of heavy vehicles on the approach. Updated December 1997
urban streets
10-68
Figure 10-32. Flow for AWSC procedures.
Table 10-39. Geometry Group No. of Lanes Geometry Group
Intersection Configuration
1 2 3a/4a 3b 4b 5 5 6
Four-leg or Four-leg or Four-leg or T Four-leg Four-leg or Four-leg or Four-leg or
Subject Approach
Opposing Approach
Conflicting Approaches
1 1 1 1 1 2 3 3
1 1 2 2 2 1 or 2 1a 2 or 3
1 2 1 2 2 1 or 2 1a 2 or 3
T T T T T T
a
If the number of lanes on the subject approach is 3 and the number of lanes on either the opposing or conflicting approaches is 1, the geometry group is 5. Otherwise, if the number of lanes on the subject approach is 3, the geometry group is 6.
Table 10-40. Saturation Headway Adjustment Factors by Geometry Group Factor
Group 1
Group 2
Group 3a
Group 3b
Group 4a
Group 4b
Group 5
Group 6
Left turn Right turn HV
0.2 −0.6 1.7
0.2 −0.6 1.7
0.2 −0.6 1.7
0.2 −0.6 1.7
0.2 −0.6 1.7
0.2 −0.6 1.7
0.5 −0.7 1.7
0.5 −0.7 1.7
DEPARTURE HEADWAY AND SERVICE TIME
Worksheet B4
The computation of the service time for each lane is a complex process; both Worksheets B4 and Worksheet B4 Supplemental are used in this process. The process is iterative and requires that Worksheet B4 Supplemental be used several times.
The total lane flow rate is entered on Line 1. The initial departure headway of 3.2 sec is entered on Line 2. The initial degree of utilization is computed using Equation 10-99 and entered on Line 3.
Updated December 1997
x = vhd /3,600
(10-99)
unsignalized intersections The degree of utilization (x) is the product of the flow rate and the departure headway divided by 3,600. The final departure headway, from Worksheet B4 Supplemental, Line 69, is entered on Line 4. (The use of Worksheet B4 Supplemental is described in the next section.) The final degree of utilization for each lane is computed using Equation 10-99 (with input values from Lines 1 and 4); the result is entered on Line 5. The move-up time for the lane is entered on Line 6; it is either 2.0 sec for geometry groups 1 through 4 or 2.3 sec for geometry groups 5 and 6. The service time is computed using Equation 10-95 using input values from Lines 4 and 6. The result is entered on Line 7. Worksheet B4 Supplemental
One copy of Worksheet B4 Supplemental is used for each lane and each iteration until the values of the departure headway for each lane change by less than 0.01 sec from the previous iteration. The worksheet is used in conjunction with Table 10-37, which gives the 64 possible occupied lane combinations (combinations of vehicles present or absent on each opposing and conflicting lane) for an intersection with one or two lanes on each approach. When three lanes exist on any or all of the approaches, these worksheets cannot be used. Each of the 64 combinations is represented by a utilization string Ci. The utilization string contains six elements, a string of 0’s and 1’s corresponding to the presence or absence of a vehicle in each lane on the opposing and conflicting approaches. The position of a 1 or 0 in the string corresponds to a specific lane, as shown in Columns 1 through 6 of this worksheet. Each element is represented by aj. Thus the utilization string consists of the concatenated elements a1a2a3a4a5 a6. If aj equals 0, no vehicle is present in the lane; if aj equals 1, a vehicle is present in the lane. The probability of each value of aj depends on both the value of aj (either 0 or 1) and whether the flow vj is 0 or >0. The probability of each value of aj is given in Table 10-41. The probability of each value of aj is entered in Columns 1 through 6 for each of the 64 combinations on the basis of Table 10-41. The probability of each of the 64 combinations is computed by multiplying the individual probabilities given in Columns 1 through 6. This value is entered in Column 7 for each of the 64 combinations. The adjusted probability is computed to account for the serial correlation in the previous probability computation. The degreeof-conflict cases are given in Table 10-37, and the equations for these degree-of-conflict cases are as follows: AdjP[C1]j = a(P[C2] + 2P[C3] + 3P[C4] + 4P[C5])
(10-100)
AdjP[C2]j = a(P[C3] + 2P[C4] + 3P[C5] − P[C2])
(10-101)
AdjP[C3]j = a(P[C4] + 2P[C5] − 3P[C3])
(10-102)
Table 10-41. Probability of aj aj
vj
P[aj]
1 0 1 0
0 0 1 1
0 1 xj 1 − xj
Note: xj is the degree of utilization, defined in Equation 10-99.
10-69
AdjP[C4]j = a(P[C5] − 6P[C4])
(10-103)
AdjP[C5]j = −a(10P[C5])
(10-104)
where a is a constant to adjust the degree-of-conflict probability to account for serial correlation between forecast headways (standard value of a = 0.01). The computed value of AdjP[Ci] is entered in Column 8 of Worksheet B4 Supplemental. The final value of P[Ci], the sum of Columns 7 and 8, is entered in Column 9 for each of the 64 combinations. The base value of the saturation headway for each of the 64 combinations is entered in Column 10. The value is determined from Table 10-42 on the basis of the lane geometry group. The saturation headway adjustment factor for each lane is entered in Column 11. This value is from Worksheet B3, Line 11. The final saturation headway, the sum of Columns 10 and 11, is computed and entered in Column 12. The flow rate for the lane is entered on Line 65; this value is from Worksheet B2, Line 8. The lane designation and iteration number are entered on Lines 66 and 67. The departure headway for each lane from the previous iteration is entered on Line 68. The new value of the departure headway is computed for each lane using Equation 10-96; it is the sum of the 64 lines of products of Columns 9 and 12. The new value of the degree of utilization is computed using Equation 10-99 using Lines 69 and 70 as input. Note that if this is not the final iteration, and if the degree of utilization exceeds 1, then it is reset to 1. If the difference between Lines 68 and 69 is less than 0.01 for each lane, the headway for the lanes has stabilized and convergence has been reached. Once convergence has been reached, the values of departure headway and degree of utilization for each lane are entered on Lines 4 and 5 of Worksheet B4. CAPACITY
The capacity of each approach is computed with the assumption that the flows on the opposing and conflicting approaches are held constant. The given flow rate on the subject lane is increased and the departure headways are computed for each approach using Worksheet B4 and Worksheet B4 Supplemental until the degree of utilization for the subject approach reaches 1. When this occurs, the final value of the subject approach flow rate is the maximum possible throughput or capacity of this lane. The result is entered on Line 5 of Worksheet B5. DELAY AND LEVEL OF SERVICE
Worksheet B5 is also used to determine delay and level of service. The total lane flow rate is entered on Line 1. The service time, from Worksheet B4, Line 7, is entered on Line 2. The degree of utilization, from Worksheet B4, Line 5, is entered on Line 3. The final departure headway, from Worksheet B4, Line 4, is entered on Line 4. Average control delay per vehicle is computed for each lane and each approach by using Equation 10-105 and entered on Line 6. d=s
3
+ 900T (x − 1) +
!(x − 1) + 1450T24 + 5(10-105) 2
hd x
where d is the average control delay per vehicle and the other terms are as previously defined. The approach delay is the Updated December 1997
10-70
urban streets
WORKSHEET B1: BASIC INTERSECTION INFORMATION
Updated December 1997
unsignalized intersections
10-71
WORKSHEET B2: VOLUME ADJUSTMENT AND SITE CHARACTERISTICS
WORKSHEET B3: SATURATION HEADWAY ADJUSTMENT FACTOR
Updated December 1997
10-72
urban streets
WORKSHEET B4: DEPARTURE HEADWAY AND SERVICE TIME
Updated December 1997
unsignalized intersections
10-73
WORKSHEET B4 SUPPLEMENTAL: COMPUTATION OF PROBABILITY STATES AND SATURATION HEADWAY (continues)
Updated December 1997
10-74
urban streets
WORKSHEET B4 SUPPLEMENTAL: COMPUTATION OF PROBABILITY STATES AND SATURATION HEADWAY
WORKSHEET B5: CAPACITY, DELAY, AND LEVEL OF SERVICE
Updated December 1997
unsignalized intersections
10-75
Table 10-42. Saturation Headway Values by Case and Geometry Group Case
NumVeha
Group 1
Group 2
Group 3a
Group 3b
Group 4a
Group 4b
Group 5
Group 6
1 2
0 1 2 ≥3 1 2 ≥3 2 3 4 ≥5 3 4 5 ≥6
3.9 4.7
3.9 4.7
4.0 4.8 x
4.3 5.1 x
4.0 4.8 x
4.5 5.3 x
4.5 5.0 6.2
5.8
5.8 x
5.9
6.2 x
5.9
6.4 x
6.4 7.2
7.0
7.0 x x
7.1 x
7.4 x x
7.1 x
7.6 x x
7.6 7.8 9.0
9.6
9.6 x x
9.7 x
10.0 x x x
9.7 x
10.2 x x x
9.7 9.7 10.0 11.5
4.5 6.0 6.8 7.4 6.6 7.3 7.8 8.1 8.7 9.6 12.3 10.0 11.1 11.4 13.3
3 4
5
a
Number of lanes on the opposing and conflicting approaches that are occupied by a vehicle.
weighted average of the delay on each lane. The intersection delay is the weighted average of the delay on each of the approaches. The level of service for each approach and for the intersection is determined using Table 10-38 and the computed values of stopped delay. PLANNING AND DESIGN APPLICATIONS
The operational analysis method described earlier in this chapter provides a detailed procedure to evaluate the performance of an AWSC intersection. Sometimes, however, an analyst may wish to estimate the level of service for a long-term time horizon. This
kind of analysis is called a planning-level analysis. It is expected that for such an analysis only a limited amount of input data is available. The planning analysis method described here is based on the operational analysis method. The planning method requires all geometric data and traffic flow data required for the operational analysis method; all computations for the planning method are identical to those for the operational analysis method. The operational analysis procedure described earlier in this chapter is not normally used for design purposes. However, through iteration the analyst can use a given set of traffic flow data and determine the number of lanes that would be required to produce a given level of service.
IV. SAMPLE CALCULATIONS SAMPLE CALCULATION B1
Sample Calculation B1 illustrates the fundamental principles of the AWSC capacity analysis methodology. Description
The setting for the problem is an intersection between two onelane, one-way streets as shown in Figure 10-33. The busiest hour at this intersection involves a flow of 300 veh/hr northbound and 200 veh/hr westbound. There are no turning movements. Important features of the methodology are illustrated by working step by step through the capacity analysis of this facility. Solution
Steps 1 and 2: Use Worksheets B1 and B2 to enter basic data and traffic flow volumes. As indicated above, both streets have singlelane approaches. The flow rates are 300 veh/hr northbound and 200 veh/hr westbound. There are no trucks and PHF is 1.0. This means that Worksheet B1 shows a northbound flow of 300 veh/hr and a westbound flow of 200 veh/hr. On Worksheet B2, Line 2 has entries
in the NB L1 and WB L1 columns with volumes of 300 and 200 veh/ hr, respectively. With a PHF of 1 and 0 percent heavy trucks, this means that the hourly flow rates on Line 6 are identical to the volumes. The geometry group is 1 and T is assumed to be 0.25 hr. Step 3: Complete Worksheet B3 for saturation headway adjustment. No adjustments are required since there are no turning movements or heavy vehicles. The end result is that hadj is zero for both lanes. Step 4: Complete Worksheet B4 for departure headway and service time. On Lines 1 and 2 for the NB L1 and WB L1 columns, the total lane volumes (300 and 200) and the departure headway initial values, which are assumed to be 3.2 sec, are entered as the methodology suggests. Step 4a: Use Worksheet B4 to compute initial degrees of utilization (Line 3). The initial degrees of utilization are computed by multiplying the mean arrival rate by the departure headway. For the northbound and westbound approaches, the initial values are computed as follows: xWB =
vWBhd,WB (200)(3.2) = = 0.18 3,600 3,600
(10-106)
xNB =
vNBhd,NB (300)(3.2) = = 0.27 3,600 3,600
(10-107)
Updated December 1997
urban streets
10-76
Figure 10-33. Traffic volumes for Sample Calculation B1.
Step 4b: Complete Worksheet B4 Supplemental for probability states and saturation headway. Since there are only two approaches, only two cases pertain: Cases 1 and 3. Therefore, only Lines 1 and 3 contain entries. The values appearing in Columns 1 through 6 are taken from Table 10-41. Their products are entered in Column 7. For simplicity, it has been assumed that no correlation among the saturation headways exists, so a has been set equal to zero. Consequently, Column 9 contains the same entries as Column 7. The next sample calculation presents an example in which the effects of correlation are taken into account. The two base saturation headway values pertaining to Cases 1 and 3, 3.9 sec/veh and 5.8 sec/veh, are entered in Column 10 on Lines 1 and 3, respectively. Since there are no adjustments, Column 12 is identical to Column 10. Step 4c: Use Worksheet B4 Supplemental to compute the first iteration departure headways (Lines 1 through 72). With the new degrees of utilization provided by Equations 10-106 and 10-107, updated departure headways can be computed for both approaches: 5
hd,NB =
o P[C ]h i=1
i
si
= hs1(1 − xWB) + hs3(xWB)
hd,NB = (3.9)(0.78) + (5.8)(0.22) = 4.3
(10-108) (10-109)
5
hd,WB =
o P[C ]h i=1
i
si
= hs1(1 − xNB) + hs3(xNB)
hd,WB = (3.9)(0.67) + (5.8)(0.33) = 4.5
(10-11 0) (10-111)
The values are entered on Line 69 of both the supplemental worksheet for the northbound and westbound approaches, respectively. Finally, the degree of utilization for each approach is computed and entered on Line 71, as shown in the next paragraph. For simplicity, it has been assumed that no correlation among the saturation headways exists, so a has been set equal to zero. The next sample calculation presents an example in which the effects of correlation are taken into account. Step 4d: Use Worksheet B4 Supplemental to iterate, using Steps 4a and 4b, until the departure headways for the current iteration match those for the previous one. Steps 4a and 4b must be executed repeatedly until the departure headways from the current iteration match those from the previous one within a given tolerance limit. To illustrate how the process starts, compute the degrees of utilization for the next iteration (values for Line 71). The results are Updated December 1997
taken from Equations 10-109 and 10-111 and Equations 10-106 and 10-107 are repeated. vWBsWB (200)(4.5) = = 0.25 3,600 3,600 (300)(4.3) v s = 0.36 = NB NB = 3,600 3,600
xWB =
(10-112)
xNB
(10-113)
The departure headways converge after only a few iterations: 4.6 sec/veh for the westbound approach and 4.4 sec/veh for the northbound approach. It is important to note that these are not the saturation headways for the approaches (i.e., the headways at capacity); rather they are the expected values of the headways between vehicles departing from the stop line given the flows on both approaches (i.e., 200 and 300 veh/hr). (Intuitively, one would not expect these to be the saturation headways. At saturation there must be a continuous queue on at least one of the two approaches, and with flows of 200 and 300 veh/hr, that is not likely to be the case.) The approach capacities have to be computed in another manner, as will be shown later. The final degrees of utilization give another insight into the intersection’s operation: the proportion of the hour during which each approach is busy processing vehicles. For the northbound approach this proportion is 37 percent of the time; for the westbound approach, it is 26 percent of the time because the final degrees of utilization are 0.37 and 0.26, respectively. In the field, the user should see vehicle-processing activity on the two approaches for about this proportion of the time. Step 4e: Use Worksheet B4 to compute the service time for each approach (Line 7). Once the final departure headway values have been determined, the service times for each approach can be computed. If the move-up time is 2.0 sec (Line 6), the service times are computed as follows: sW = 4.6 − 2.0 = 2.6 sec sN = 4.4 − 2.0 = 2.4 sec
(10-114) (10-115)
Step 5: Complete Worksheet B5 for capacity, delay, and level of service. The total lane volumes and service times are obtained from Worksheet B4. The remaining lines are to be completed as described below.
unsignalized intersections Step 5a: Compute the capacity of each approach. An iterative process is used to compute the capacity of each approach. It is necessary to ascertain the maximum volume that can be accommodated on the subject approach given that the volumes on the other approaches remain unchanged. Put another way, it must be determined how much the flow rate on the subject approach can be increased, with all other flows remaining unchanged, without the overall processing capacity of the intersection being exceeded. The process employed is as follows. First the northbound flow rate is increased while the westbound flow rate remains fixed until the degree of utilization on the northbound approach reaches 1.0. At that point, the capacity limit of the northbound approach has been reached. Conversely, to obtain the capacity of the westbound approach, its flow rate is increased while the northbound flow rate remains fixed at 300 veh/hr until the degree of utilization on the westbound approach reaches 1.0. What are the quantitative results? If the flow on the northbound approach is increased, the intersection reaches capacity at 800 veh/ hr. At that flow rate, the degree of utilization on the northbound approach reaches 1.0. Conversely, if the flow on the westbound approach is increased (while the flow on the northbound approach is left at 300 veh/hr), capacity is reached at a flow of 750 veh/hr. (The lower value results from the fact that the northbound flow is greater than the westbound flow, 300 veh/hr versus 200 veh/hr.) Step 5b: Compute the delay (Lines 4, 6, and 8). This next-tolast step involves applying Equation 10-105 to compute the delay per vehicle on each approach. For the northbound approach, the computation of the average delay involves the following: dNB = 7.4 + (900)(0.25)
3(0.37 − 1) + !(0.37 − 1) + 1 (450)(0.25) 24 = 9.9 2
(4.38)(0.37)
(10-116) The value of 7.4 sec in the above equation includes both the 2.4sec service time and a 5-sec adjustment to account for acceleration and deceleration delay. The corresponding value for the westbound approach is 9.2 sec/veh. These values pertain to both Lines 6 and 8 since there is only one lane on each approach. For Line 10, the weighted average delay for the intersection is found as follows: (300)(9.9) + (200)(9.2) = 9.6 (10-117) 300 + 200 Step 5c: Determine level of service. Table 10-38 provides the correspondence between values of delay and level of service. In this case, since all the delays are less than 10 sec, the level of service for both approaches is LOS A. d=
SAMPLE CALCULATION B2
Description
This example problem involves a three-leg (T-) AWSC intersection between two two-lane streets. Sixth Street southbound deadends at Line Street as shown in Figure 10-34.
10-77
volumes for the intersection. These are entered on both Worksheets B1 and B2. The PHF is 1.0, the proportion of heavy trucks is 0 percent, and there is only one lane per approach, so the volumes shown in Figure 10-34 carry forward to Line 8 of Worksheet B2. The intersection fits geometry Group 1, and the value of T is assumed to be 0.25 hr. Step 3: Complete Worksheet B3 for saturation headway adjustment: Left-turn and right-turn adjustments are applied using the factors given in Table 10-40. For the southbound approach, the adjustment factor computation (Line 11) is as follows: hadj = (0.67)(0.2) + (0.33)(−0.6) + (0)(1.7) = −0.067
(10-118)
The resulting adjusted saturation headways are 3.83, 4.63, 5.73, and 6.93 sec/veh for Cases 1–4. Step 4: Complete Worksheet B4 for departure headway and service time. On Lines 1 and 2 the total lane volumes (0, 150, 350, and 400 for the northbound, southbound, eastbound, and westbound L1 cells, respectively) and the departure headway initial values (3.2 sec) are entered. The initial x-values are 0.17, 0.39, and 0.44 for the southbound, eastbound, and westbound approaches, respectively. A sequence of iterations then follows using Worksheet B4 Supplemental until the departure headways converge to constant values—5.46, 4.79, and 4.57 sec for the southbound, eastbound, and westbound approaches, respectively. In this case, since correlation among the saturation headways is being taken into account, the value of a is 0.01, which means that the computations involved in accounting for this effect need to be performed. Table 10-43 shows the final set of iteration values. It can be seen that for the southbound approach, computation of the probability adjustment factors requires the following calculations: Padj[C1] Padj[C2] Padj[C3] Padj[C4]
= = = =
0.0171 0.010 −0.013 −0.014
(10-119) (10-120) (10-121) (10-122)
In addition, the adjusted departure headway (5.46 sec/veh) is computed as follows: hd = 3.83 ∗ (0.26 + 0.017) + 4.63 ∗ (0.000 + 0.010) + 5.73 ∗ (0.50 − 0.0013) + 6.93 ∗ (0.24 − 0.0014) = 5.46 (10-123) The service times are computed by subtracting the move-up time from the adjusted departure headways. Since the move-up time is 2.0 sec, this implies service times that are 2.0 sec shorter than the departure headways, or 3.46 sec/veh in the case of the southbound approach, for example. Step 5: Complete Worksheet B5 for capacity, delay, and level of service. The total lane volumes and service times are from Worksheet B4. The remaining lines are completed as was set forth for Sample Calculation B1. The results are presented in Table 10-44. SAMPLE CALCULATION B3
Solution
Description
Steps 1 and 2: Use Worksheets B1 and B2 for basic data and traffic flow volumes. Figure 10-34 presents the turning movement
The third sample problem illustrates the AWSC methodology for a four-way AWSC intersection. The intersection shown in Updated December 1997
urban streets
10-78
Figure 10-34. Traffic volumes for Sample Calculation B2.
Table 10-43. Departure Headways Approach Parameter x, degree of utilization P[C1] P[C2] P[C3] P[C4] Padj[C1] Padj[C2] Padj[C3] Padj[C4] h, departure headway
SB
EB
WB
0.23 0.26 0.00 0.50 0.24 0.017 0.010 −0.013 −0.014 5.46
0.47 0.38 0.39 0.11 0.12 0.010 −0.001 −0.002 −0.007 4.79
0.51 0.41 0.36 0.12 0.11 0.009 −0.000 −0.003 −0.006 4.57
Table 10-44. Capacity, Delay, and Level of Service Approach Parameter Approach capacity (veh/h) Approach delay (sec/veh) Approach level of service Overall delay (sec/veh)
SB
EB
WB
585 10.1 B
720 11.9 B 11.7
760 12.2 B
Figure 10-35 is between two two-lane arterials that are controlled by stop signs in each direction. Each approach has 10 percent trucks. Solution
Steps 1 and 2: Use Worksheets B1 and B2 for basic data and traffic flow volumes. For this sample calculation, all of the turning movements on Worksheets B1 and B2 have nonzero values. The turning movement volumes and percentages of heavy vehicles are shown in Figure 10-35. The PHF is 1, and T is assumed to be 0.25 hr. The hourly flow rates are the same as the volumes since PHF = 1. Since the intersection falls into Group 1 (one lane on each approach), no lane usage distribution is necessary. Step 3: Complete Worksheet B3 for saturation headway adjustment. The base saturation headways are computed using the values Updated December 1997
given in Table 10-42. Left-turn and right-turn adjustments are applied using the factors given in Table 10-40. The results for each approach are given in Table 10-45. Step 4: Complete Worksheet B4 for departure headway and service time. The initial departure headways are set to 3.2 sec for each approach. These values converge to the final values shown in Table 10-46 in just a few interations. With a correlation adjustment parameter (a) of 0.01, the departure headway values are recomputed at each iteration as shown in Table 10-46, which shows the final set of iteration values. The service times are 2.0 sec less than the departure headways since the move-up time is 2.0 sec. The resulting values for service time are shown in Table 10-47. Step 5: Complete Worksheet B5 for capacity, delay, and level of service. The capacity of each approach is computed by assuming that the flows on the opposing and conflicting approaches are held constant. For each approach, the flow rate is increased using Step 4 until the degree of utilization for the subject approach reaches 1. This produces the results given in Table 10-48.
SAMPLE CALCULATION B4
Description
Sample Calculation B4 concerns the intersection of Eighth Avenue and Sixteenth Street. The diagram in Figure 10-36 shows that both streets are four-lane arterials, and there are stop signs on all approaches. The lane markings are left-and-through and throughand-left on each approach. For purposes of analysis it is assumed that the lanes are utilized in a balanced fashion, with an equal number of vehicles per hour using each lane on each approach. The proportion of trucks is 0 percent, PHF = 1, and T is assumed to be 0.25 hr.
Solution
Steps 1 and 2: Use Worksheets B1 and B2 for basic data and traffic flow volumes. For this sample calculation, all of the turning move-
unsignalized intersections
10-79
Figure 10-35. Traffic volumes for Sample Calculation B3.
Table 10-45. Saturation Headways
Table 10-48. Capacity, Delay, and Level of Service
Approach
Approach
Case
NB
SB
EB
WB
Parameter
NB
SB
EB
WB
1 2 3 4 5
4.0 4.8 5.9 7.1 9.7
4.0 4.8 5.9 7.1 9.7
4.0 4.8 5.9 7.1 9.7
4.0 4.8 5.9 7.1 9.7
Approach capacity (veh/hr) Approach delay (sec/veh) Approach level of service Overall delay (sec/veh) Overall level of service
445 29.3 D
430 23.9 C
475 42.3 E
435 26.0 D
Table 10-46. Departure Headways Approach Parameter x, degree of utilization P[C1] P[C2] P[C3] P[C4] P[C5] Padj[C1] Padj[C2] Padj[C3] Padj[C4] Padj[C5] h, departure headway
NB
SB
EB
WB
0.74 0.01 0.03 0.13 0.44 0.39 0.032 0.022 +0.008 −0.023 −0.039 7.61
0.65 0.01 0.03 0.09 0.42 0.45 0.033 0.022 +0.010 −0.021 −0.044 7.77
0.87 0.03 0.06 0.13 0.44 0.33 0.030 0.020 +0.007 −0.023 −0.033 7.37
0.69 0.01 0.08 0.06 0.44 0.42 0.032 0.021 0.011 −0.022 −0.042 7.65
Table 10-47. Service Times Parameter
NB
SB
EB
WB
Service time
5.6
5.8
5.4
5.7
31.3 D
ments on Worksheets B1 and B2 have nonzero values. The intersection falls into Geometry Group 5 (two lanes on each approach), and the distribution of flows by lane is shown in Figure 10-36. The hourly flow rates are the same as the volumes since PHF = 1. Step 3: Complete Worksheet B3 for saturation headway adjustment. The base saturation headways are computed using the values given in Table 10-42. Left-turn and right-turn adjustments are applied using the factors given in Table 10-40. The results for each approach are given in Table 10-49. Step 4: Complete Worksheet B4 for departure headway and service time. The departure headway for each lane begins at 3.2 sec. Iterations ensue until convergence is reached. The final degrees of utilization and departure headways for each approach are given in Table 10-50. The service times are 2.3 sec less than the departure headways since the move-up time is 2.3 sec. The resulting values for service times are shown in Table 10-51. Step 5: Complete Worksheet B5 for capacity, delay, and level of service. The capacity of each approach is computed assuming that the flows on the opposing and conflicting approaches are held constant. The given flow rate on the subject lane is increased and the departure headways are computed for each approach using Step 4 until the degree of utilization for that lane reaches 1. The results from the capacity calculations are given in Table 10-52.
Updated December 1997
urban streets
10-80
Figure 10-36. Traffic volumes for Sample Calculation B4.
Table 10-49. Saturation Headways Case
NB
SB
EB
WB
No. of Vehicles
Lane 1
Lane 2
Lane 1
Lane 2
Lane 1
Lane 2
Lane 1
Lane 2
0 1 2 1 2 2 3 4 3 4 5 ≥6
4.70 5.20 6.40 6.60 7.40 7.80 8.00 9.20 9.90 9.90 10.20 11.70
4.36 4.86 6.06 6.26 7.06 7.46 7.66 8.86 9.56 9.56 9.86 11.36
4.60 5.10 6.30 6.50 7.30 7.70 7.90 9.10 9.80 9.80 10.10 11.60
4.08 4.58 5.78 5.98 6.78 7.18 7.38 8.58 9.28 9.28 9.58 11.08
4.72 5.22 6.42 6.62 7.42 7.82 8.02 9.22 9.92 9.92 10.22 11.72
4.34 4.84 6.04 6.24 7.04 7.44 7.64 8.84 9.54 9.54 9.84 11.34
4.70 5.20 6.40 6.60 7.40 7.80 8.00 9.20 9.90 9.90 10.20 11.70
4.22 4.72 5.92 6.12 6.92 7.32 7.52 8.72 9.42 9.42 9.72 11.22
1 2 3 4
5
Table 10-50. Degrees of Utilization and Departure Headways NB Parameter x, degree of utilization h, departure headway
SB
EB
WB
Lane 1
Lane 2
Lane 1
Lane 2
Lane 1
Lane 2
Lane 1
Lane 2
0.61 8.8
0.58 8.4
0.60 8.7
0.57 8.2
0.56 8.9
0.53 8.5
0.61 8.8
0.58 8.3
Table 10-51. Service Times NB Parameter
SB
EB
WB
Lane 1
Lane 2
Lane 1
Lane 2
Lane 1
Lane 2
Lane 1
Lane 2
6.5
6.1
6.4
5.9
6.6
6.2
6.5
6.0
Service time
Table 10-52. Capacity, Delay, and Level of Service NB Parameter Approach capacity (veh/hr) Lane delay (sec/veh) Approach delay (sec/veh) Overall delay (sec/veh) Updated December 1997
SB
EB
WB
L1
L2
L1
L2
L1
L2
L1
L2
400 24.1
415 22.3
405 23.7
430 21.0
395 22.1
410 20.4
400 24.2
420 21.6
23.2
22.3
21.2 22.4
22.9
unsignalized intersections
10-81
V. REFERENCES 1. Kyte, M., Tian, Z., Mir, Z., Hameedmansoor, Z., Kittelson, W., Vandehey, M., Robinson, B., Brilon, W., Bondzio, L., Wu, N., and Troutbeck, R., Capacity and Level of Service at Unsignalized Intersections, Final Report, Volume 2: All Way Stop Controlled Intersections, National Cooperative Highway Research Program 3-46 (April 1996).
2. Richardson, A., A Delay Model for Multiway Stop-Sign Intersections, Transportation Research Record 1112, Transportation Research Board, Washington, D.C. (1987).
PART C. ROUNDABOUTS
I. INTRODUCTION Procedures for analysis of roundabouts are described in this section. A variety of terminology is introduced applying to the unique characteristics of roundabout capacity. For ease of reference, these terms are defined in the next section. The terms are also more fully described as they are used in the succeeding sections. These procedures are to provide guidance in the estimation of the capacity of a roundabout. It is acknowledged that the parameters used here to estimate capacity are based on limited U.S. data; the parameters will be adjusted as more data become available. VARIABLES USED IN ANALYSIS OF ROUNDABOUTS
ca = approach capacity (veh/hr); tc = critical gap, minimum length time interval that allows intersection entry to one minor-stream vehicle (sec); tf = follow-up time, time span between departure of one vehicle from minor street and departure of next vehicle, using same major-stream gap during periods of continuous queue on minor traffic stream (sec); va = approach flow rate (veh/hr); and vc = circulating flow rate (veh/hr). CHARACTERISTICS OF ROUNDABOUTS
Three main features of a roundabout are illustrated in Figure 10-37—the central island, the circulating roadway, and the splitter island (1). A roundabout is distinguished from a traffic circle in general by a set of common characteristics. Traffic circles that do not exhibit these characteristics are not considered to be roundabouts. For comparison purposes the nonconforming features found at some traffic circles are indicated in italics in the following list of common characteristics that define roundabouts: 1. Vehicles entering a roundabout on all approaches are required to yield to vehicles within the circulating roadway. Traffic circles sometimes employ stop or signal control or give priority to entering vehicles. 2. Circulating vehicles are not subjected to any other right-ofway conflicts, and weaving is kept to a minimum. These characteristics provide the means by which the priority is distributed and
alternated among vehicles. A vehicle entering as a subordinate vehicle immediately becomes a priority vehicle until it exits the roundabout. Some traffic circles impose control measures within the circulating roadway or are designed with weaving areas to resolve conflicts between movements. 3. The speed at which a vehicle is able to negotiate the circulating roadway is controlled by the location of the central island with respect to the alignment of the right entry curb and the circulating roadway cross section. It is important that the speeds of vehicles on the roundabout be low. This feature is responsible for the improved safety record of roundabouts. Some large traffic circles provide straight paths for major movements or are designed for higher speeds within the circulating roadway. Some small traffic circles do not achieve adequate deflection for speed control because of the small central island diameter. 4. No parking is allowed on the circulating roadway. Parking maneuvers prevent the roundabout from operating in a manner consistent with its design. Some larger traffic circles permit parking within the circulating roadway. 5. No pedestrian activities take place on the central island. Pedestrians are not intended to cross the circulating roadway. Some larger traffic circles provide for pedestrian crossing to, and activities on, the central island. 6. All vehicles circulate counterclockwise, passing to the right of the central island. In some small traffic circles (sometimes called mini-traffic circles) left-turning vehicles are allowed to pass to the left of the central island. 7. Roundabouts are designed to properly accommodate specified design vehicles. Some smaller traffic circles are often unable to accommodate large vehicles, usually because of right-of-way constraints. 8. Roundabouts have raised splitter islands on all approaches. Splitter islands are an essential safety feature, required to separate traffic moving in opposite directions and to provide refuge for pedestrians. Some smaller traffic circles do not provide raised splitter islands. 9. When pedestrian crossings are provided for the approach roads, they are placed approximately one car length back from the entry point. Some traffic circles accommodate pedestrians in other places, such as the yield point. Updated December 1997
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urban streets
Figure 10-37. Basic roundabout.
10. Entry deflection is the result of the physical features of a roundabout. Some traffic circles rely on pavement markings to promote deflection.
5. Adequate lighting must be provided for safe operation at night.
Although not explicit roundabout characteristics, the following features are necessary for a roundabout to perform safely and efficiently:
OVERVIEW OF PROCEDURES
1. It must be easily identified in the road system, 2. The layout must be clearly visible and marked appropriately, 3. The layout must encourage drivers to enter the intersection slowly, 4. Adequate sight distance must be provided at all entry points to enable the driver to enter the intersection and to observe the movements of pedestrians and bicycles, and
Roundabouts have been used successfully in many cities throughout the world and are gaining popularity in the United States. Although extensive literature on roundabout modeling has evolved worldwide, there is limited experience with their application in this country. It is therefore not possible to offer a comprehensive analysis methodology for all situations. The procedures described in this section make the best use of the limited field data
Updated December 1997
unsignalized intersections collected at U.S. roundabouts to modify the operating parameters of established performance analysis techniques. Although the procedures should be used with care until additional research is conducted, they do provide the U.S. practitioner with basic guidelines concerning the capacity of roundabouts. Existing intersection analysis models fall into two general categories. Empirical models rely on field data to develop relationships between geometric design features and performance measures such
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as capacity and delay. Analytical models are based on the concept of gap acceptance theory. The choice of an analysis approach depends on the calibration data available. Empirical models are generally better but require a number of congested roundabouts for calibration. Gap acceptance models, however, can be developed for uncongested roundabouts (2). Given the limited gap acceptance calibration data and the lack of empirical data at the time this section was written, a gap acceptance approach was used.
II. METHODOLOGY CONCEPTUAL APPROACH
The capacity of a roundabout can be estimated using gap acceptance techniques with basic parameters of critical gap and followup time. It has generally been assumed that the performance of each leg of a roundabout can be analyzed independently from the other legs, and consequently most techniques tend to use information about only one leg in the analysis (3, 4) (see Figure 10-38). This assumption is reasonable, up to a point. It has also been shown (5) that origin-destination paths at roundabouts affect capacity. This assumption is reasonable because more drivers who use a smaller radius when making a left turn will travel farther around the roundabout, will travel slower, and may have a longer intraplatoon headway (or lower saturation flow). This longer intraplatoon headway will reduce the opportunities for drivers to enter the roundabout, and capacity will be reduced.
Drivers have been found to use longer gaps when the flow is low. Drivers are prepared to wait for a longer gap that may come after a shorter gap so that driving may be more leisurely. In other circumstances, drivers at roundabouts in other countries have been found to accept quite small gaps. This behavior has now been found to cause the following circulating drivers to slow and the following headways to be reduced. This affects the predicted capacity only if circulating headways are used. Good estimates have been found for single-lane roundabouts if the circulating flows are assumed to be random. This is the same assumption that has been used in the analysis of TWSC intersections. Because drivers make a right turn onto the roundabout, the gap acceptance characteristics of drivers are expected to be the same as or similar to those of drivers making right turns at TWSC intersections. The concepts described in Part A of this chapter dealing with TWSC intersections are generally applicable to roundabouts. These concepts are only suitable, however, for single-
Figure 10-38. Analysis of one roundabout leg. Updated December 1997
urban streets
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Table 10-53. Critical Gap and Follow-Up Time
Upper-bound solution Lower-bound solution
Critical Gap (sec)
Follow-Up Time (sec)
4.1 4.6
2.6 3.1
lane roundabouts. There are more traffic interactions at multilane roundabouts that influence driver behavior and cause this technique to be inappropriate. More details of the U.S. experience are required before a more elaborate procedure can be recommended. CAPACITY
The equation to forecast the capacity of an entry to a roundabout with one approach lane is as follows: ca =
vc e−vc tc /3 ,600 1 − e−vc t f /3,600
(10-124)
where ca = approach capacity; vc = conflicting circulating traffic flow rate; tc = critical gap; and tf = follow-up time. Limited studies of U.S. roundabouts (6), as well as comparisons with existing roundabout operations in countries with extensive experience in the design and operation of roundabouts (7), indicate that a range of values of critical gap and follow-up time should provide the U.S. analyst with a reasonable estimate of the likely capacity of a planned roundabout. The recommended value ranges are given in Table 10-53. The relationship between approach capacity and circulating flow for these upper- and lower-bound values of critical gap and follow-up time is shown in Figure 10-39. Until more definitive U.S. data become available, it is recommended that the roundabout’s present performance be based on the lower-bound solution and that the upper-bound solution be used to estimate the expected performance as drivers become more experienced with roundabouts. The conflicting flows are calculated by evaluating the 15-min volumes of vehicles passing in front of the entering vehicles. In other countries, the effect of vehicles exiting into the road where drivers are entering has been found to be a second-order effect. At most well-designed roundabouts the exiting traffic can be ignored. In practice, it is necessary to convert intersection turning movements into circulating flows; flows v1 to v12 are shown in Figure
Figure 10-39. Roundabout approach capacity.
10-40. For example, circulating traffic for entry by Streams 7, 8, and 9 is Streams 1, 2, and 10. Consequently, vc would be equal to v1 + v2 + v10. Roundabouts can often be used to facilitate Uturns, and the flow of U-turns should also be included. The foregoing methodology applies to single-lane roundabouts. Experience with multiple-lane roundabouts in the United States is not sufficient to support an analysis procedure. Experience in other countries indicates that capacity may be increased by increasing the number of lanes on the approaches and on the circulating roadway, but the effect is less than that of an additional full lane. In other words, doubling the number of entry or circulating lanes does not double the capacity. In addition, the performance of multiple-lane roundabouts is affected to a greater extent by site geometrics and by driver characteristics. It is widely recognized that each of the approach lanes is likely to have substantially different gap acceptance characteristics. When capacity values are required for multiple-lane roundabouts, a comprehensive roundabout analysis model should be used in lieu of the procedures presented here. Some caution is necessary in the interpretation of the results produced by these models because their internal assumptions and parameters have not generally been well validated in the United States. A choice of roundabout analysis software is available; this software is based on established models developed by researchers in other countries. For the most part, the models are supported by much more extensive field data than the method described here. Although the applicability of these data to U.S. conditions is unknown, the models themselves have demonstrated credibility in a wide range of analysis tasks and therefore should be recognized as useful tools for evaluating capacity and delay at roundabouts.
III. PROCEDURES FOR APPLICATION The basic structure of the methodology is described in this section. Worksheet C1 is provided to assist the analyst in completing the computations. This worksheet is only applicable to single-lane roundabouts with circulating flows less than 1,200 veh/hr. 1. Define the existing geometry and traffic conditions for the intersection under study. For each leg, the approach traffic needs to be defined as shown earlier. The input data are entered on Lines Updated December 1997
1 through 3 of the worksheet. The approach volumes are entered on Line 1 for each turning movement. The PHF is entered on Line 2. The approach flow rates for each turning movement are entered on Line 3. The total approach flow is computed and entered on Lines 4 through 7. 2. Determine the conflicting (circulating) traffic at each leg of the roundabout. For each leg, the approach and the circulating
unsignalized intersections
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Figure 10-40. Flow stream definitions. traffic need to be defined as shown above. The circulating flows are entered on Lines 8 through 11. If the circulating flow exceeds 1,200 veh/hr, this procedure should not be used unless field data have been collected for the critical gap and follow-up time. 3. Determine the capacity of the entry lanes using Equation 10124. The analyst must select the appropriate values of the critical gap and follow-up time from Table 10-53. The results are entered on Lines 12 and 13.
4. The analyst can make an assessment of the sufficiency of the capacity of the roundabout based on the v/c ratio. It is important to remember that this assessment is of the adequacy of the geometry of the roundabout design and not of the level of service provided to the driver. The result is entered on Lines 14 and 15.
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urban streets
WORKSHEET C1: CAPACITY CALCULATIONS FOR ROUNDABOUTS
Updated December 1997
unsignalized intersections
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IV. SAMPLE CALCULATIONS SAMPLE CALCULATION C1
Sample Calculation C1 illustrates the use of the roundabout capacity analysis procedure. Description
The juncture of Buena Vista and El Moro is a four-leg roundabout similar to the one shown in Figure 10-41. The methodology described here can be applied since the roundabout is one lane wide and its circulating flows are all less than 1,200 veh/hr. Figure 10-41 shows the turning-movement volumes. The eastbound approach has the highest volume at 660 veh/hr, whereas the northbound approach has the smallest, 427 veh/hr. Heavy leftturn volumes can be found on both the eastbound and southbound approaches at 247 and 254 veh/hr, respectively (see Figure 10-42, for example). Solution
Figure 10-42 shows the worksheet for the capacity calculations. Columns v1 through v12 contain the turning-movement volumes, and Lines 4 through 7 summarize these values by approach. Lines 8 through 11 contain the circulating flow calculations and show how these flows are derived from the turning movements. To illustrate, the circulating volume of 451 veh/hr conflicting with
the eastbound approach is composed of the westbound left-turning, the southbound left-turning, and the southbound through volumes (103 + 254 + 94 = 451 veh/hr). It is important to note that each of the four circulating flow volumes (451, 597, 809, and 639) is less than 1,200 veh/hr, part of the basis upon which it was determined that this methodology could be applied. For each approach, Lines 12 and 13 present the capacity calculations based on Equation 10-124. For the eastbound approach, the numerical values involved are as follows: cupper =
451e−(451)(4.1)/3,600 = 971 1 − e−(451)(2.6)/3,600
clower =
451e−(451)(4.6)/3,600 = 788 1 − e−(451)(3.1)/3,600
Further, the v/c ratio for this approach ranges from 0.68 to 0.84. From an interpretive standpoint, Figure 10-43 portrays the relationship between the circulating volumes and the approach capacities (from Equation 10-124). The approach volume values are also plotted so that a graphical representation of the v/c ratios can be displayed. For example, in the case of the westbound approach, it was indicated earlier that the circulating flow was 597 veh/hr. This is shown at W on the Circulating Volume axis. The corresponding capacity is 770 veh/hr, as can be seen at W on the Capacity or Volume axis. The actual approach flow is 619 veh/hr, as indicated by the data point in the middle of the graph, the vertical location of which relative to the capacity indicates the v/c ratio. One can immediately see that this v/c ratio is the highest (the data point is closest to the capacity line). The next highest v/c ratio pertains to the eastbound approach (E), followed by the southbound and northbound approaches. Parametric Analysis
Figure 10-41. Traffic volumes for Sample Calculation C1.
As a concluding comment, it is useful to show how variations in the critical gap and follow-up time values can affect the analysis results. The results obtained above can be used as a point of reference. For the capacities and v/c ratios presented in Figure 1042, tc = 4.35 and tf = 2.85, inasmuch as these are midway between the upper-bound and lower-bound values presented in Table 1054. To see what happens when alternative values are used, the results obtained from these values are compared with those obtained by using the upper-bound and lower-bound combinations. Table 10-54 shows that shifting to the upper-bound solution produces about an 11 percent increase in the v/c ratio, whereas shifting to the lower-bound values produces about a 10 percent decrease. For the westbound approach, the capacity increases to 864 veh/hr for the upper-bound values and decreases to 693 veh/hr with the lower-bound values. The implication is that variations of about 610 percent can be obtained by deviating from the midpoints of the value ranges presented in Table 10-54.
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urban streets
Figure 10-42. Worksheet for Sample Calculation C1.
Updated December 1997
unsignalized intersections
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Figure 10-43. Sample Calculation C1 capacity and volume analysis.
Table 10-54. Effects of Changes in Critical Gap and Move-Up Time Scenario tf tc Capacity (Eq. 10-124) EB WB NB SB v/c Ratio EB WB NB SB
A
B
C
3.10 4.60
2.85 4.35
2.60 4.10
788 693 573 667
871 770 644 744
971 864 728 835
0.84 0.89 0.74 0.75
0.76 0.80 0.66 0.67
0.68 0.72 0.59 0.60
V. REFERENCES 1. Florida Roundabout Guide, Florida Department of Transportation (March 1996). 2. Kyte, M., Tian, Z., Mir, Z., Hameedmansoor, Z., Kittelson, W., Vandehey, M., Robinson, B., Brilon, W., Bondzio, L., Wu, N., and Troutbeck, R., Capacity and Level of Service at Unsignalized Intersections, Final Report, Volume 1, Two-Way Stop-Controlled Intersections, National Cooperative Highway Research Program Project 3-46, TRB, National Research Council, Washington, D.C. (April 1996). 3. Brilon, W., and Stuwe, B., Capacity and Design of Roundabouts in Germany, Transportation Research Record 1398, Transportation Research Board, Washington, D.C. (1994).
4. Troutbeck, R.J., The Capacity and Design of Traffic Circles in Australia, Transportation Research Record 1398, Transportation Research Board, Washington, D.C. (1994). 5. Akcelik, R., and M. Besley, SIDRA 5 User’s Guide, ARRB Transport Research Limited (1996). 6. Flannery, A., and Datta, T., Operational Performance Measures of American Roundabouts, Transportation Research Record 1572, Transportation Research Board, Washington, D.C. (1997). 7. Troutbeck, R., The Analysis of the Performance of Roundabouts, unpublished Technical Memorandum to Committee on Highway Capacity and Quality of Service (1996).
Updated December 1997
chapter 11
ARTERIAL STREETS
CONTENTS i.
introduction .......................................................................................................................................................................... Applications ........................................................................................................................................................................... Characteristics of Arterial Flow............................................................................................................................................ Arterial Level of Service.......................................................................................................................................................
11-2 11-2 11-2 11-4
ii.
methodology and procedures for application .............................................................................................................. Step 1—Establish Arterial To Be Considered...................................................................................................................... Step 2—Determine Arterial Class and Free-Flow Speed .................................................................................................... Step 3—Divide Arterial into Sections .................................................................................................................................. Step 4—Compute Arterial Running Time............................................................................................................................ Step 5—Tabulate Intersection Information and Compute Delay ........................................................................................ Step 6—Compute Average Travel Speed............................................................................................................................. Step 7—Assess Level of Service..........................................................................................................................................
11-4 11-5 11-6 11-6 11-6 11-9 11-12 11-13
iii.
planning applications.......................................................................................................................................................... Objectives .............................................................................................................................................................................. Data Requirements ................................................................................................................................................................ Computational Steps.............................................................................................................................................................. Interpretation of Results ........................................................................................................................................................
11-15 11-15 11-15 11-16 11-17
iv.
sample calculations ............................................................................................................................................................ Calculation 1—Arterial Classification .................................................................................................................................. Calculation 2—Computation of Arterial Level of Service .................................................................................................. Step 1. Establish Arterial To Be Considered.................................................................................................................. Step 2. Determine Arterial Classification ....................................................................................................................... Step 3. Define Arterial Sections...................................................................................................................................... Step 4. Compute Running Time...................................................................................................................................... Step 5. Compute Intersection Delay................................................................................................................................ Step 6. Compute Average Travel Speed ......................................................................................................................... Step 7. Assess Level of Service ...................................................................................................................................... Calculation 3—Computation of Arterial Level of Service .................................................................................................. Calculation 4—Effect of Traffic Flow Rate on Arterial Level of Service ......................................................................... Calculation 5—Effect of Traffic Flow Rate and Length on Arterial Level of Service ..................................................... Calculation 6—Evaluation Based on Field Data.................................................................................................................. Calculation 7—Arterial with Large Signal Spacings........................................................................................................... Calculation 8—Planning Application: Determining Level of Service ................................................................................ Calculation 9—Planning Application: Determining Volumes............................................................................................. Calculation 10—Stop Control on Arterial............................................................................................................................ Calculation 11—Two-Lane Arterial .....................................................................................................................................
11-17 11-17 11-17 11-18 11-18 11-18 11-20 11-20 11-20 11-20 11-20 11-21 11-23 11-23 11-25 11-29 11-31 11-32 11-35
appendix i. Test-Car Method for Existing Arterials.............................................................................................................. 11-40 appendix ii. Worksheets for Use in Analysis ........................................................................................................................ 11-41
11-1
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11-2
urban streets
I. INTRODUCTION Urban and suburban arterials are signalized streets that primarily serve through traffic; secondarily, they provide access to abutting properties. For purposes of this manual, they are defined generally as facilities with lengths of at least 1 mi in downtown areas and at least 2 mi in other areas, with a signalized intersection spacing ranging from as little as 200 ft in downtown areas and 400 ft for interchanges and elsewhere to as long as 2 mi, and with turning movements at intersections that usually do not exceed 20 percent of total traffic volume. Roadside development along arterials can be intense, producing friction for through traffic that generally limits a driver’s ability to travel at the desired speed. In the hierarchy of urban highway transportation facilities, arterial streets are ranked between collector and downtown streets on one level and multilane suburban highways and rural roads on another. The difference in ranking is mainly determined by function and by the character and intensity of roadside development. Collector streets provide both land access and traffic circulation service within residential, commercial, and industrial areas. Their access function is more important than that of arterials, and, unlike arterials, their operation is not always dominated by traffic signals. Downtown streets are signalized facilities that often resemble arterials. They not only move through traffic but also provide access to local business by passenger cars, transit buses, and trucks. Turning movements at downtown intersections are often greater than 20 percent of total traffic because downtown flow involves a substantial amount of circulatory traffic. Typical of downtown streets are numerous pedestrian conflicts and lane obstructions caused by stopping or standing taxicabs, buses, trucks, and parking vehicles that cause turbulence in the traffic flow. Downtown street function may change with the time of the day, and for this reason certain strategically located downtown streets are converted to arterial-type operation during peak traffic hours. Multilane suburban highways and rural roads differ from arterials in the following features: (a) roadside development is not as intense, (b) density of traffic access points is not as high, and (c) signalized intersections are more than 2 mi apart. These conditions result in a smaller number of traffic conflicts, a smoother flow, and a dissipation of the platoon structure associated with arterial traffic. Urban and suburban arterials include multilane divided arterials; multilane undivided arterials; two-lane, two-way arterials (one travel lane in each direction); and one-way arterials. Federal Highway Administration (FHWA) statistics from the early 1980s indicate the following distribution of urban and suburban arterial miles in urbanized areas of more than 100,000 people: multilane divided arterials constitute approximately 37 percent; multilane undivided arterials total 27 percent; two-lane, two-way arterials make up 33 percent; and one-way arterials represent the remaining 3 percent.
arterial capacity analysis by analyzing the capacity of the signalized intersections and other such points. It is important to note that capacity analysis of signalized intersections is necessary because when demand exceeds capacity at any point along the arterial, the arterial evaluation methodology based on average travel speed becomes inappropriate. The methodology of this chapter is oriented toward the evaluation of an existing operations situation or a specific design proposal by a level-of-service (LOS) determination. The person doing such design or operations work will be able to investigate the effect of signal spacing, arterial classification (as defined here), and traffic flow on the arterial level of service. The methodology uses the signalized intersection procedure in Chapter 9 for the lane group containing the through traffic. By redefining lane arrangement (e.g., presence or absence of left-turn lanes, number of lanes), the analyst may influence the projected traffic flow in the through-traffic lane group and the capacity of the lane group. This redefinition, in turn, influences the arterial LOS determination by changing the intersection evaluation and possibly the arterial classification. Those interested in planning applications may use the entire arterial methodology in a straightforward but somewhat simplified way by computing control delay using certain default values as outlined in Chapter 9. Knowledge of the intended signal timing and quality of progression, however, is vital. If it is lacking or cannot be estimated, no meaningful estimation of arterial level of service is possible, even on a planning level. LOS criteria can be applied when travel time and delay runs are used to assess the impact of optimizing signal timing or other improvements to the arterial and periodically to evaluate the entire arterial system in an urban area. Arterial level of service also can be estimated by arterial traffic models, provided that 1. Input parameters such as running speeds and saturation flow rates are determined in a manner consistent with the procedures in this manual, 2. The delay calculated or estimated by the model is defined consistent with the definitions in this manual, and 3. The delay outputs from the model are based on the delay equations in this manual or have been validated with field data. These applications of the methodology always require determination of the level of service and associated measures of effectiveness (i.e., travel time, delay, speed). In certain cases determination of LOS values is the final objective; in other cases LOS values associated with different alternatives are computed, and decisions are made using these values. CHARACTERISTICS OF ARTERIAL FLOW
APPLICATIONS
The methodology contained in this chapter can be used by those concerned with the planning, design, and operation of arterials to evaluate the level of service of an existing or proposed facility. The methodology does not address arterial capacity, which is generally determined by the capacity of an arterial’s signalized intersections, addressed in Chapter 9. In some cases, special midblock restrictions also limit capacity. In general, the user can best conduct an Updated December 1997
The operation of vehicles on arterial streets is influenced by three main factors: arterial environment, interaction among vehicles, and effect of traffic signals. These factors contribute to the capacity of an arterial street and the quality of service offered to its users. They constitute the basic elements of the methodology discussed in Section II of this chapter. Arterial environment includes the geometric characteristics of the facility and adjacent land uses. Number of lanes and lane
arterial streets
11-3
Figure 11-1. Typical time-space trajectories of vehicles on one-lane arterial segment.
width, type of median, driveway-access-point density, and spacing between signalized intersections are among the environmental factors, as are the existence of parking, level of pedestrian activity, speed limit, and population of the city. The arterial environment affects a driver’s notion of safe speed. Even if the effect of the other factors is negligible, the environment restricts a driver’s desired speed, that is, the maximum speed at which a driver would like to travel under a given set of environmental conditions. The average desired speed of all drivers on an arterial segment or section is termed free-flow speed in this chapter. Interaction among vehicles is determined by traffic density, the proportion of trucks and buses, and turning movements. This interaction affects the operation of vehicles at intersections and, to a lesser extent, between signals. Seldom can a driver travel at the desired speed. Most of the time, the presence of other vehicles restricts the speed of a vehicle in motion because desired speeds differ among drivers or because downstream vehicles are accelerating from a stop and have not yet reached their drivers’ desired speeds. Therefore, the average speed of a vehicle in motion over a certain length of road, or running speed, is usually lower than the desired speed of its driver because of the effect of vehicle interactions. Likewise, the average running speed of all vehicles on an arterial segment is usually lower than the free-flow speed of the segment. Traffic signals force vehicles to stop and to remain stopped for a certain time, and then release them in platoons. The delays and speed changes caused by traffic signal operation considerably reduce the quality of traffic flow on arterial streets.
The average delay per vehicle depends mainly on the proportion of red time displayed to the arterial segment, the proportion of vehicles arriving on green (or the quality of traffic signal progression), and the traffic volume. The travel speed over an arterial segment (which includes time lost due to intersection effects, including stops and all associated control delay for the through movements) is generally lower than the corresponding running speed. Similarly, the average travel speed of all vehicles on the segment is lower than their average running speed unless no vehicles stop. Figure 11-1 shows simplified time-space trajectories of representative vehicles along one lane of an arterial. Vehicles 1 and 2 turned onto the arterial from side streets, and the rest were discharged from the upstream signal. Vehicles 1, 2, and 3 arrived at the downstream signal approach during the red interval and had to stop. Vehicle 4 could have arrived at the stop line on green but had to stop because it was blocked by Vehicle 3, which was not yet in motion. Vehicles 5, 6, and 7 did not stop but had to reduce their speeds because they were still affected by the stoppages caused by the signal. Vehicle 8 was delayed because its driver’s desired speed was higher than that of Vehicle 7’s driver. Vehicles 9 and 10 traveled at their drivers’ desired speeds. The travel speeds of Vehicles 1, 2, 3, and 4 were lower than their respective running speeds, which in turn were lower than the desired speeds of their drivers. The travel speeds of Vehicles 5, 6, 7, and 8 were equal to their corresponding running speeds, but lower than their drivers’ desired speeds. Finally, for Vehicles 9 and 10, whose drivers were traveling at their desired speeds, the three types of speeds have the same value. Updated December 1997
urban streets
11-4 ARTERIAL LEVEL OF SERVICE
Arterial level of service is based on average through-vehicle travel speed for the segment, section, or entire arterial under consideration. This parameter is the basic measure of effectiveness for Chapter 11. The average travel speed is computed from the running time on the arterial segment or segments and the control delay for through movements at all intersections. To ensure that the arterial is of sufficient length so that average travel speed is a reasonable measure of effectiveness, the arterial’s length generally should be at least 1 mi in downtown areas and at least 2 mi in other areas. Arterial level of service is defined in terms of average travel speed of all through vehicles on the arterial. It is strongly influenced by the number of signals per mile and the average intersection control delay. On a given facility, such factors as inappropriate signal timing, poor progression, and increasing traffic flow can substantially degrade arterial level of service. Arterials with medium to high signal densities (more than two signalized intersections per mile) are even more susceptible to these factors, and poor arterial level of service will probably be observed even before substantial intersection problems occur. The following general statements may be made regarding arterial level of service: 1. LOS A describes primarily free-flow operations at average travel speeds, usually about 90 percent of the free-flow speed for the arterial classification. Vehicles are seldom impeded in their ability to maneuver in the traffic stream. Delay at signalized intersections is minimal. 2. LOS B represents reasonably unimpeded operations at average travel speeds, usually about 70 percent of the free-flow speed for the arterial classification. The ability to maneuver in
the traffic stream is only slightly restricted and delays are not bothersome. 3. LOS C represents stable operations; however, ability to maneuver and change lanes in midblock locations may be more restricted than in LOS B, and longer queues, adverse signal coordination, or both may contribute to lower average travel speeds of about 50 percent of the average free-flow speed for the arterial classification. 4. LOS D borders on a range in which small increases in flow may cause substantial increases in approach delay and hence decreases in arterial speed. LOS D may be due to adverse signal progression, inappropriate signal timing, high volumes, or some combination of these. Average travel speeds are about 40 percent of free-flow speed. 5. LOS E is characterized by significant delays and average travel speeds of one-third the free-flow speed or less. Such operations are caused by some combination of adverse progression, high signal density, high volumes, extensive delays at critical intersections, and inappropriate signal timing. 6. LOS F characterizes arterial flow at extremely low speeds, from less than one-third to one-quarter of the free-flow speed. Intersection congestion is likely at critical signalized locations, with long delays and extensive queuing. Table 11-1 contains the arterial LOS definitions, which are based on average travel speed over the arterial segment being considered (up to and including the entire facility). It should be noted that if demand volume exceeds capacity at any point on the facility, average travel speed may not be a good measure of the arterial level of service. Thus, intersection demand-to-capacity ratios greater than 1.0 will probably result in an unacceptable level of service on the arterial. The arterial classification concept in Table 11-1 is defined as part of the methodology to follow.
II. METHODOLOGY AND PROCEDURES FOR APPLICATION This methodology provides the framework for arterial evaluation. If field data are available, this framework can be used to determine the level of service of a given arterial without reference to running time and intersection delay estimates. Instead of treating field evaluation as a less desirable method than estimation, the transportation analyst should consider field data a better alternative
for arriving at accurate arterial evaluations. If field data are unavailable, arterial traffic models are an alternative that can be used provided certain conditions are met. Input parameters such as running speeds and saturation flow rates must be determined in a manner consistent with the procedures in this manual, the delay calculated or estimated by the model must be defined consis-
Table 11-1. Arterial Levels of Service arterial classification Range of free-flow speeds Typical free-flow speeds
i
ii
iii
iv
45 to 55 50
35 to 45 40
30 to 35 33
25 to 35 30
level of service A B C D E F NOTE: Units are miles per hour.
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average travel speed ≥42 ≥34 ≥27 ≥21 ≥16 1.50 and ≤2.00 >2.00
0.333 0.667 1.000 1.333 1.667 2.000
Very poor Unfavorable Random arrivals Favorable Highly favorable Exceptional
NOTE: Rp = P × (C/g).
Table 11-6. Uniform Delay (d1) Progression Adjustment Factor (PF) green ratio (g/C)
AT 1
AT 2
arrival type (at) AT 3 AT 4
AT 5
AT 6
0.20 0.30 0.40 0.50 0.60 0.70 Default, fp Default, Rp
1.167 1.286 1.445 1.667 2.001 2.556 1.00 0.333
1.007 1.063 1.136 1.240 1.395 1.653 0.93 0.667
1.000 1.000 1.000 1.000 1.000 1.000 1.00 1.000
0.833 0.714 0.555 0.333 0.000 0.000 1.00 1.667
0.750 0.571 0.333 0.000 0.000 0.000 1.00 2.000
NOTES: 1. 2. 3. 4.
1.000 0.986 0.895 0.767 0.576 0.256 1.15 1.333
PF = (1 − P)fp /(1 − g/C). Tabulation is based on default values of fp and Rp. P = Rp ∗ g/C (may not exceed 1.0). PF may not exceed 1.0 for AT 3 through AT 6.
(stationary or moving) while the green phase is displayed. The value of PF may be computed from measured values of P using the default values for fp. Alternately, Table 11-6 may be used to determine PF as a function of the arrival type based on the default values for P (i.e., Rp × g/C) and fp associated with each arrival type. If PF is estimated by Equation 11-6, its calculated value may exceed 1.0 for Arrival Type 4 with extremely low values of g/C. As a practical matter, PF should be assigned a maximum value of 1.0 for Arrival Type 4. This constraint has already been taken into consideration in the values shown in Table 11-6. Application of the progression adjustment factor requires detailed knowledge of offsets, travel speeds, and intersection signalization. When delay is estimated for future situations involving coordination, particularly when alternatives are analyzed, it is advisable to assume Arrival Type 4 as a base condition for coordinated lane groups, in which case P may be estimated from Table 11-5 and Equation 11-5 as Rp × g/C. Arrival Type 3 should be assumed for all uncoordinated lane groups. Movements made from exclusive left-turn lanes on protected phases are not usually provided with good progression. Thus, Arrival Type 3 is usually assumed for coordinated left turns. When the actual arrival type is known, it should be used. When the coordinated left turn is part of a protected-permitted phasing, only the effective green for the protected phase should be used to determine the PF since the protected phase is normally associated with platooned coordination. When a lane group contains movements that have different levels of coordination, a flow-weighted average of P should be used in determining the PF.
a k-value of 0.50 is used. This value is based on a queuing process with random arrivals and uniform service equivalent to the lane group capacity. Actuated controllers, on the other hand, have the ability to adjust the green time to the cyclic demand, thus reducing the overall incremental delay component. The delay reduction depends in part on the controller’s unit extension and the prevailing degree of saturation. Recent research indicates that lower unit extensions result in lower values of k and d2; however, when the degree of saturation approaches 1.0, an actuated controller behaves similarly to a pretimed controller, resulting in k-values of 0.50 at X ≥ 1.0. Table 11-7 illustrates recommended k-values for pretimed and actuated lane groups with different unit extensions and degrees of saturation. Upstream Filtering/Metering Adjustment Factor (I )
The incremental delay adjustment term I in Equation 11-4 incorporates the effects of metering arrivals from upstream signals. For isolated signals, an I-value of 1.0 is used. This value is based on a queuing process with random arrivals such that the ratio of the variance to mean arrivals per cycle is equal to 1.0. Upstream signals decrease the variance by metering arrivals at the downstream intersection, thus reducing the ratio of the variance to mean arrivals per cycle. The I-value and the resultant delay reduction depend on the through movement’s degree of saturation at the upstream intersection and the amount of entering and exiting traffic between the two intersections. Table 11-8 illustrates recommended values of I for different upstream degrees of saturation at the upstream intersection.
Actuated Control Adjustment Factor (k)
Example
The incremental delay adjustment term k in Equation 11-4 incorporates the effect of controller type on delay. For pretimed signals,
Delay is a complicated variable that is sensitive to a variety of local and environmental conditions. The procedures provided here Updated December 1997
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Table 11-7. Recommended k-Values for Lane Groups Under Actuated and Pretimed Control unit extension (UE) (sec)
degree of saturation (X) ≤0.50
0.60
0.70
0.80
0.90
≥1.0
≤2.0 2.5 3.0 3.5 4.0 4.5 5.0
0.04 0.08 0.11 0.13 0.15 0.19 0.23
0.13 0.16 0.19 0.20 0.22 0.25 0.28
0.22 0.25 0.27 0.28 0.29 0.31 0.34
0.32 0.33 0.34 0.35 0.36 0.38 0.39
0.41 0.42 0.42 0.43 0.43 0.44 0.45
0.50 0.50 0.50 0.50 0.50 0.50 0.50
NOTES: 1. k = 0.50 for nonactuated lane groups. 2. For a given UE and its kmin value at X p 0.5, k = (1 − 2kmin) (X − 0.5) + kmin. 3. For UE > 5.0, extrapolate to find k, keeping k ≤ 0.5.
Table 11-8. Recommended I-Values For Lane Groups With Upstream Signals degree of saturation at upstream intersection (Xu) I
0.40 0.922
0.50 0.858
0.60 0.769
0.70 0.650
0.80 0.500
0.90 0.314
≥1.0 0.090
NOTE: I = 1.0 − 0.91Xu2.68 and Xu ≤1.0.
present reasonable estimates for delays expected for average conditions. They are most useful when used to compare operational conditions for various geometric or signalization designs. When existing conditions are evaluated, it is advisable to measure delay in the field. Appendix III of Chapter 9 contains guidelines for intersection delay measurements using lane occupancy and volume counts. Description: Consider an arterial segment with a through lane group with two lanes, a demand volume of 1,500 veh/hr, and peak hour factor of 0.91. Further, a pretimed signal has a cycle length of 90 sec, the g/C ratio is 0.60, and X or the v/c ratio is 0.90. Vehicles arrive as a dense platoon at the beginning of the green. What is the estimated control delay for the through lane group? Solution: To use Equations 11-3 and 11-4 to compute control delay, it is necessary to know C, g/C, X, and c. The last term must be computed. The adjusted demand flow rate is v = (1,500/0.91) = 1,648 veh/hr Once it is known that X or the v/c ratio is 0.90, c can be calculated as c = v/(v/c) c = 1,648/(0.90) = 1,831 veh/hr The intersection control delay is computed as d = 17.8 + 3.5 = 21.3 sec/veh. From the description of the arriving vehicles, the arrival type is 5. On the basis of a pretimed signal, a g/C ratio of 0.60, and Arrival Type 5, Tables 11-6, 11-7, and 11-8 are consulted to find PF = 0.0, k = 0.5, and I = 1.0, respectively. Thus, the estimated control delay = 3.5 sec/veh. The computations must be done for each signalized intersection or obtained from the results of Chapter 9 evaluations. Figure 11-5 Updated December 1997
is a summary worksheet for intersection delay computations. An additional blank worksheet may be found in Appendix II to this chapter.
STEP 6—COMPUTE AVERAGE TRAVEL SPEED
The average speed is to be computed by segment and over the entire arterial. It is recommended that the user also prepare a speed profile of the facility and supplement the LOS assessment with insights gained from the speed profile and the levels of service of the individual intersections. Figure 11-6 shows a worksheet, with some illustrative data filled in, which is provided to ease the task of assembling the information. Equation 11-1 is used to compute the arterial speed for each segment and for the overall facility. Performing these computations results in the speed profile shown in Figure 11-7. For segments 1 and 9, the running time per mile for a segment 0.10 mi long is used, but is multiplied by the actual segment lengths. Sample Computation. Fourth Avenue is a principal arterial of intermediate design with a 35-mph free-flow speed (Figure 11-6). From Table 11-3, it is arterial Classification III. In Section 2 of the arterial, the average segment length is 0.20 mi. From Table 11-4, the running time per mile is 128 sec. The total running time in the section is given by 128 × (0.20 + 0.20 + 0.20) = 76.8 sec The control delay for the arterial through movements at the three intersections in Section 2 is given in Figure 11-6 as 5.0 + 7.0 + 10.0 = 22.0 sec, so the total travel time is 76.8 + 22.0 = 98.8 sec. The arterial speed in the section is 3,600 x 0.60/98.8 = 21.9 mph.
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Figure 11-5. Worksheet for summary of arterial intersection delay estimates.
STEP 7—ASSESS LEVEL OF SERVICE
A distinct set of arterial LOS criteria has been established for each arterial classification. These sets of criteria are based on the differing expectations drivers are judged to have for the different classes of arterials. In the arterial LOS definitions, both the free-flow speed of the arterial classification and the intersection LOS definitions are taken into account. In general, the arterial LOS criteria are based on the smooth and efficient movement of through traffic along an entire arterial. Therefore, it is necessary to expect less delay per segment than the corresponding intersection level of service. Table 11-1 gives the arterial LOS criteria for each of the four arterial classifications. The lower the arterial classification (i.e., the larger the classification number), the lower the driver’s expec-
tations while driving on that facility and the lower the speed associated with a given level of service. Thus, a Classification III arterial provides LOS B at a lower speed than does a Classification I arterial. The analyst should be aware of this relationship in explaining before-and-after assessments of arterials when upgrading is involved. If reconstruction results in upgrading a facility from Classification II to Classification I, it is possible that the level of service will not change (or may even technically degrade), despite higher average speed and other improvements, because expectations are higher. Note that the concept of an overall arterial level of service is generally meaningful only when all segments on the arterial are of the same classification. If different arterial classifications are represented, the LOS criteria are different. Updated December 1997
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Figure 11-6. Worksheet for computation of arterial level of service.
Updated December 1997
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Figure 11-7. Speed profile by arterial section.
III. PLANNING APPLICATIONS OBJECTIVES
The objective of an arterial LOS analysis at a planning level is to approximate the operating conditions of the facility. A major use for this type of analysis is related to growth management issues. The accuracy of the planning LOS analysis is largely dependent upon the degree of generalization of input data and should not be used for design or operational analyses. The planning method is most applicable when 1. LOS estimates are desired, 2. Field data are lacking, 3. Relatively long planning horizons are used, and 4. Individuals with limited transportation planning experience are involved. A major difference between the planning analysis of signalized intersections and that of arterials is the treatment of turning vehicles. Whereas the purpose of a signalized intersection is to move vehicles (including turning vehicles) past a point, the purpose of an arterial is to move (through) vehicles over a reasonable length of roadway. Because the emphasis of an arterial is on through movement, the major simplifying assumption in this planning application is that left turns are accommodated by providing left-turn bays at major intersections and controlling the left-turn movement with a separate phase that is properly timed. With this simplifying assumption, many of the inputs and complexities of intersection analyses can be handled abstractly as default values, allowing a relatively easy-to-use planning application; however, as a result of
this assumption, planning application results should not be used for intersection design or traffic operations analyses. DATA REQUIREMENTS
To conduct a planning analysis, traffic, roadway, and signal input values or assumed defaults are needed for the following characteristics: Traffic characteristics: Annual average daily traffic (AADT), Planning analysis hour factor (K), Directional distribution factor (D), Peak hour factor (PHF), Adjusted saturation flow rate, Percentage of turns from exclusive lanes; Roadway characteristics: Number of through lanes (N), Free-flow speed, Arterial classification, Medians, Left-turn bays or exclusive left-turn lanes; Signal characteristics: Arrival type, Signal type, Cycle length (C), Effective green ratio (g/C). Some of these characteristics are discussed in the remainder of this section. Updated December 1997
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Planning Analysis Hour Factor (K )
The planning analysis hour factor represents the percentage of AADT occurring in the peak hour. For planning purposes many possible peak hours may be appropriate. K30 (the 30 highest hour volumes of the year) is widely accepted as the design hour in nonurban areas. K100 approximates the typical weekday peak hour during the peak season in developed areas and is frequently used in long-range urban transportation models. K200 to 400 is a better representation of a typical peak hour of the year. In many urban areas, general ranges for K30, K100, and K200 to 400 are 8.5 to 11.0 percent, 8.0 to 10.0 percent, and 7.0 to 9.0 percent, respectively. The analyst needs to determine the appropriate peak hour.
saturation flow rate may be reduced 5 percent for roadways that do not have medians.
Left-Turn Bays or Exclusive Left-Turn Lanes
Left-turn bays or lanes are storage areas at signalized intersections to accommodate left-turn movements. These bays or lanes must be long enough to accommodate left turns without impeding the through movement. For planning purposes, the saturation flow rate should be reduced 20 percent for roadways that do not have left-turn bays at major intersections. (This value is a 15 percent additional reduction for a roadway that does not have a median.)
Adjusted Saturation Flow Rate
Effective Green Ratio (g /C)
Numerous factors affect the saturation flow rate per lane (see Chapter 9). For a planning analysis, these adjustments may reasonably be combined and multiplied by the ideal saturation flow rate to determine an adjusted saturation flow rate. On the basis of an ideal saturation flow rate of 1,900 passenger cars per hour of green time per lane (pcphgpl), a reasonable range for urban arterials during the peak hour is 1,750–1,850 pcphgpl.
The parameter g/C is the ratio of the time allocated for the through traffic movement (red clearance minus the startup lost time minus effective green time) to the cycle length (C). An arterial’s through g/C for each intersection is desirable; however, for broad planning purposes a weighted g/C may be appropriate. The weighted g/C of an arterial is the average of the critical-intersection through g/C and the average-intersection through g/C. For example, if an arterial section has three signalized intersections with effective green ratios of 0.4, 0.7, and 0.7, the critical intersection has a g/C of 0.4 (the lowest g/C); the average intersection has a g/C of 0.6 [(0.4 + 0.7 + 0.7)/3], and the weighted g/C is 0.5 [the average of the critical g/C and the average g/C, (0.6 + 0.4)/2]. Thus, the weighted g/C takes into account the adverse impact of the critical intersection and the overall quality of flow for the arterial length. Average weighted effective green ratios for arterials vary by road purposes and by areas.
Percentage Turns from Exclusive Lanes
Turns from exclusive lanes represent the percentage of vehicles performing left- or right-turn movements at signalized intersections from lanes dedicated solely to turning movements. The planning methodology assumes that left turns are accommodated by separate lanes and phases so that they have minimal effect on through vehicles. Where a separate right-turn lane exists, it is reasonable to add the percentage of right turns to the percentage of left turns (assuming a left-turn bay or lane) to determine the percentage of turns from exclusive lanes. Number of Through Lanes
Because significant delays seldom occur in midblock locations, a parameter of importance is the number of through and shared right-turn lanes at signalized intersections; however, when significant midblock delays occur or reasonable lane continuity between intersections is not maintained, caution should be used in strictly applying the concept of the number of such lanes. Free-Flow Speed
For planning purposes, an arterial’s free-flow speed should be based on actual studies of the road or on studies of similar roads and should be consistent with arterial classifications. The actual or probable posted speed limit may be used as a surrogate for freeflow speed if comparable roadway free-flow studies do not exist. Medians
Medians are painted, raised, or grassed areas that separate opposing midblock traffic lanes and that are wide enough to serve as bays for turning vehicles. For planning purposes, the adjusted Updated December 1997
COMPUTATIONAL STEPS
The calculation process for determining arterial level of service is illustrated in Figure 11-8 and consists of the following steps: 1. Convert daily volumes to the planning analysis hour by an appropriate planning analysis hour factor (K). 2. Multiply K by the directional distribution factor (D) to obtain hourly directional volumes. 3. Adjust the hourly directional volumes based on PHF and turns from exclusive lanes to yield estimated through volumes for 15-min service flow rates. 4. Calculate the running time on the basis of arterial classification, intersection spacing, and free-flow speed. 5. Calculate the intersection control delay on the basis of adjusted saturation flow rates, number of lanes (N), arrival type, signal type, cycle length (C), and g/C for each intersection using Equations 11-3 and 11-4. 6. Calculate the average travel speed using running time and intersection control delay. 7. Obtain arterial level of service on the basis of the average travel speed. Calculation 8 in Section IV of this chapter illustrates the computational steps in a planning analysis. Frequently in a planning analysis, however, the level of service may be given and the desired outcome is a volume—hourly direc-
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tional, hourly nondirectional, or daily. For such applications, the calculation process is essentially reversed, as follows: 1. Select the level of service and the corresponding average travel speed (range or minimum) based on arterial type and freeflow speed as selected from Table 11-1. 2. Compute the total section running time for the given arterial type, number of intersections, free-flow speed, and section length. 3. Calculate the control delay at all intersections (d) using Equation 11-1 and Steps 1 and 2. 4. Compute v by using the value of average control delay, given number of lanes, adjusted saturated flow rate, arrival type, C, and weighted g/C in Equations 11-2 to 11-4. 5. Determine the hourly directional volume for the design hour using the percentage of turns from exclusive lanes, basic through 15-min volumes, and the PHF. 6. Calculate the two-way hourly directional volume for the design hour using the hourly directional volume and the directional distribution factor. 7. Determine AADT using the two-way hourly directional volume and the applicable K factor. INTERPRETATION OF RESULTS
Figure 11-8. Arterial LOS calculation process.
Planning analysis results range from a rough estimate of level of service to an operational analysis, depending primarily on the degree to which default values are used as input. For example, using statewide defaults for appropriate traffic, roadway, and signal characteristics results in rough LOS estimates. Using area- or roadway-specific data but treating all signal characteristics the same (e.g., using a weighted g/C approach) should provide more accurate LOS estimates. Using specific traffic, roadway, and signal data for each road segment and traffic signal should provide an even more accurate LOS estimate. The next level of precision is a detailed treatment of turning movements and signal timing, which is essentially an operational analysis except that projected rather than actual traffic volumes are used.
IV. SAMPLE CALCULATIONS CALCULATION 1—ARTERIAL CLASSIFICATION
1. Description: An arterial with three lanes in each direction and signal spacing of 0.15 mi passes through an area with moderate roadside development. Virtually all of the traffic passes through the area; there is very little pedestrian activity. Identify the arterial classification. 2. Solution: To determine the arterial classification, it is necessary to decide the design and functional categories of the arterial and then to use Table 11-3 to specify the arterial classification. The statement that ‘‘virtually all of the traffic passes through the area’’ defines the functional category: the roadway is a principal arterial. Table 11-2 can be used to assist in determining the design category. Note that the arterial is a multilane undivided facility with approximately seven signals per mile (based on 0.15-mi spacing), moderate roadside development, and very little pedestrian activity. The design category is therefore intermediate. Referring to Table 11-3, one concludes that the arterial is Classification III. This information is used in determining the LOS defi-
nitions to be used in evaluating the arterial. Further, lacking more specific information, one can expect a free-flow speed on the order of 33 mph (refer to the top of Table 11-1), with a range of 30 to 35 mph.
CALCULATION 2—COMPUTATION OF ARTERIAL LEVEL OF SERVICE
1. Description: A multilane divided facility functions as a principal arterial. There is significant access control, no parking, and a signal spacing of approximately 0.30 mi between pretimed signals. The arterial has little roadside development, two lanes in each direction, and a measured free-flow speed of 39 mph. Detailed information on the intersection parameters and the arterial segments for the southbound flow is contained in Figures 11-9 and 11-10. The progression is excellent in the southbound direction. Updated December 1997
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Figure 11-9. Calculation 2, description: using worksheet for summary of arterial intersection delay estimates.
Determine the arterial level of service by segment and for the entire facility. Do not aggregate the segments. 2. Solution: This solution proceeds according to the steps outlined in Figure 11-2. In some applications, it may not be necessary to perform all steps, or it may be easier to do certain steps before others. For instance, if the intersection evaluations have been done previously (or if the summary information is available), that information may be entered on the appropriate worksheet (Figure 11-5) and the control delay computed before the arterial running times are computed.
T T T T T
Multilane divided, Significant access control, No parking, Little roadside development, Seven signals in 2.1 mi (three signals per mile).
The facility clearly belongs to the suburban design category. On the basis of a functional category of principal arterial and a design category of suburban, the facility is found to be a Classification II arterial by referring to Table 11-3.
Step 1. Establish Arterial To Be Considered
This step has been performed in the preceding statement. Step 2. Determine Arterial Classification
The functional category, principal arterial, is given. The design category may be established by referring to Table 11-2 and noting the following characteristics: Updated December 1997
Step 3. Define Arterial Sections
Step 3 may be skipped because the instructions in the description were not to aggregate the segments. Nonetheless, note that some sections could be aggregated on the basis of average segment lengths and volume pattern. For instance, the following aggregations could be made:
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Figure 11-10. Calculation 2, description: using worksheet for computation of arterial level of service.
Updated December 1997
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11-20 Segment 1 2 3 4 5 6 7
Section 1 1 2 2 2 3 3
If the volume differences make the user uncomfortable with this aggregation, it could be checked after the intersection delay has been estimated. Step 4. Compute Running Time
The arterial is Classification II with a free-flow speed of 39 mph, which establishes the relationship to be used for the running time computation (see Table 11-4). Consider Segment 1. For a Classification II arterial and a segment length of 0.20 mi, Table 11-4 indicates a running time per mile of 115 sec for a free-flow speed of 40 mph and 125 sec for a free-flow speed of 35 mph. It may be interpolated that for 39 mph the running time would be 117 × 0.20 = 23.4 sec. This information is entered on the computation of arterial LOS worksheet. Step 5. Compute Intersection Delay
Figure 11-11 shows the arterial intersection delay estimates for Calculation 2. Note that because this computation is an arterial evaluation, the information must be for the lane group containing the principal part of the through movement. This information is generally available for the desired lane group from evaluations of individual intersections based on procedures described in Chapter 9. Equations 11-3 and 11-4 are used to compute the uniform delay (d1) and the incremental delay (d2), which can then be entered on the summary worksheet. The selection of the arrival type for the approaching vehicles is a special consideration. In this case, it is straightforward because of the information given in the description that progression is excellent in the southbound direction. When this information is matched with the arrival type definitions, Arrival Type 5 is selected because it is defined as a dense platoon arriving at the beginning of the green phase with a highly favorable progression quality. Table 11-6 shows the progression factors (PFs) for the pretimed signals and arrival types given. As shown in Figure 11-11, all the intersections have g/C ratios of 0.60, so a PF of 0.00 is used for all of them. The results of the intersection computations are shown transferred to the arterial LOS worksheet in Figure 11-12. Step 6. Compute Average Travel Speed
With the running time from Step 4 and the delay time from Step 5, the computations may be summarized using the arterial LOS worksheet. The completed worksheet is shown in Figure 1112, with the calculation for each section (in this case, each segment) identical in form to that shown on the bottom of the worksheet for the entire arterial. Updated December 1997
Figure 11-13 shows the speed profile for the arterial. This drawing is a valuable depiction of the operation and should be constructed as part of each evaluation. Step 7. Assess Level of Service
With all of the preliminary work done, the final determination of LOS values is straightforward. The speeds computed in the summary arterial LOS worksheet can be compared with the definitions for the appropriate arterial classification (in this case, Classification II, as established in Step 2) given in Table 11-1. These are entered on the arterial LOS worksheet in Figure 11-12 and, together with the intersection levels of service determined previously, on the speed profile in Figure 11-13. As stated in Section I, intersection LOS values are generally better than the arterial LOS values. This difference is logical, because an intersection with less than 5 sec of delay per vehicle is certainly LOS A, whereas an arterial on which one could travel at a speed of 39 mph but instead has to travel at 30 to 35 mph is somewhat less than LOS A. CALCULATION 3—COMPUTATION OF ARTERIAL LEVEL OF SERVICE
1. Description: The northbound side of the arterial described in Calculation 2 has intersection traffic as shown in Figure 11-14 and very poor progression, with virtually the entire northbound platoon arriving in the middle of the red at each intersection. Determine the arterial level of service by segment and for the entire facility. Do not aggregate the segments. 2. Solution: The calculations for this solution are identical in form and sequence to those of Calculation 2 and will not be repeated; however, certain key points must be highlighted: T The evaluation of an arterial is by direction, and a two-way arterial usually requires two evaluations, one for each direction, just as was required in Calculation 2. T The arrival types in the two directions are generally different because the progression of the signal timing is often set to favor one direction over the other. This difference has a major impact on the intersection delay estimates. T It is useful to include the segment numbers in the speed profile (as shown in Figure 11-13), to make the final presentation clear. It is also useful to mark the direction of travel clearly. T The intersections analyzed are those at the input and output ends of each segment. The results of the computations are shown in Figures 11-15 and 11-16, and the speed profile is shown in Figure 11-17, which for comparative purposes also shows the southbound speed profile as well as the intersection and arterial levels of service for both directions. One additional point stands out: the determination of arrival type so that correct PFs may be selected. The description states that there is ‘‘very poor progression, with virtually the entire northbound platoon arriving in the middle of the red at each intersection.’’ It is important to note that this situation is not the worst condition: a careful reading of the arrival type descriptions makes it clear that Type 2 covers the present case, whereas the worst case—Type 1—is reserved for a dense platoon arriving at the beginning of the red phase.
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Figure 11-11. Calculation 2, solution: using worksheet for summary of arterial intersection delay estimates. CALCULATION 4—EFFECT OF TRAFFIC FLOW RATE ON ARTERIAL LEVEL OF SERVICE
1. Description: An arterial with two lanes in each direction and a 35-mph free-flow speed has been found to be a Classification III arterial. Ten signals are spaced 0.20 mi apart. The intersections all have pretimed signals with a 60-sec cycle length and g/C of 0.50. The progression is excellent. For a range of adjusted traffic demand from a flow rate of 600 to 1,600 veh/hr, plot the arterial segment speed and find the arterial level of service, as well as the intersection levels of service. 2. Solution: The relationships shown in this chapter for arterial running time do not depend explicitly on arterial volume or flow rate (see Note 5, Table 11-4). The arterial speed is sensitive to traffic volume because the intersection delay is dependent on that volume. Recall that the basic relation is Equation 11-1, which is repeated here for convenience: ART SPD =
3,600 * (length) [(running time/mile) * (length) + (∑ inters. control delay)]
(11-1)
For the stated situation, the segment running time per mile is
found from Table 11-4 to be 128 sec for a segment length of 0.20 mi. The running time in the segment is therefore 128 × 0.20 = 25.6 sec. The intersection control delay is based on Equations 11-3 and 11-4 and the application of the PF. Two parameters are given (C = 60 sec and g/C = 0.50). The other two, arterial lane group capacity (c) and v/c ratio (X), are not directly given. Without specific information on the lane group capacity, it is both possible and necessary to compute c = 1,600 × 2 × 0.50 = 1,600 veh/hr, for all segments. If the g/C differed from segment to segment, the computed value would also differ. When this relationship is used for a specific site, the evaluation becomes highly approximate; however, this sample calculation is for a typical or representative arterial. In the information given, the adjusted demand flow rate varies from v = 600 veh/hr to v = 1,600 veh/hr. For each value of v, the corresponding value of X = v/1,600, because c = 1,600 veh/hr was just computed above. The arrival type is 5 because the progression is excellent. The PF is selected from Table 11-6 for Arrival Type 5 and a g/C of 0.50. The results of the computations are given in Table 11-9. The Updated December 1997
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Figure 11-12. Calculation 2, solution: using worksheet for computation of arterial level of service.
estimated control delay is the uniform delay multiplied by the PF plus the incremental delay. The levels of service are identified by referring to Table 111 for a Classification III arterial and to Table 9-1 for the intersections. Note that the intersection level-of-service is based Updated December 1997
on control delay and is shown for the lane group containing the through traffic. Figure 11-18 is a plot of arterial segment speed as a function of arterial volume for the stated condition of a 0.20-mi segment length. Note that the intersection approach delay ranges from 13 to 32 per-
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Figure 11-13. Speed profile for Calculation 2, southbound traffic.
cent of the total time spent on the segment, depending on the traffic flow rate. Figure 11-19 is a plot of arterial segment average travel speed as a function of arterial flow rate for a 0.10-mi segment length. For comparative purposes, the plot for a 0.20-mi segment length is also shown. The facts that the speeds are much lower and that the arterial level of service is now significantly lower than the intersection level of service deserve attention. First, it is necessary to observe that with the 0.10-mi segment, the intersection delay per mile has increased (relative to that in Calculation 4) because there are now more intersections per mile: 5 intersections per mile for the 0.20-mile segment have become 10 intersections per mile for the 0.10-mi segments. Thus, a delay of 8.0 sec/veh per intersection now contributes 10 × 8.0 = 80 sec/ mi to the arterial travel time, whereas it was 5 × 8.0 = 40 sec/mi in the previous computation. Thus, two radically different arterials are being compared. The driver’s expectation is more demanding for an arterial than for an individual intersection. With 10 signals per mile, very little delay per intersection is required to degrade the quality of flow for through traffic; however, any intersection with less than 5.0 sec of stopped delay is operating rather well (i.e., LOS A is a realistic evaluation of such an intersection). CALCULATION 5—EFFECT OF TRAFFIC FLOW RATE AND LENGTH ON ARTERIAL LEVEL OF SERVICE
1. Description: Reevaluate Calculation 4 using a signal spacing of 0.10 mi. All other information is the same as that given in Calculation 4, including the arterial classification. 2. Solution: Numerically, the computations are the same as in Calculation 4, and all the introductory remarks are the same. The results of the computations are given in Table 11-10.
The levels of service are again identified by referring to Table 11-1 for a Classification III arterial and to Table 9-1 for the intersections. Table 11-10 illustrates the following point: because of the close signal spacing and the control delay per unit length, it is possible for arterial level of service to be two or even three levels worse than that of a typical intersection. (As will be shown in Calculation 7, it is also possible for the arterial level of service to be better than the intersection level of service when the segment is very long.) Note that in this calculation, the intersection delay ranges from 20 to 45 percent of the total time spent on the segment, depending on the traffic flow rate. In Calculation 4, the range was 13 to 32 percent.
CALCULATION 6—EVALUATION BASED ON FIELD DATA
1. Description: On a given multilane two-way divided arterial with left-turn bays and good access control, the free-flow speed is measured along its length as 45 mph. The following data are collected along its eight eastbound segments, using the field data procedures of Appendix I:
Segment 1 2 3 4 5 6 7 8
Length (mi) 0.20 0.15 0.15 0.20 0.25 0.25 0.25 0.20
Average Travel Time (sec) 28.3 19.2 21.8 29.4 49.7 40.6 35.2 28.1
Average Control Delay (sec/veh) 3.4 1.7 3.6 5.3 17.6 0.5 6.2 3.2
Updated December 1997
urban streets
11-24
Figure 11-14. Calculation 3, description: using worksheet for summary of arterial intersection delay estimates.
These data are based on an appropriate number of travel time runs that include both the running time and the intersection control delay. Find the arterial level of service, by segment and for the entire facility, as well as the intersection levels of service. 2. Solution: To determine the arterial classification, consult Tables 11-2 and 11-3 and note that T The facility is multilane divided, T Access control is good, T There are eight signals in 1.65 mi, or about five signals per mile. It is likely that the design category would be suburban on the basis of Table 11-2. Because the facility is a principal arterial, Table 11-3 leads one to determine that it belongs in arterial Classification Updated December 1997
II. The ranges of free-flow speed shown in Table 11-4 indicate that a measured free-flow speed of 45 mph is consistent with arterial Classification II. The field data can also be used to compute the arterial speed by segment and for the entire facility without any need to use Table 11-4. The computations of the arterial speed are shown in the summary of calculations on the completed arterial LOS worksheet in Figure 11-20. The speed calculations are straightforward; for instance, for Segment 1, ART SPD = 3,600 × 0.20/28.3 = 25.4 mph. The LOS determination is made by referring to Table 11-1 for arterial Classification II and applying the definitions; for instance, Segment 1 with a computed speed of 25.4 mph is LOS C. Figure 11-21 shows the speed profile for the arterial and graphically demonstrates where the problem occurs. Note that the overall
arterial streets
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Figure 11-15. Calculation 3, solution: using worksheet for summary of arterial intersection delay estimates.
level of service does not highlight the problem as well as the speed profile or the set of segment levels of service does. The field data also allow a direct determination of intersection levels of service, based on measured control delay. With the LOS definitions of Table 9-1, the determination is straightforward:
Segment 1 2 3 4 5 6 7 8
Intersection LOS A A A A B B A A
Measured Control Delay (sec/veh) 3.4 1.7 3.6 5.3 17.6 10.5 6.2 3.2
These levels of service are also shown in Figure 11-21.
CALCULATION 7—ARTERIAL WITH LARGE SIGNAL SPACINGS
1. Description: Route 25 is a suburban arterial with a free-flow speed of 51 mph measured in field studies. It is an undivided facility, with two lanes in each direction and left-turn bays, and is dominated by its signals. A pretimed set of signals is used on the portion of the facility of interest. The following information is available for westbound traffic for the period being studied:
Segment
Length (mile)
C (sec)
g/C
X
c (veh/hr)
1 2 3 4 5
0.7 0.6 0.7 0.7 0.7
70 70 70 70 70
0.60 0.57 0.60 0.60 0.60
0.89 0.97 0.94 0.94 0.94
1,800 1,710 1,800 1,800 1,800
Updated December 1997
urban streets
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Figure 11-16. Calculation 3, solution: using worksheet for computation of arterial level of service.
Updated December 1997
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Figure 11-17. Speed profile for Calculation 3, northbound traffic.
Table 11-9. Computations for Sample Calculation 4 dist = 0.20 miles, cycle length = 60 seconds, g/C = 0.50 intersection flow (vph)
capacity (vph)
v/c ratio X
600 700 800 900 1,000 1,100 1,200 1,300 1,400 1,500 1,600
1,600 1,600 1,600 1,600 1,600 1,600 1,600 1,600 1,600 1,600 1,600
0.38 0.44 0.50 0.56 0.63 0.69 0.75 0.81 0.88 0.94 1.00
uniform delay d1
PF
9.2 9.6 10.0 10.4 10.9 11.4 12.0 12.6 13.3 14.1 15.0
0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33
I
incremental delay d2
control level of service
approach control delay
segment running time
sum time (sec)
average travel speed (mph)
arterial level of service
0.93 0.90 0.86 0.81 0.74 0.67 0.58 0.48 0.36 0.23 0.09
0.6 0.8 1.0 1.2 1.4 1.6 1.9 2.3 2.7 3.5 6.8
A A A A A A A A A A B
3.7 4.0 4.3 4.6 5.0 5.4 5.9 6.5 7.2 8.2 11.8
25.6 25.6 25.6 25.6 25.6 25.6 25.6 25.6 25.6 25.6 25.6
29.3 29.6 29.9 30.2 30.6 31.0 31.5 32.1 32.8 33.8 37.4
24.6 24.3 24.1 23.8 23.5 23.2 22.8 22.4 22.0 21.3 19.3
B B B C C C C C C C C
The signal progression is good, with less than 10 percent of the through traffic stopping. Determine the arterial level of service by segment and for the entire facility. 2. Solution: On the basis of the free-flow speed, the facility is arterial Classification I. Refer to Table 11-1 or Table 11-4. The intersection delay may be computed using Equations 11-3 and 11-4, with the computations summarized on the worksheet for summary of arterial intersection delay estimates (Figure 11-22). On the basis of PF descriptions in this chapter, the arrival type is 5—a dense platoon arriving at the beginning of the green phase, a highly favorable progression. This judgment is based on the given condition that the signal progression is good, with less than 10 percent of the through traffic stopping.
Table 11-6 indicates the following PF values for pretimed control and Arrival Type 5: Progression g/C Ratio Factor, PF 0.50 0.60
0.333 0.000
From these values, the PF for a g/C ratio of 0.57 may be interpolated as 0.099. Given the free-flow speed of 51 mph and the relatively long signal spacing, the free-flow speed can be used as the arterial speed in computing the running time: Segment running time = 3,600 × (segment length)/(ART SPD) Updated December 1997
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Figure 11-18. Sample calculation speed as a function of arterial flow rate.
Figure 11-19. Calculation 5 speed as a function of arterial flow rate on two different segment lengths. For instance, in Segment 1, Segment running time = 3,600 × (0.70)/(51 mph) = 49.4 sec To this computed running time is added the intersection delay time in the usual way, as shown in Figure 11-23. If Table 11-4 is inspected carefully, a more precise estimate of the computed running time can be generated. For instance, for a Updated December 1997
segment length of 0.50 mi and a free-flow speed of 50 mph, the segment running time is (78/72) or 1.08 times the value of a 1.0mi segment. Thus, more precise estimates for such segment lengths as 0.60, 0.80, and 0.90 mi could be generated for a free-flow speed of 51 mph by similar logic. However, the better and more accurate approach would be to rely on field data for such an arterial. Figure 11-23 also indicates the level of service for each arterial
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Table 11-10. Computations for Sample Calculation 5 dist = 0.10 miles, cycle length = 60 seconds, g/C = 0.50 intersection flow (vph)
capacity (vph)
v/c ratio X
600 700 800 900 1,000 1,100 1,200 1,300 1,400 1,500 1,600
1,600 1,600 1,600 1,600 1,600 1,600 1,600 1,600 1,600 1,600 1,600
0.38 0.44 0.50 0.56 0.63 0.69 0.75 0.81 0.88 0.94 1.00
uniform delay d1
PF
9.2 9.6 10.0 10.4 10.9 11.4 12.0 12.6 13.3 14.1 15.0
0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33
I
incremental delay d2
control level of service
approach control delay
segment running time
sum time (sec)
average travel speed (mph)
arterial level of service
0.93 0.90 0.86 0.81 0.74 0.67 0.58 0.48 0.36 0.23 0.09
0.6 0.8 1.0 1.2 1.4 1.6 1.9 2.3 2.7 3.5 6.8
A A A A A A A A A A B
3.7 4.0 4.3 4.6 5.0 5.4 5.9 6.5 7.2 8.2 11.8
14.5 14.5 14.5 14.5 14.5 14.5 14.5 14.5 14.5 14.5 14.5
18.2 18.5 18.8 19.1 19.5 19.9 20.4 21.0 21.7 22.7 26.3
19.8 19.5 19.2 18.8 18.4 18.1 17.6 17.2 16.6 15.8 13.7
C C C C C C D D D D E
segment, based on the fact that the arterial is Classification I, and referring to the LOS boundaries in Table 11-1. Figure 11-24 depicts the speed profile for the arterial and also indicates the arterial and intersection levels of service based on the average travel speed and control delay values, respectively. Note that with the large signal spacings on such an arterial, one can expect the intersections to provide the driver with poorer levels of service than the arterial, simply on the basis of LOS criteria for arterials and signalized intersections. Even on a Classification I arterial, LOS A can be achieved with a speed of 42 mph or greater; however, more than 5.0 sec of stopped delay per vehicle removes an intersection from LOS A (refer to Table 9-1). CALCULATION 8—PLANNING APPLICATION: DETERMINING LEVEL OF SERVICE
1. Description: The following information has been determined about an arterial section for the predominant directional flow: Traffic characteristics: AADT = 30,000, K100 = 0.091, D = 0.568, PHF = 0.925, Adjusted saturation flow = 1,850 pcphgpl, Percentage of turns from exclusive lanes = 12; Roadway characteristics: Through lanes = 4 (2 through lanes in each direction), Arterial classification = II, Free-flow speed = 45 mph, Section length = 2 mi, Median = yes, Left-turn bays = yes; Signal characteristics: Signalized intersections = 4 (thus, average segment length = 0.5 mi), Arrival type = 3, Signal type = actuated, C = 120 sec, Weighted g/C = 0.42. Find the following: 1. Two-way hourly volume for the planning analysis hour,
2. Hourly directional volume based on the predominant directional flow, 3. Basic through-volume 15-min flow rate, 4. Running time, 5. Control delay, 6. Average travel speed, and 7. Level of service for the arterial section. 2. Solution: The solution is reached with the following steps: Step 1. The two-way hourly volume for the planning analysis hour is 2,730 (AADT × K = 30,000 × 0.091). Step 2. The hourly directional volume for the planning analysis hour is 1,550 (two-way hourly volume × D = 2,730 × 0.568). Step 3. The basic through-volume 15-min flow rate is 1,475 or the hourly directional volume divided by the product of the PHF and the quantity 1 minus the percentage of turns from exclusive lanes [1,550/0.925 × (1 − 0.12)]. Step 4. The running time of 88 sec/mi is obtained directly from Table 11-4 with arterial Classification II, a segment length of 0.5 mi, and a free-flow speed of 45 mph as entries. Step 5. The control delay (d) for all the intersections of 140.0 sec is obtained using Equations 11- 2, 11-3, and 11-4, the number of signalized intersections, and the following inputs: adjusted saturation flow rate, number of through and through/right lanes, arrival type, signal type, C, g/C, progression adjustment factor (PF), and incremental delay adjustment factors (k,I). The 140.0 sec is calculated from Equations 11-2, 11-3, and 11-4 with the inputs that follow. d = d1 × PF + d2 + d3 d1 =
0.5C f1 − sg/Cdg2 1 − sg/Cd [min (X,1.0)]
d2 = 900T [(X − 1) + √(X − 1)2 + 8kIX/Tc ] where d1 = 33.6 sec, d2 = 3.9 sec, d3 = 0 sec, d = 33.6 + 3.9 + 0 = 37.5 sec, and Sd = 37.5 × 4 = 140.0 sec, c = 1,850 × 2 × 0.42 = 1,554; the v/c ratio (X) = 1,475/(1,850 × 2 × 0.42) = 0.949; PF = 1.00 (Table Updated December 1997
urban streets
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Figure 11-20. Calculation 6, solution: using worksheet for computation of arterial level of service.
Updated December 1997
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Figure 11-21. Speed profile for Calculation 6.
11-6); T = 0.25 hr; k = 0.5 (for planning purposes); I = 0.209 (Table 11-8); and the number of signalized intersections = 4. Step 6. The average travel speed is 22.8 mph, which is calculated by applying Equation 11-1 with running time and control delay for all signalized intersections as inputs. ART SPD = (3,600 × 2)/[(88 × 2) + (D)] = 7,200/(176 + 140.0) = 7,200/316.0 = 22.8 mph Step 7. On the basis of an average travel speed of 22.8 mph and the criteria in Table 11-1 for a Classification II arterial, the arterial’s level of service is C. CALCULATION 9—PLANNING APPLICATION: DETERMINING VOLUMES
Left-turn bays = yes; Signal characteristics: Signalized intersections = 6 (thus, segment length = 0.33 mi), Arrival type = 5, Signal type = semiactuated, C = 120 sec, Weighted g/C = 0.42. Find the following: 1. The lowest acceptable average travel speed for LOS C, 2. The maximum acceptable hourly directional volume based on the predominant directional flow, 3. The maximum acceptable two-way hourly directional volume, and 4. The maximum acceptable AADT. 2. Solution: The solution is found as follows:
1. Description: In preliminary design it is desired to know the maximum volume of vehicles that a six-lane facility could handle at LOS C given the following traffic, roadway, and signal characteristics: Traffic characteristics: K30 = 0.095, D = 0.55, PHF = 0.95, Adjusted saturation flow = 1,750 pcphgpl, Percentage of turns from exclusive lanes = 12; Roadway characteristics: Through lanes = 6 (3 through lanes in each direction), Arterial classification = II, Free-flow speed = 40 mph, Section length = 2 mi, Median = yes,
Step 1. From Table 11-1, the lowest acceptable average travel speed for arterial Classification II and LOS C is 22 mph. Step 2. A running time of 100 sec/mi is obtained by interpolation from Table 11-4 with arterial Classification II, a segment length of 0.33 mi, and a free-flow speed of 40 mph as entries. Step 3. The control delay for all the intersections of 127.3 sec is calculated by applying Equation 11-1 with average travel speed and running time as inputs: 22 = (3,600 × 2)/[(100 × 2) + d] Solving for d: d = 127.3 sec/veh control delay. Step 4. The average control delay per vehicle per intersection of 21.2 sec is calculated as follows: d = 127.3/6 Solving for d: d = 21.2 sec/veh. Updated December 1997
urban streets
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Figure 11-22. Calculation 7, solution: using worksheet for summary of arterial intersection delay estimates. Step 5. The basic 15-min flow rate of 2,156 is obtained by using Equations 11-2, 11-3, and 11-4; the average control delay of 21.2 sec/veh; PFs from Table 11-6; and the following inputs: adjusted saturation flow rate, number of through and through/right lanes, arrival type, signal type, C, g/C, k, and T. The capacity of the lane group (c) = 1,750 × 3 × 0.42 = 2,205; PF = 0.508 (Table 11-6); T = 0.25 hr (15-min period); k = 0.5 (for planning purposes). Solving for v/c ratio: X = 0.978. Solving for the flow rate: v = 2,156. Step 6. The hourly directional volume for the design hour is 2,328, the product of the basic 15-min through volume and the PHF divided by the quantity 1 minus the percentage of turns from exclusive lanes [2,156 × 0.95/(1 − 0.12)]. Step 7. The two-way hourly directional volume for the design hour is 4,232, the hourly directional volume divided by the directional distribution factor (2,328/0.55). Step 8. The AADT based on the design hour and LOS C is 44,545, the two-way hourly directional volume divided by design hour factor (4,232/0.095). Updated December 1997
It should be noted that this example applies to a preliminary design problem, and the planning application and results obtained should not be used beyond preliminary design. A more detailed planning analysis could have used signal-specific effective green ratios, variable turning movements, variable lengths between signalized interesections, and other traffic, roadway, and signal characteristics. The use of 12 percent for turns from exclusive lanes and the application of a weighted effective green ratio of 0.42 to all signalized intersections in this problem are broad planning assumptions and are inappropriate for design and operational analyses.
CALCULATION 10—STOP CONTROL ON ARTERIAL
1. Description: Humboldt Boulevard is a minor arterial of intermediate design with a free-flow speed of 30 mph. It is an undivided facility with two lanes per direction and the layout and intersection spacing given in Figure 11-25. The intersections of Keefe Avenue, Locust Street, Center Street, and North Avenue are signal con-
arterial streets
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Figure 11-23. Calculation 7, solution: using worksheet for computation of arterial level of service.
Updated December 1997
urban streets
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Figure 11-24. Speed profile for Calculation 7.
trolled, while Wright Street is all-way-stop controlled (AWSC). The signals are pretimed and coordinated with a 90-sec cycle length. The coordinated through movements have an arrival type of 4. Table 11-11 provides further information. Determine the southbound arterial level of service by segment and for the entire facility. Do not aggregate the segments. 2. Solution: This is a slightly different problem because one of the intersections on the arterial is stop controlled. Neverthless, the methodology in Chapter 11 can be used, provided that the following conditions are met: T The control delay at the stop-controlled intersection is calculated with the procedures presented in Chapter 10. T Arrival Type 3 is used for the intersection directly downstream from the stop-controlled intersection. This should be done because stop control breaks up platoons and results in random arrivals downstream from the stop-controlled intersection. T A stop-controlled intersection has a filtering effect similar to that of a traffic signal, and therefore the value of the filtering and metering factor (I) downstream from a stop-controlled intersection should be calculated as for a signal-controlled intersection.
Table 11-11. Input Data for Sample Calculation 10
intersection
segment
green ratio g/C
Locust Street Center Street Wright Street North Avenue
1 2 3 4
0.411 0.706 —a 0.467
a
All-way-stop control.
Updated December 1997
degree of saturation X
capacity (vph) c
0.403 0.284 0.880 0.396
1,628 2,302 749 1,655
Figure 11-25. Arterial geometry for Calculation 10.
arterial streets A summary of the arterial delay estimates is given in Figure 11-26. The value of I is selected from Table 11-8. The intersection control delay is calculated using Equation 11-2 for the signalcontrolled intersection and Equation 10-1 for the stop-controlled intersection. Based on the functional and design categories, free-flow speed, and intersection spacing, the arterial can be identified as belonging to Classification III. The segment running times are calculated as before from Table 11-4. Because the 0.50-mi length of Segment 1 exceeds the values given in Table 11-4, the free-flow speed is used to calculate the running time on the segment. The results of the LOS computations are shown in Figure 11-27. 3. Discussion: The intersection levels of service for Segments 1 to 4 are C, A, D, and B, respectively. Note that the same delay at signalized and stop-contolled intersections may represent different levels of service, because of the different LOS thresholds for signalized and stop-contolled intersections. From Figure 11-27 it can be seen that the stop-controlled intersection LOS is slightly worse than the arterial LOS. This difference is not surprising because all vehicles should stop at the stop-controlled intersection, whereas only a portion of all vehicles stop at signal-controlled intersections.
11-35
CALCULATION 11—TWO-LANE ARTERIAL
1. Description: Park Avenue is an undivided two-lane arterial with heavy traffic in both directions during the peak hour and relatively heavy turning volumes. The intersection spacing is given in Figure 11-28. Most of the arterial intersection approaches have exclusive left-turn lanes with permitted left-turn phasing. Several movements fail during the afternoon peak hour, when the signals operate on a 90-sec cycle. Table 11-12 provides information obtained from a capacity analysis of the individual intersections. Because of heavy side volumes, the through movements have an arrival type of 3. The free-flow speed on the facility is 30 mph. Determine the arterial level of service in the eastbound direction by segment and for the entire facility. Do not aggregate the segments. 2. Solution: The facility can be classified as a minor arterial because it has a substantial access function. In terms of design, the arterial falls in the intermediate category because no parking is allowed along the facility, separate left-turn lanes are provided at most intersections, and four signals are found in approximately a mile. Minor arterials in the intermediate design category can be
Figure 11-26. Calculation 10, solution: using worksheet for summary of arterial intersection delay estimates. Updated December 1997
urban streets
11-36
Figure 11-27. Calculation 10, solution: using worksheet for computation of arterial level of service.
Updated December 1997
arterial streets identified as Classification III or IV. In this case Classification III was selected because of the relatively high density of access points. A summary of the arterial delay estimates is given in Figure 1129. The value of I is selected from Table 11-8. Park Avenue is a westbound one-way facility west of Atherton Street; therefore inflow to Segment 1 takes place only from the cross streets. Consequently, an I of 1.0 is assumed for Segment 1. The intersection delay is calcu-
11-37
lated using Equation 11-2. The segment running times are calculated from Table 11-4. For segment lengths outside the values given in Table 11-4, running times per mile are extrapolated. The results of the LOS computations are shown in Figure 11-30. 3. Discussion: As shown in Figure 11-30 and in the speed profile in Figure 11-31, the average speed during the peak hour along the arterial is 14 mph in the eastbound direction. The corresponding level of service is C, which is somewhat better than the level field observations indicate. A possible reason for this discrepancy may be that queue interaction occurs because of the high degrees of saturation. Queue interaction occurs whenever a downstream queue reduces saturation flow at an upstream intersection, thereby reducing capacity and increasing delay. In this case, the queue from the oversaturated eastbound approach at University Drive may extend back far enough to affect capacity at Bigler Street and intersections even further upstream. Queue interaction may also occur between left-turn movements and the adjacent through movements. Because high left-turn volumes are serviced by permitted phasing only, left-turn queues may spill out of the left-turn bays and block the through movements, reducing saturation and capacity and increasing delay. This example illustrates the care required when analysing oversaturated conditions, because the methodology presented herein does not take into account queue interaction.
Figure 11-28. Arterial geometry for Calculation 11.
Table 11-12. Input Data For Sample Calculation 11
Segment
intersection Atherton Allen Shortlidge Bigler University
effective green time ratio g/C
degree of saturation X
capacity (vph) c
EB
WB
EB
WB
EB
WB
EB
WB
— 1 2 3 4
1 2 3 4 —
— 0.556 0.633 0.556 0.489
0.289 0.556 0.467 0.556 0.600
— 0.667 0.906 0.589 1.075
0.022 0.951 0.977 1.105 0.456
— 1,004 1,037 1,033 911
538 1,007 869 1,018 1,115
Updated December 1997
urban streets
11-38
Figure 11-29. Calculation 11, solution: using worksheet for summary of arterial intersection delay estimates.
Updated December 1997
arterial streets
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Figure 11-30. Calculation 11, solution: using worksheet for computation of arterial level of service.
Updated December 1997
urban streets
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Figure 11-31. Speed profile for Calculation 11, eastbound traffic.
APPENDIX I TEST-CAR METHOD FOR EXISTING ARTERIALS
The following steps are used when applying the test-car method for determining levels of service on existing urban and suburban arterials. 1. Identify and inventory the geometry and the access control of each arterial segment, the segment lengths, existing signal timing, and the 15-min flow rates for selected times of the day (such as the peak a.m. period, the peak p.m. period, and a representative off-peak period, by direction of flow). 2. Determine the appropriate free-flow speed for the arterial section being evaluated. For existing arterials, this speed may be determined by making runs with a test car equipped with a calibrated speedometer at times of low volumes. An observer should read the speedometer at midblock locations where the vehicle is not impeded by other vehicles, and readings should be recorded for each segment of an arterial. These observations may be supplemented by spot speed studies made at typical midblock locations during low-volume conditions. Other data, such as design type, access points, roadside development, and speed limit, may be considered also. 3. Use Tables 11-2 and 11-3 along with the physical information and free-flow speed already cited to determine the arterial classification. 4. Make test-car travel time runs over the arterial section during the selected times of the day. a. The observer should use appropriate measurement equipment to obtain the information specified in the travel time field worksheet in Appendix II. The equipment may be a computer-based collection system or a pair of stopwatches. b. Travel times between centers of signalized intersections should be recorded, along with the location, cause, and duration of each delay. c. Test-car runs should begin at different times in the signal cycle to avoid making all trips the first in a platoon. Updated December 1997
d. Some midblock speedometer readings should also be recorded to check on unimpeded travel speeds and to see how they relate to free-flow speed. e. Data should be summarized for each segment and time period to provide the average travel time and the average delay time for a signal and for other delays and events (four-way stops, parking disruptions, etc.). f. The minimum number of test-car runs depends on the variance in the data and the occurrence desired. Six to 12 runs for each traffic-volume condition may be adequate. (See HRB Proc., 1952, pp. 864–866.) g. An instrumented test car should be used if available to reduce labor requirements and to facilitate recording and analysis. Computer-produced summaries of test-car runs, with all data recorded and analyzed by the computer, are now common. 5. For each segment and time period, the average travel speed should be determined by using travel times and segment lengths. Average travel speed for each arterial section should also be determined. 6. Table 11-1 should be used to obtain a LOS value for each arterial segment and for the overall arterial, for each time period and each direction of flow. This determination is made by comparing the average travel speed obtained in Step 5 with the speed values given in Table 11-1 for the appropriate arterial classification. 7. The test-car data can be modified to permit evaluation of different signal timing plans. As shown in Table 11-6, the adjustment factors can be applied to control delays to evaluate effects on control delay of changes in offsets. It is then possible to evaluate effects of these changes on average travel speeds and levels of service.
arterial streets
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APPENDIX II WORKSHEETS FOR USE IN ANALYSIS WORKSHEETS
Page
Summary of Arterial Intersection Delay Estimates................................................................................................................................. 11-42 Computation of Arterial Level of Service ............................................................................................................................................... 11-43 Travel Time (TT) Field Worksheet.......................................................................................................................................................... 11-44
Updated December 1997
11-42
Updated December 1997
urban streets
arterial streets
11-43
Updated December 1997
11-44
Updated December 1997
urban streets
chapter 12
TRANSIT CAPACITY
CONTENTS
i.
introduction .......................................................................................................................................................................... Context................................................................................................................................................................................... Concepts................................................................................................................................................................................. Person Movement............................................................................................................................................................. Person-Capacity................................................................................................................................................................ Basic Factors and Equations............................................................................................................................................ Level of Service ............................................................................................................................................................... Vehicle Capacities and Loading Criteria ........................................................................................................................
12-2 12-2 12-4 12-4 12-4 12-4 12-7 12-7
ii.
transit capacity experience ............................................................................................................................................... Bus Capacity Experience ...................................................................................................................................................... Bus Flow and Equivalency Studies................................................................................................................................. Effects of Buses on Vehicular Capacity ......................................................................................................................... Observed Bus Flows—Streets and Highways................................................................................................................. Observed Bus Flows—Terminals .................................................................................................................................... Passenger Service Times and Bus Headways................................................................................................................. General Capacity Ranges................................................................................................................................................. Rail Transit Capacity Experience ......................................................................................................................................... Observed Train and Passenger Flows ............................................................................................................................. General Capacity Ranges.................................................................................................................................................
12-9 12-9 12-10 12-10 12-10 12-11 12-11 12-12 12-14 12-15 12-16
iii.
methods and procedures—on-street transit ................................................................................................................. Bus Berth and System Capacity ........................................................................................................................................... General Considerations .................................................................................................................................................... Equations and Guidelines ................................................................................................................................................ Applications...................................................................................................................................................................... Bus Priority Treatments ........................................................................................................................................................ Operational Overview ...................................................................................................................................................... Planning Considerations................................................................................................................................................... Guidelines for Specific Treatments .................................................................................................................................
12-18 12-18 12-18 12-19 12-26 12-30 12-30 12-30 12-33
iv.
applications and sample problems .................................................................................................................................... General Approach.................................................................................................................................................................. Types of Problems................................................................................................................................................................. Sample Calculations .............................................................................................................................................................. Calculation 1—Person-Flow ............................................................................................................................................ Calculation 2—Person-Capacity ...................................................................................................................................... Calculation 3—Effect of Buses on Freeway Capacity ................................................................................................... Calculation 4—Effect of Buses on Arterials .................................................................................................................. Calculation 5—Passenger Service Times (Bus Stop)..................................................................................................... Calculation 6—Passenger Service Times (Bus Routes) ................................................................................................. Calculation 7—Planning Applications, Downtown Street, Level of Service ................................................................ Calculation 8—Bus Terminal (Transit Center)............................................................................................................... Calculation 9—Berth Capacity for Loading ................................................................................................................... Calculation 10—Bus Berth Unloading............................................................................................................................ Calculation 11—Berth Capacity for Loading at Major Stops........................................................................................
12-34 12-34 12-39 12-40 12-40 12-40 12-40 12-41 12-41 12-41 12-42 12-42 12-42 12-44 12-45
12-1
urban streets
12-2 Calculation Calculation Calculation Calculation Calculation v.
12—Arterial Street Capacity........................................................................................................................ 13—CBD Busway ........................................................................................................................................ 14—Arterial Bus Turnout ............................................................................................................................ 15—Rail Rapid Transit ................................................................................................................................ 16—Light Rail Transit on City Street.........................................................................................................
12-45 12-46 12-46 12-47 12-47
references .............................................................................................................................................................................. 12-47 appendix i. Bus Capacity Experience..................................................................................................................................... 12-49 appendix ii. Rail Capacity Experience ................................................................................................................................... 12-55 appendix iii. Examples of Boarding and Alighting Time ..................................................................................................... 12-59
I. INTRODUCTION This chapter contains guidelines and procedures for estimating bus and rail transit capacities. It defines basic capacity concepts and principles; summarizes previous studies and current experience; develops analytical relationships; presents capacity guidelines; and sets forth illustrative applications. The guidelines and procedures may be used to estimate: 1. The effects of bus flows on freeway and signalized intersection capacity. 2. Total passenger or person flow based on roadway operating conditions, and the prevailing mix of cars and buses (or rail vehicles). 3. Generalized ranges of bus capacities for arterial streets, downtown streets, and busways. 4. Bus berth (stop) requirements at terminals and along downtown busways, bus-only streets, and other city streets. 5. Passenger flows on rail transit lines for varying car sizes, train lengths, service frequencies, and loading conditions—for both light rail and rapid transit lines. The chapter also provides ways to address various questions normally encountered in transit service planning and operations. For instance: 1. How many passengers can be carried per unit of time? 2. How many transit vehicles are needed to provide a specific rate of passenger flow? 3. How many passengers can be carried with a given vehicle fleet? It emphasizes bus transit capacities because buses operate over the street and highway systems in most urban areas. However, it also presents salient rail transit characteristics and capacities. It builds upon and extends previous transit capacity analysis. The initial research on transit capacity relative to streets and highways was developed in 1961 by the Transit Subcommittee of the Committee on Highway Capacity and Quality of Service. It summarized operating experience in the United States and contained broad guidelines for passenger dwell times and vehicle occupancies. More detailed analyses of bus capacity were contained in NCHRP Reports 143 and 155 on Bus Use of Highways (2,4). These reports summarized, synthesized, and interpreted available information on bus flows, passengers, and service times.
They also analyzed bus berth capacity. The findings on bus transit capacity were summarized in ‘‘Bus Capacity Analysis,’’ Transportation Research Record 546 (5). Rail transit capacity has a long history of actual operating experience and analysis. The Board of Supervising Engineers for Chicago Traction, for example, analyzed street railway capacity in 1912, and passenger dwell times by door width in 1916. Lang and Soberman derived formulas for rapid transit track capacity in 1964 (40). More recent studies by Homburger, Pushkarev, and Vuchic further addressed rail transit capacity theory and practice (7,8,9). Relevant materials from the more recent references are incorporated into this chapter.
CONTEXT
Transport system management solutions to urban transport problems have increased the interest in the person-capacity characteristics of transportation facilities in addition to their vehiclecapacity characteristics. The underlying rationale is that although buses and rail transit cars require more street space per vehicle than private automobiles, they carry many more passengers per vehicle than automobiles, especially during peak hours. Thus, public transportation emerges as an important way to increase the number of people carried by urban transportation systems. Transit vehicles carry a substantial number and proportion of peak-hour person trips to and from the downtown areas, and along many urban freeways, arterials, and downtown streets. Table 12-1 indicates the peak period use of public transport, bus and rail combined, by persons entering the central business districts of selected cities in Canada and the United States (1). Transit carries more than two-thirds of all peak-hour travelers to or from the New York, Chicago, Philadelphia, and Toronto downtown areas, and more than a third of all peak-hour travelers entering or leaving most other CBD’s. The variations in transit use reflect differences in population, central business district employment, extent of bus and rail transit services, and geographic characteristics. Buses carry over 85 percent of all peak-hour person-trips through the Lincoln Tunnel in the City of New York, account for about half of all peak-hour travelers on the Shirley Highway
transit capacity (I-95), Virginia, and the Long Island and Gowanus Expressways (New York City), and for more than a quarter of all passengers on radial freeways approaching or leaving other large-city CBD’s. Buses carry an even higher proportion of peak-hour travelers on many city streets. More than 80 percent of all peak-hour passengers on Hillside Avenue and Madison Avenue in New York City, Market Street in Philadelphia, and Main Street in Dallas are carried by buses. Buses accommodate more than half of all peak-hour person-trips on downtown streets in many other cities (2). These observations do not necessarily represent maximum possible bus volumes or total traffic volumes. They do, however, clearly indicate that while buses account for a relatively small proportion of the vehicles in a traffic stream, they carry a sizable part of the total person flow. Rail transit, operating mainly off-street, becomes important in serving large, intensively developed city centers where it accounts for more than half of all people entering or leaving in the peak hour.
12-3
Table 12-1. Peak-hour Use of Public Transport by Persons Entering or Leaving the Central Business District
urban area
year
percent by public transport in peak direction
New York, New York Chicago, Illinois Toronto, Ontario Boston, Massachusetts Cleveland, Ohio Ottawa, Ontario Vancouver, British Columbia Los Angeles, California Washington, D.C. Detroit, Michigan Baltimore, Maryland Denver, Colorado Dallas, Texas Milwaukee, Wisconsin Providence, Rhode Island New Haven, Connecticut Minneapolis, Minnesota Houston, Texas
1982 1974 1970 1974 1970 1974 1970 1974 1979 1974 1982 1977 1971 1974 1977 1982 1965 1971
89a 82a 68a 49a 44a 40 40 37 36b 35 33 30 28 25 21 20 20 14
a
With rail transit. Includes Pentagon area; data for 6:30–9:30 AM SOURCE: Cordon Counts for each city, mainly compiled in Ref. 1. b
CONCEPTS
Transit capacity is more complex and less precise than highway capacity: it deals with the movement of both people and vehicles, depends on the size of the transit vehicles and how often they operate, and reflects the interaction between passenger traffic concentrations and vehicle flow. It depends on the operating policy of the transit agency, which normally specifies
service frequencies and allowable passenger loadings. Accordingly the traditional concepts applied to highway capacity must be adapted and broadened. Table 12-2 defines the important terms that relate to transit capacity.
Table 12-2. Important Terms in Transit Capacity T Clearance Time—All time losses at a stop other than passenger dwell times, in seconds. It can be viewed as the minimum time, in seconds, between one transit vehicle leaving a stop and the following vehicle entering, i.e., the clearance time between successive buses should not be less than 15 sec. T Crush Capacity—The maximum number of passengers that can be physically accommodated on a transit vehicle. It is also defined as level-of-service F. It can be viewed as an ‘‘offered’’ capacity, since it cannot be achieved on all vehicles for any sustained period of time. T Dwell Time—The time, in seconds, that a transit vehicle is stopped for the purpose of serving passengers. It includes the total passenger service time plus the time needed to open and close doors. T Interrupted Flow—Transit vehicles moving along a roadway or track and having to make service stops at regular intervals. T Maximum Load Point—The point, actually section, along a transit route at which the greatest number of passengers is being carried. T Passenger Service Time—The time, in seconds, that is required for a passenger to board or alight from a transit vehicle. T Person-Capacity—The maximum number of persons that can be carried past a given location during a given time period under specified operating conditions without unreasonable delay, hazard, or restriction. Usually measured in terms of persons per hour. T Person Level of Service—The quality of service offered the passenger within a transit vehicle, as determined by the available space per passenger. T Productive Capacity—A measure of efficiency or performance. The product of passenger capacity along a transit line and speed. T Seat Capacity—The number of passenger seats on a transit vehicle. T Standees—The number of standing passengers on a transit vehicle. The ratio of total passengers carried to the number of seats during a specified time period is called the load factor. The percent standees represents the number of standing passengers expressed as a percentage of the number of seats. A transit vehicle with 40 seats and 60 passengers has a load factor of 1.5 and 50 percent standees. T Uninterrupted Flow—Transit vehicles moving along a roadway or track without stopping. This term is most applicable to transit service on freeways or on its own right-of-way.
urban streets
12-4 Person Movement
Each roadway or transit facility should be analyzed in terms of the number of people it carries in a specific time period. This calls for knowing both the number and occupancies of each type of vehicle. For example, an urban freeway lane carrying 1,800 passenger cars per lane per hour with an average occupancy of 1.5 persons would have a person movement of 2,700 people per hour. Likewise, an arterial street carrying 600 automobiles per hour and 50 buses per hour, with occupancies of 1.5 and 40, respectively, would have a total person movement of 2,900 persons per hour of which approximately 70 percent would be carried by public transport.
Person-Capacity
The person-capacity or passenger-carrying capability for any given transport route can be defined as ‘‘the maximum number of people that can be carried past a given location during a given time period under specified operating conditions without unreasonable delay, hazard, or restriction, and with reasonable certainty.’’ This definition is less absolute than definitions for vehiclecapacity, because it recognizes that when dealing with transit, additional considerations enter the picture. More specifically, person-capacity depends on the mix in the traffic stream, including the number and occupancy of each type of vehicle that can reasonably be expected to pass a point on a roadway. It is a function of vehicle size, type, occupancy, and headway. The number of transit vehicles should be based on a specified flow. The number of cars should reflect the auto capacity of the facility after deducting the passenger car equivalents of the buses. The total person-capacity then represents the number of people that can be carried by the specified number of buses and the remaining passenger car capacity. The person-capacity of a freeway lane with bus and car traffic under prevailing conditions of flow can be estimated as follows: cp = f ′ O1 + [(1,800 − 1.5 f ′) O2 ]
(12-1)
where: f′ = number of buses per hour; O1 = bus occupancy; O2 = car occupancy; and cp = person-capacity, people per hour. The number of persons that can be carried in buses depends on the number of buses scheduled. This may be below the maximum capacity of a street to accommodate buses. It is certainly the case for most urban freeways, as illustrated by the following example. Figure 12-1 shows the person-capacities for an urban freeway lane, with various numbers of buses in the traffic stream. This example assumes a maximum freeway capacity of 1,800 vph without buses, a bus-passenger car equivalency of 1.5, and occupancies of 1.5 and 50 for cars and buses respectively. As the number of buses on the freeway increases to 300, the total personcapacity increases from 2,700 to nearly 17,000, while the vehicle-
capacity drops from 1,800 to 1,620. (Note that this figure only refers to capacity, not demand or actual use.) If each car carried five passengers, then with 1,320 cars and 300 buses, the total person-capacity would be 21,600. A slightly different approach should be used for downtown streets. The person-capacity of the bus or street car lane (assuming only transit use) can be estimated by the procedures outlined in this chapter (Sec. II and III). The vehicular capacities of the general traffic lanes can be estimated based on the procedures outlined in Chapter 9 and weighted by their passenger occupancies. The total person-capacity equals the sum, and may be higher than figures based entirely on actual usage. Note that this approach is different from that for freeways, where it is usually unrealistic to preempt an entire lane for buses; however it could be applied where dedicated freeway bus lanes are considered, by taking into account the limits on bus capacity resulting from approaches to and from the freeway, as well as stops along it.
Basic Factors and Equations
The passenger capacity of a transit line is the product of the number of vehicles per hour (usually past the busiest stop) and the number of passengers that each vehicle can carry. Four basic factors determine the maximum passenger capacity: 1. The maximum number of vehicles per transit unit (bus, car, train). 2. The passenger capacity of the individual transit vehicles. 3. The minimum possible headway or time spacing between individual vehicles or trains. 4. The number of movement channels or loading positions. The many variables that influence these factors and transit capacities are given in Table 12-3. Some affect the number of passengers per unit, while others affect the number of units that can pass a given location within a specified time period. The capacity of a transit line varies along the route. Limitations may occur (1) between stops (i.e., way capacity) (2) at stops or stations (i.e., station capacity), (3) at major intersections with cross traffic, or (4) at terminals (station capacity). In most cases station capacity rather than way capacity is the critical constraint. Capacities are generally governed by the critical stops where major passenger boarding or alighting takes place, or where vehicles terminate or turn around. This is similar to estimating arterial street system capacity based on critical intersections along a route. Sometimes, however, outlying rail transit terminals limit system capacity due to heavy passenger boardings, and track configurations or operating practices that limit train turnarounds. The actual mix of automobiles and transit vehicles in a traffic stream results from the choice of travel mode by the traveler and from the number of transit vehicles scheduled over the facility. The number of persons that can be carried by a given bus or rail line, therefore, reflects the operating policy of the transit property with respect to minimum service frequency and passenger loading conditions (i.e., number of standees). The following considerations are important:
transit capacity
12-5
Figure 12-1. Example of freeway person-capacity.
1. A transit line with a relatively uniform distribution of boarding passengers among stops will usually have a higher capacity than one where passenger boarding is concentrated at a single stop. 2. Short-term fluctuations in ridership demand must be considered to avoid unacceptable passenger queuing or overcrowding. Variations in arrival patterns and dwell times at stops will tend to reduce capacity.
3. The maximum rate of passenger flow is usually constrained by such factors as acceptable levels of passenger comfort, the presence of other traffic sharing the same right-of-way, and safety considerations. Therefore, transit operators generally are more concerned with the realistic rates of flow that can be achieved by different modes, rather than with physical capacity in the theoretical engineering sense. 4. Operations at ‘‘capacity’’ tend to strain transit systems,
urban streets
12-6
Table 12-3. Factors That Influence Transit Capacity 1. T T T T T T T T
Vehicle Characteristics Allowable number of vehicles per transit unit (i.e., single unit bus, or several unit-cars per train) Vehicle dimensions Seating configuration and capacity Number, location, width of doors Number and height of steps Maximum speed Acceleration and deceleration rates Type of door actuation control
T T T T
Right-of-Way Characteristics Cross-section design (i.e., number of lanes or tracks) Degree of separation from other traffic Intersection design (at grade or grade separated, type of traffic controls) Horizontal and vertical alignment
T T T T T T T T
Stop Characteristics Spacing (frequency) and duration Design (on-line or off-line) Platform height (high level or low level loading) Number and length of loading positions Method of fare collection (prepayments, pay when entering vehicle; pay when leaving vehicle) Type of fare (single-coin, penny, exact) Common or separate areas for passenger boarding and alighting Passenger accessibility to stops
T T T T
Operating Characteristics Intercity versus suburban operations at terminals Layover and schedule adjustment practices Time losses to obtain clock headways or provide driver relief Regularity of arrivals at a given stop
2.
3.
4.
5.
Passenger Traffic Characteristics T Passenger concentrations and distribution at major stops T Peaking of ridership (i.e., peak-hour factor)
6.
Street Traffic Characteristics T Volume and nature of other traffic (on shared right-of-way) T Cross traffic at intersections if at grade
7.
Method of Headway Control T Automatic or by driver/trainman T Policy spacing between vehicles
SOURCE: Adapted from Canadian Transit Handbook (Ref. 12).
and do not represent desirable operating conditions. Moreover, most U.S. transit systems operate at capacity for a relatively short period of time, if at all. 5. Capacity relates closely to system performance and service quality in terms of speed, comfort, and service reliability. A single fixed number often can be misleading. The concept of ‘‘productive capacity,’’ the product of passenger flow and speed, provides an important index of system efficiency (9). 6. Capacities obtained by analytical methods must be crosschecked against actual operating experience for reasonableness. The capacity of a transit line can be estimated from the following equations: cv =
3,600 R 3,600 R = h D + tc
(12-2a)
3,600 nSR D + tc
(12-2b)
cp = nScv = where:
cv = vehicles per hour per channel or berth (maximum); cp = people per hour per channel or berth (maximum); h = headway between successive units, in sec; tc = clearance between successive vehicles, in sec;
D = dwell time at major stop under consideration, in sec; S = passengers per vehicle; n = vehicles per unit (n = 1 for buses; n = 1 to n = 11 for rail vehicles); and R = reductive factor to compensate for dwell time and arrival variations. The factor R reduces the capacity to account for variations in bus arrival patterns and in dwell times at stop. It may approach 1.00 for a rail transit system on private right-of-way with wayside cab signal control or with automatic train operations. For bus operations, especially on city streets, it is always less than 1—a value of 0.833 is suggested for maximum capacity. Using this factor, the term (3,600 R) in Eqs. 12-2a and 12-2b becomes 3,000 for maximum capacity. In effect, it increases headways by 20 percent. These equations, with further adjustments for the reductive effects of traffic signals, form the basis for all transit capacity computations. In this case the basic equation becomes: cp =
(g/C) 3,600 nSR (g/C) D + tc
(12-2c)
where: g = green time, in seconds, and C =cycle length in seconds.
transit capacity Equations 12-2b and 12-2c may be used to estimate passenger capacity when the number of effective loading positions is taken into account. They provide a realistic estimate where loading patterns and/or door configurations enable vehicles to fill up as they reach the maximum load point. Where this condition is not likely, as along many bus routes, more detailed analyses are needed. In such cases, the detailed methods described in Section III should be applied. Level of Service
The concept of level of service (LOS) for transit is far more complex than for highways. It includes such factors as coverage of major residential and activity areas, comfort, speed, and reliability (i.e., on-time performance). Convenient schedules, comfortable vehicles, and frequent, fast, and reliable service contribute to LOS. Speed is influenced not only by the number of riders using a transit line, but, to an even greater extent, by stop frequency and dwell times, traffic interferences, and rightof-way design. Productive capacity, the product of passenger capacity and speed, is an important measure of transport system efficiency. It is important in that it distinguishes between equal passenger throughputs achieved at different speeds. Thus, express bus service normally has a higher productive capacity than local bus service; similarly, commuter rail line operating at 40 mph is twice as ‘‘productive’’ as an urban rail transit line carrying the same number of people at 20 mph. In general, ‘‘productive
12-7
capacity’’ will be influenced by the type of technology (rail versus bus), the method of operation (private right-of-way versus shared), and the spacing of stops (9). Two aspects of level of service are important from a capacity perspective: the number of passengers per vehicle, and the number of vehicles per hour. Capacity-related level-of-service criteria should reflect both. Figure 12-2 illustrates this two-dimensional nature of urban transit capacity. It can be seen that it is possible to operate many transit vehicles, each carrying few passengers. From a roadway capacity perspective, the number of vehicles could be at or near capacity, even if they run nearly empty. A few vehicles could operate, each overcrowded. This represents a poor level of service from a passenger comfort (user) perspective. Long waiting times would also detract from user convenience. Finally the domain of peak-period operation commonly involves a large number of vehicles, each heavily loaded. Vehicle Capacities and Loading Criteria
Typical transit vehicle types, dimensions, and passenger capacities are given in Table 12-4. The total passengers carried varies depending on bus or rail car capacity and the tradeoff between seated capacity and standees. The largest number of seats and lowest number of standees should occur on longer suburban bus routes or on commuter rail routes where higher levels of comfort are essential.
Figure 12-2. The two-dimensional nature of transit level of service as related to transit capacity.
urban streets
12-8
Table 12-4. Characteristics of Typical Transit Vehicles—United States and Canada type of vehicle or train
typical capacitya
length (ft)
width (ft)
seats
standeesb
total
18–25
6.5–8.0
15–25
0–15
15–40
Transit bus
30.0 35.0 40.0
8.0 8.0 8.5
36 45 53
19 25 32
55 80 85
Example: General Motors, RTS II, 1978
Articulated transit bus
55.0 59.7
8.5 8.5
66 73
34 37
100 110
Chicago-am General-MAN am General-MAN
Street car
46.7
9.0
59
40–80
99–139
P.C.C.c
151.2
8.7
128
248–272
376–400
142.0
8.8
104
250–356
354–460
San Diego—6-axle car, 2-car train (Duewag) Boston—6-axle car, 2-car train (Boeing Vertol)
605.0
10.0
500
1,300–1,700
1,800–2,200
600.0
10.0
576
1,224–1,664
1,800–2,240
Minibus-short haul
Light rail car train
Rail rapid transit train
Commuter rail train
remarks
448.6
10.3
504
876–1,356
1,380–1,860
10-car train, IND New York 8-car train, R-46 cars, New York 8-car train, Toronto
85.0
10.5
1,100
200–1,200
1,300–2,300
Regular car, 10-car train
a
In any transit vehicle the total passenger capacity can be increased by removing seats and by making more standing room available, and vice-versa. b Higher figures denote crush capacity; lower figures, schedule-design capacity. c Presidents’ Conference Committee Cars. SOURCE: Refs. 8 and 34.
Table 12-5. Passenger Loading Standards and Levels of Service for Bus Transit Vehicles (50-Seat, 340-Sq Ft Bus) peak-hour level of service A B C D E (Max. scheduled load) F (Crush load)
passengers 0 27 41 54 67 81
to to to to to to
26 40 53 66 80 85
approx. sq ft/pass. 13.1 13.0 8.4 6.3 5.1
or more to 8.5 to 6.4 to 5.2 to 4.3
