# chapter-2

September 12, 2017 | Author: Rajeswara Reddy | Category: Regression Analysis, Logistic Regression, Poisson Distribution, Traffic, Traffic Collision

sdf...

#### Description

CHAPTER-II LITERATURE REVIEW 2.1 GENERAL This chapter presents a detailed review of literature regarding black spot investigation procedures, models for prediction of Road Accidents, and remedial measures to minimize the accidental rates. 2.2 METHODS FOR IDENTIFICATION OF BLACK SPOTS To make the road safer, it is important to identify the right site for safety improvement, if not, resources can be wasted on sites that are incorrectly identified as potentially unsafe but sites that are truly unsafe can go untreated and remain unsafe. Therefore, black spot identifications an essential step for black spot improvement program. The technique to determine a black spot location varies from place to place. Methodologies vary from the simple flag sites that have high-accident records to the more complicated ones of which the expected number of accidents is estimated and potential for safety improvements is determined. The following subsections discuss the method to identify black spots. 2.2.1 Number of accidents method The Crash Frequency Method summarizes the number of crashes at location and the stretches having the more number of crashes are taken as accident prone stretches. The main advantage to this method is that it is simple to use and doesn’t require additional information beyond number and location of crashes. Location are ranked by descending crash frequency and those with more than a predetermined number of crashes are classified as high-crash locations to be further scrutinized for statistical significance. It is useful initially to identify locations for further analysis and ranking. The main disadvantage is that exposure (traffic volume) is not accounted for. Without being able to account for variations in traffic volume, locations that have high crash frequency due to high traffic volumes rather than some deficiency may be misidentified as high crash locations.

Transportation Division, NIT Warangal

Page 5

2.2.2 Accident density method The Crash Density Method is closely related to the crash frequency method, the crash density method summarizes the number of crashes per mile for highway sections. Sections are defined as a minimum length of roadway with consistent characteristics, with the minimum distance used frequency being one mile. Locations are ranked by descending crash density and those with more than a predetermined density of crashes are classified as highcrash locations to be further scrutinized for statistical significance. Crash Density = the number of crashes per mile for Highway Sections 2.2.3 Accident rate method The crash rate method does account for both exposure and the total number of crashes. For links, crash rate is a function of the number of crashes, traffic volume, and the length of the segment. At nodes, crash rate is a function of the number of crashes and daily entering vehicles. Crash rate is typically expressed as the number of crashes per million vehicle miles travelled for road segments and number of crashes per million daily entering vehicles for intersections. Second, each site is ranked according to the crash rate. For nodes and links up to 0.6 miles, the crash rate is calculated using the following equation Crash rate/MEV = (Number of crashes/DEV) * 1000000/ (n*365days/year)

(2.1)

Where, MEV = Million Entering Vehicles DEV = Daily Entering Vehicles for nodes or average daily traffic (ADT) for links. n

= Analysis Time Period, generally taken as 5 years

For links 0.6 miles or longer, the DEV is determined using the following equation. DEV = ABS (Link length/0.3) * DEV

(2.2)

Where, ABS = Absolute Value The site that has the largest crash rate receives the top ranking. The same implication of a tie applies to this ranking as well. For locations where their traffic volumes are unknown the ranking of zero is assigned.

Transportation Division, NIT Warangal

Page 6

2.2.4 Severity index method Weighted severity index method assigns weight to different types of accident and their weighted severity total is being calculated. This value ranges from 0 to 100, the stretches that are having 90 or more are taken as accident prone stretches. Under the Weighted severity index method, causalities have been divided into three groups Fatal Grievous Injury Minor Injury Non Injury Based on the analysis of cost of accident fatalities, Weightage is given to type of accident. WST (j) = ∑ Wi * Ai

(2.3)

WSI (j) = WST (j) * K / PCU (j)

(2.4)

Where, WST (j) = Weightage Severity total of jth stretch Ai

= Number of accidents of type: Fatal, Grevious injury, Minor injury,

Non injury Wi

= Weightage of ith type of accident

WSI (j)

= Weightage Severity Index of jth stretch

PCU (j) = Traffic volume on jth stretch K

= constant factor, 10,000

2.2.5 GIS Applications Since accident is spatially distributed in nature, use of Geographic Information

System

(GIS) and database software will provide the capability to store data, update data, retrieve data, compare data and spatially display the data. These modern computer technologies allow black spot map to be electronically generated from a well-designed accident database. Computer record systems can also produce rankings of high-accident locations based on either total accidents occurring or accident rates

Transportation Division, NIT Warangal

Page 7

2.2.6 Empirical Bayes Method Hauer and Persuad (1984) suggest an Empirical Bayes(EB) method for identification of high crash locations. The EB method attempts overcome the difficulties with some of the convectional techniques. The EB controls the randomness of crash data by using an estimate of the long term mean number of crashes at a location. This method is used for predicting crashes in the future and then ranking based on the predicted number of crashes. The broad techniques for the identification of black spot may be categorized as a) Statistical methods b) Bio medical engineering approach c) Engineering methods d) Subjective assessment techniques 2.3 MODELLING METHODS FOR CRASH-FREQUENCY DATA The following techniques are available for accident modelling Multiple Linear Regression Model Poisson Model Negative Binominal Model Multilevel Analysis 2.3.1 Linear Regression Model The form of a linear regression model is given as, Yi = a0 + a1 X1 + a2X2 + a3X3 +……+ anXn

( 2.5)

Yi = no of accidents at the road section i X1, X2, X3, Xn are input parameters like roadway width, shoulder width, section length, pavement condition etc. a0, a1, a2, an are regression coefficients. 2.3.2 Exponential Regression Model The form of a exponential regression model is given as, Yi = exp (a0 + a1 X1 + a2X2 + a3X3 +……+ anXn)

(2.6)

Yi = Number of accident at Road section ‘i’

Transportation Division, NIT Warangal

Page 8

X1, X2, X3, Xn are input parameters like, roadway width, shoulder width, flow speed, section length, pavement condition, etc. a0, a1, a2, an are regression coefficients. 2. 3.3 Poisson Regression Model Poisson model approximates rare-event count data, such as accident occurrence. Miaou et al (1992) employed Poisson regression techniques to model accidents. Poisson models assume that vehicle accidents are independent and follow Poisson distribution. Consider the number of accidents occurring per year at various road sections. By Poisson regression model, the probability of a road section i having yi accidents per year (where yi is a non-negative integer) can be computed as P ( yi ) =

e − µ µ i yi yi !

(2.7)

Where P(yi) = The probability of occurrence of y accidents for a given time period on roadway segment yi = The number of accidents for a given time for a roadway segment i; µi = The mean value of accident occurred for a given time period, i.e. Poisson parameter for section i. Poisson regression models are estimated by specifying the Poisson parameter µi as a function of explanatory variables. The most common relationship between explanatory variables and the Poisson parameter is the log-linear model, µi = Exposure x exp (βjXij)

(2.8)

Exposure = Traffic exposure for road segment i Xij = Vector of independent variables for roadway segment i; βj = Vector of coefficient for the independent variables In this formulation, the expected number of accidents per period is given by E(yi) = Exposure x exp(βjXij)

(2.9)

One of the limitation of Poisson’s regression model is the variance of the dependent variable is equal to the mean. 2.3.4 Negative Binomial Regression Model The negative binomial model is derived by rewriting such that, for each observation i, µi = Exposure x exp(βjXij + ϵi) Transportation Division, NIT Warangal

(2.10) Page 9

Where exp(ϵi ) is a gamma-distributed error term with mean 1 and variance α2. The addition of this term allows the variance to differ from the mean as below Var ( y i ) = E [ y i ][1 + α E [ y i ]] = E [ E [ y i ] + α E [ y i ]]2

P ( yi ) =

exp( − µi exp(ε i ))µi yi yi !

(2.11)

(2.12)

The Poisson regression model is regarded as a limiting case of the negative binomial regression model as α approaches zero, which means that the selection between these two models is dependent on the value of α. The parameter α is often referred to as the over dispersion parameter. 2.4 STUDIES ON ACCIDENT MODELLING Dahee Hong, Youngkyun Lee (2000), considered study of accident on National ways and rural ways in the urban areas of Cheolla province in Korea, by considering accident data from 2001 to 2003 and accident prediction models were developed by road types using multiple regression. They found that more number of accidents are occurred at the intersections in the urban areas. The number of intersections has the largest effect on accidents in case of two lane roads in the urban areas. The suggested accident prediction model for Two Lane roads: Y =0.174+ 1.164 * (X1) + 0.835 * (X2)

(2.13)

Where, Y = Number of Accidents (accident/km), X1 = Number of Intersections (unit/km) X2 = Number of Pedestrian Traffic Signals. The suggested accident prediction model for four lane roads in non existence of median barrier Y = 0.920 + 3.135* (X1)

(2.14)

Where, Y = Number of Accidents (accident/km), X1 = Number of Intersections (unit/km) More than four lane roads in existence of median barrier: Where, Y= 0.729 + 1.757* ( X1)

Transportation Division, NIT Warangal

(2.15)

Page 10

Stamatiadis and Deacon (1995) and Hing et al (2003), developed Multiple Logistic Regression Model. Logistic regression belongs to the group of regression methods for describing the relationship between explanatory variables and a discrete response variable. A binary logistic regression is proper to use when the dependent is a dichotomy (an event happened or not) and can be applied to test association between a dependent variable and the related potential factors, to rank the relative importance of independents, and to assess interaction effects. Binary logistic regression is used in this study since the dependent variable Y (accident classification) can only take on two values: Y = 1 for rear-end accidents and Y = 0 for non-rear-end accidents. The probability that a rear-end accident will occur or not is modelled as logistic distribution is shown.

(2.16)

The logit of the multiple logistic regression model (Link Function) is given as

(2.17)

Where, π(x) = is conditional probability of a rear-end accident, which is equal to the number of rearend accidents divided by the total number of accidents. xn = are independent variables (driver/vehicle/environment factors). The independent variables can be either categorical or continuous, or a mixture of both. Both main effects and interactions can generally be accommodated. βn = is model coefficient, which directly determines odds ratio involved in the rear-end accident. The odds of an event are defined as the probability of the outcome event occurring divided by the probability of the event not occurring. The odds ratio that is equal to exp(βn) tells the relative amount by which the odds of the outcome increase (or greater than 1.0) or decrease (or less than 1.0) when the value of the predictor value is increased by 1.0 units. Especially for categorical independent variables, the odds ratios represent the accident risk comparison among different levels of drivers/vehicles/environments.

Transportation Division, NIT Warangal

Page 11

Wass et al (1983) and Kronbak and Greibe (1994), have investigated Generalised Linear Models based on different flow functions of some with flows for cyclists and moped drivers as well. The general conclusion was that the models shown below are suitable for Danish conditions, and since these new models for urban roads were to be used along with existing models for rural roads, it was decided to use the same model structure here as well The model structure for road links (2.18) Where E(µ) is the expected number of accidents (accidents per year per km), N the motor vehicle traffic flow (AADT), x variables describing road geometry or environment of the road a, p, βj are estimated parameters. For junctions:

(2.19) where E(µ) is the expected number of accidents (per year), Npri the incoming motor vehicle traffic flow (AADT) from the primary direction, Nsec the incoming motor vehicle traffic flow (AADT) from the secondary direction, x variables describing road geometry, a, p1, p2, βj are estimated parameters. For non-signalised junctions, the primary direction represents the two arms where traffic has the right of way. For signalised junctions, the primary direction at the junction represents the two arms with the highest traffic volumes. It cannot be rejected that the primary direction in signalized junctions represents two arms which are not opposite in the junction. This will be very seldom though. Ali P. Akgungor and Osman Yıldız (2001) used fractional factorial method for the sensitivity analysis of accident prediction model. The evaluation of sensitivity analysis indicated that average daily traffic (ADT), lane width (W), width of paved shoulder (PA), median (H) and their interactions (i.e., ADT–W, ADT–PA and ADT–H) have significant effects on number of accidents. The effects due to each parameter and parameter interactions are estimated using the following equation: Ej = Sij(Xi)/Nj

Transportation Division, NIT Warangal

(2.20)

Page 12

in which Ej represents the effect of the jth factor (i.e., in jth column), n the total number of experimental runs (i.e., n = 8), Sij represents the sign in row i and column j, Xi represents the value of the prediction variable obtained from the ith experimental run and Nj is the number of “+” signs in column j. The sensitivity of analysis of the selected accident prediction model is defined by A=0.0019(ADT)0.882(0.879)w(0.919)PA(0.932)UP(1.232)H*0.882)T1 (1.322)T2

(2.21)

in which A is the number of run-off-road, head on, opposite direction sideswipe, and samedirection sideswipe accidents per mile per year, ADT the two-directional average daily traffic, W the lane width in feet, PA the width of paved shoulder in feet, UP the width of unpaved (gravel, turf, earth) shoulder in feet, H the median roadside hazard rating for the highway segment, measured subjectively on a scale from 1 (least hazardous) to 7 (most hazardous), T1 = 1 for flat terrain, 0 otherwise. T2 = 1 for mountainous terrain, 0 otherwise. From this analysis the authors had found that ADT–W, ADT–PA and ADT–H, as twoparameter interactions, are detected to be outliers which have major effects on the model. Fajaruddin Mustakim et al (2008) studied on black spots and develop an accident prediction model by using multiple linear regression analysis. The study area was Federal Route (FT50) Batu Pahat – Ayer Hitam. The regression model was In (APW) 0.5 = 0.0212( AP ) + 0.0007 (HTV 0.75 + GAP 1.25) + 0.0210 ( 85th PS) (2.22) Where, APW = accident point weightage AP = number of access points per kilometer HTV = hourly traffic volume Gap = amount of time, between the end of one vehicle and the beginning of the next in second. 85th PS = 85th percentile speed The model has R-square value of 0.9987. The results of this paper have shown that the existence of a larger major junction density, an increase in traffic volume and vehicle speed in Federal Route 50 are the contributors to traffic accidents. Reduction of vehicle speed, access point, traffic volume and gap are likely to have an influential effect on the road traffic accidents.

Transportation Division, NIT Warangal

Page 13

Nassar and Nassar et al (2005) developed a Poisson regression model based on the Ontario data. This model is of the form E(m)i = ADTL1.242 LEN0.696 exp(0.1955 LN – 0.1775 SHW + 0.2716 MT2 + 0.5669 TS 0.1208 PTC – 0.0918 Y91)

( 2.23)

Where E(m)i

= expected accident frequencies on road section i,

(2.24) where E(Λ) = expected accident frequency, Transportation Division, NIT Warangal

Page 14

V1 = major road traffic volume [annual average daily traffic (AADT)], V2 = minor road traffic volume (AADT), and a0, a1, a2 = model parameters. Kulmala, Maher and Summersgill (2002), proposed to model these additional variables along with traffic flows as follows:

(2.25) Where xj represents any additional variable and bj is a model parameter. Andrew P. Tarko (2000), developed a Safety Prediction Model for links and nodes. Use of Safety Performance Function (SPF) seems to be the most reliable method of predicting future safety at individual road intersections and links. SPFs connect various roadway and traffic characteristics with crash frequency and various levels of severity. The most common structures of the models for links (segments) and nodes (intersections) are as follows:

where a = expected annual number of crashes of certain severity; E = exposure to risk function; L = segment length; Q=

annual average daily traffic (AADT) on the segment;

Q1 = AADT on the major road of the intersection; Q2 = AADT on the minor road of the intersection; X1, . . . , Xn =

road, traffic, and other characteristics; and

α, β, γ1,……… γn = model parameters. SPFs are expected to be used in the forthcoming Highway Safety Manual to predict and evaluate roadway safety. Ziad Sawalha(2003), stated that the mathematical form used for any Accident Prediction Model (APM) should satisfy two conditions. First, it must yield logical results. This means that (a) it must not lead to the prediction of a negative number of accidents and (b) it must ensure a prediction of zero accident frequency for zero values of the exposure variables, which for road sections or section length and Average Annual Daily Traffic (AADT). Transportation Division, NIT Warangal

Page 15

The second condition that must be satisfied by the model form is that, in order to use generalized linear regression in the modeling procedure, there must exist a known link function that can linearize this form for the purpose of coefficient estimation. These conditions are satisfied by a model form that consists of the product of powers of the exposure measures multiplied by an exponential incorporating the remaining explanatory variables. Such a model form can be linearized by the logarithm link function. Expressed mathematically, the model form was E (Y) = a0 * La1 * Va2 * exp ∑ bj xj

(2.26)

Where, E (Y) = predicted accident frequency L = section length V = section AADT xj = any variable additional to L and V a0, a1, a2, bj = model parameters.

2.5 CASE STUDY “Analysis of Road Accidents in Thiruvananthapuram City” has been conducted by Sony Vincent in 2008. After detailed analysis of data collected, the dangerous routes of Thiruvananthapuram road net work which need to be improved were identified. Major part of the study stretch runs through plain terrain with few curves. It passes through a highly commercial region of Thiruvananthapuram city and hence there are numbers of side roads meeting the stretch at frequent intervals. The stretch is of 15 km long and is a part of NH47.The entire stretch was divided into ten sections of 1.5 km each. The various data collected for the study stretch include accident data, road geometric data, and speed of vehicles (kph), pedestrian volume (no. of pedestrians per hour) and traffic volume (pcu/hr). From the accident information collected, a preliminary analysis shows the trend of total number of accidents and the rear end accidents that occurred in the study stretch over a period of 9 years from 2000 to 2008. The collected data were statistically analyzed to evaluate the effect of the selected parameters on accidents. The relationship between the accidents and various factors were also given. The data was analyzed by using SPSS (Statistical Package for Social Sciences) software. The number of accidents was taken as the dependent variable and width of the road, alignment of the road, number of side roads and traffic volume were taken as independent variables and models developed are given. Transportation Division, NIT Warangal

Page 16

Transportation Division, NIT Warangal

Page 17

Page 18

Page 19

2.8 SPECIFIC SCOPE OF THE STUDY The specific scope of study of Tirumala roads includes the Collection of Accident data To identify the Accident prone stretch Investigations of Accident prone stretches Remedial measures for safer roads. To develop model for down ghat road, up ghat road and hill roads of Tirumala To conduct road safety Audit and recommendations for identified Accident prone stretches 2.9 SUMMARY This chapter presented the review of various black spot identification, methods used for model development for prediction of road accidents, Road safety audit and measures for traffic improvement.

Transportation Division, NIT Warangal

Page 20