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1 Assessment of vehicles headway during queue dissipation at signal controlled intersection under mixed traffic Satyajit Mondal and Ankit Gupta Authors Mr. Satyajit Mondal, M.Tech. Research Scholar Department of Civil Engineering Indian Institute of Technology (Banaras Hindu University) Varanasi Uttar Pradesh, India, Pin Dr. Ankit Gupta, Ph.D. (Corresponding Author) Assistant Professor Department of Civil Engineering Indian Institute of Technology (Banaras Hindu University) Varanasi Uttar Pradesh, India, Pin Mob: Fax: Word count: 4,034 (Abstract + Test) o Unedited ver on published n 13/11/2018

2 intersections from three different cities (Allahabad, Delhi and Chandigarh) of India. The discharge headway value of vehicles is analyzed after the onset of green while initial queue departs through the intersection. A box-and-whisker plot is generated for discharge headway of vehicles to quantify its equitable profile. The diagram delineates that headway of vehicle decreases with the initial queue dispersion. Although, the differences between vehicle s headway are almost immutable after the 5 th queue position, gives a saturation headway of 2.05 sec/veh. The headway distribution at each queue position is also evaluated using various continuous distribution models. The Kolmogorov-Smirnov (K-S) test is performed to define the adequate distribution model. The statistical results obtained from K-S test explains that the discharge headway distribution at each queue position pursue a log-normal distribution. Multilinear regression technique is applied to analyze and develop a model for discharge headway using green time and vehicle type as independent variables. The result indicates that longer green time has a significant impact on discharge headway. The outcomes of the study may be beneficial in the microsimulation model development for signalized intersection to assess the performance of the intersection. Keywords: Discharge Headway, Headway Distribution, K-S test, Mixed Traffic, Regression Analysis, Signalized Intersection. 1. Introduction

3 Intersections are the crucial part of any road network and significantly affect the efficiency of the entire transportation system (1). While discharge characteristics during the onset of green are fundamental parameters to evaluate the performance of a signalized intersection (2). Headway of vehicle is the crucial microscopic measure accentuates majorly on discharge flow estimation at the signalized intersection (3, 4). Vehicle s headway is the time difference of two successive vehicles with respect to some reference point (stop line for signalized intersection) (5). The headway of vehicle standing in front of the queue is measured as the time between the vehicle cross the stop line from the initiation of green. Consequently, headway of the vehicle standing in the second position of the queue is the time between the proceeding vehicle crossed the stoppage line to the time the vehicle cross the stoppage line and so on. The vehicle s rear wheels are considered as a reference line over the stoppage line to measure vehicle s headway. Highway Capacity Manual (HCM 2010) stated that a vehicle standing in front of the queue would take more time to react while the signal changes from red to green (5). This reaction time is getting minimized with every subsequent vehicle standing in a queue and vehicle s headway is decreasing gradually until it becomes a constant value as shown in figure 1. This stabilized headway begins from the 4th or 5th vehicle position when the vehicles have fully accelerated to cross the stop line. Generally, this phenomenon is known as discharge headway vehicles. HCM 2010 suggested that the saturation flow can be estimate directly using the constant discharge headway value known as saturation headway (5). Result depicts in figure 1 is describes a lane wise homogeneous traffic conditions with proper traffic regulations. But in the case of the heterogeneous traffic stream, a mix of slow and fast moving vehicles is traveling through the same stretch without any segregation. Also, the static (vehicle dimension) and dynamic (speed, acceleration, power) characteristics of motorized vehicles have a significant impact on the discharge headway where motorized two-wheelers and three-wheelers usually stand in front of the queue and can travel between the gaps available

4 in larger vehicle size. This makes the discharge less disciplined and corresponding it is challenging to measure the headway value. A number of literature have been focused on homogeneous traffic conditions where partial effort has been made to analyze discharge headway under heterogeneous traffic conditions. Therefore, the present study is an attempt to analyze vehicle discharge headway for least lane discipline mixed traffic stream at signalized intersection. Figure 1: Discharge headway during queue dissipation as per HCM Literature Review An accurate discharge headway may provide an adequate estimation of discharge flow and reasonable design of a signalized intersection. A significant effort has been made in the last few decades to analyze the discharge headway of vehicles during queue dissipation through the intersection in green time. Initially, the discharge headways for the first five vehicles in the queue were analyzed and reported the average headway value (6). Researchers from various countries have investigated the discharge headway characteristics for different traffic and geometric conditions, and they found that discharge headway displays a significant changeability for different locations due the change in both traffic and geometric conditions (7, 8). Bonneson (9) developed a model to analyze the discharge headway using several parameters such as driver reaction time, vehicle speed and acceleration in which they found the stabilized headway can only be obtained after eighth and ninth vehicle position in the queue. Several

5 authors have analyzed the headway distribution for different vehicle positions in a queue in different traffic flow conditions (10, 11, and 12). Jin et al. (10) found that discharge headway for vehicles standing in subsequent queue position follow a log-normal distribution. Although the vehicle standing in front of queue follows a normal distribution. They proposed a car following model to describe the specific distribution of vehicle s headway. Authors have also found that in free flow condition the headway follows lognormal distribution whereas in the congested condition the vehicle s headway is more suited to log-logistic distribution during peak hours (11, 12). Authors have analysed queue discharge characteristics such as vehicle s headway, speed, and acceleration at the signalized intersection under mixed traffic conditions. The vehicle s headway shows a decreasing pattern and the requirement of time is decreasing with increase the position of the vehicle in the queue to cross the intersection due to the minimization of driver s response time and initial lost time (13). As a result, the clearing speed of queued vehicles was increasing with increase in the position of vehicles in the queue. Although the vehicle s headway shows a decreasing trend with increases the queue position, but after the 12 th vehicle position, the discharge headway shows an increasing trend. Also, the vehicle s headways of through lane stream exhibited an elongation tendency with an optimal discharge speed of 27 kmph for lowest average headway (14). Digital countdown display has a significant impact on discharge characteristics of vehicles. A number of studies have been focused on analysing the effect of digital signal countdown timers on the performance of the signalized intersection (15, 16, and 17). Authors have found that the mean headway for all vehicle position has a smaller value for the countdown intersection which gives a higher significant value of saturation flow rate. It can be seen from the previous literature that many researchers have pointed out that headway of vehicles gives a decreasing trend with increases the queue position and gives a stabilized headway value after 4th or 5th vehicle position. The Highway Capacity Manual (2010)

6 provides a steady headway of 1.9 sec after its stabilization (5). However, each study in previous literature shows a different headway value as it is varying in serval roadway, traffic, and control conditions (16). Also, most of the studies were based on homogeneous and lane disciplined traffic condition where traffic stream is mainly car dominating. A limited study has reported the headway value and its distribution at each queue position under heterogeneous traffic conditions. The present study is directed to analyze discharge headway of departing vehicles through a signalized intersection under mixed traffic conditions. 3. Traffic Data Collection and Extraction Field data collection for the present study is more challenging for the mix properties of traffic stream with less lane wised flow. During the red time, smaller size vehicles like two-wheeler and three-wheeler are able to penetrate through the gap available between big sized vehicles and stand at the front of the queue, make a number of streamlines haphazardly. During the green time, vehicles discharge through the intersection together and move randomly depending upon the gaps available between the vehicles. This makes it more difficult to identify the vehicles that are following each other. In order to get an accurate headway value, it is required to collect the data from a vantage point so that the movement of every vehicle can trace correctly. The recording was done to trace the vehicular movement through the intersection by installing a video camera at a higher point nearside the selected site. Initially, three different cities were chosen for traffic data collection. All the selected sites have a channelized section for left turn movement with less pedestrian influence at the intersection area. The traffic data collection was carried out in the morning and evening peak hours. Table 1 provides the values various parameters for each selected site. Table 1: Values of various parameters of selected sites Sl no Location Width of approach (m) Cycle length (sec) Cycle analysed

7 I Allahabad I I Delhi I I-5 Chandigarh The existing traffic was categorized into six vehicle classes i.e Car, Big Car (BC), Motorized Two Wheeler (TW), Motorized Three Wheeler (M3W), Bus and light commercial vehicle (LCV) (18). The compositional share of each vehicle class is extracted from the collected video data shown in figure 2. Also, the discharge headways of vehicles were extracted with respect to the stoppage line (marking on the pavement surface) at the intersection approach area. At all the selected intersections, vehicles were usually standing before the line provided for stop during the red time. Although, in some cases, vehicles (generally TW and M3W) were standing after the stop line during the red interval. In such situations, those vehicles are not considered in the headway data analysis. Figure 3 shows such conditions where vehicles are standing before and after the approach stop line. Figure 2: Vehicular composition at all the selected intersections

8 (a) (b) (c) Figure 3: Vehicle stoppage position before (a) and after (b, c) the approach stop line during red interval 4. Discharge Headway Characteristics Discharge headway is a vital traffic measure widely used in the evaluation of various performance measures in traffic studies (19, 20). An appropriate estimation of discharge flow can be done using the accurate value of discharge headway lead to a proper evaluation of capacity at a signalized intersection. Figure 4 illustrates a fundamental discharge headway profile of vehicles after the onset of green. Figure 4: Conceptual discharge headway pattern of vehicles (Limanond et al., 2009) The discharge headway shows a decreasing trend until it reaches a stabilized interval. At the onset of green, headways of few vehicles are higher as they need extra time to perceive the signal variations. The headway of consecutive vehicles progressively decreases until it tends to a constant interval till the initial queue depart. This constant interval is termed as saturation headway. Whereas, the discharge headway evaluation for mixed traffic stream is more

9 complicated due to the haphazard movement of vehicles during the onset of green. Vehicles are traveling irregularly as per their physical dimension and make a number of streamlines without following its preceding vehicle. Consequently, estimation of saturation headway is more tenacious for the existing traffic stream. Therefore, the saturation headway is estimated using Eq. 1. m hi i= n hs = ( m n+ 1) Where hs stands for saturation headway (sec/veh), n denotes the vehicle position in the queue at the start of saturation region and m represents the position of the last vehicle of the initial queue. All the video graphic data were processed to extract vehicular headway value during the onset of green. Discharge headway for individual vehicle in the queue is analyzed by considering the approach stop line as a reference point. The headway statistics up to 10 th vehicle position are enlisted in table 2. A box-and-whisker plot is generated using the mean discharge headway value presented in figure 5. Table 2: Headway value at each queue position Position Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Mean S.D Sample size (1) Figure 5: Discharge headway pattern of vehicles

10 Figure 5 depicts that headway of vehicle decreases with the initial queue dispersion. Also, it is observed that the differences between vehicle s headway are almost immutable after the fifth vehicle position of the initial queue. Thus, saturation headway of 2.05 sec/veh can be found using Eq. 1. Also, the saturation flow can be estimated using Eq. 2 as: 5. Discharge Headway Distribution 3600 S = (2) h S = 1756 veh/hr The driving behavior of a mixed traffic stream is tedious to evaluate due to the presence of a variety of vehicles with vast driving culture (22, 23). Vehicles headway and their distribution is an important parameter to understand the driving behavior in order to estimate several traffic stream parameters and formulate a suitable policy for mixed traffic stream (24). The initial queue formed during the red time is considered for headway analysis whereas vehicles join in green are abdicated. It was perceived that an initial queue contains maximum 15 entirely stopped vehicles. Therefore, headway analysis is carried out up to 10 th queue position for each initial queue formed during the red time. The descriptive statistics of headway for each queue position are enlisted in table 3. Table 3: Statistical result of the discharge headway Position Sample Mean Min Max Median Variance Skewness size (sec) (sec) (sec) (sec) (sec) (Yes/No) Q (Y) Q (Y) Q (Y) Q (Y) Q (Y) Q (Y) Q (Y) Q (Y) Q (Y) Q (Y) s

11 Result enlisted in table 3 illustrates that a positive skewness is observed with different mean and median at each queue position (from Q1 to Q10). This phenomenon is noticed due to the presence of a variety of vehicles in the traffic stream and their enormous driving nature. As a result, the suitability of normal distribution digresses for headway distribution for each queue position due to the random arrival of a vehicle type. Consequently, several types of continuous distributions such as Normal distribution, Exponential distribution, Logistic distribution, Loglogistic distribution, Log-normal distribution, Erlang distribution and Weibull distribution are tested. The apposite headway distribution is selected as per the statistical significance of observed headway value for each queue position. A statistical test Kolmogorov-Smirnov (K- S) is performed to define the adequate distribution model by quantifying of Kolmogorov- Smirnov statistic between the empirical distribution of headway data and cumulative distribution of the reference distribution. Also, the statistical hypothesis test for each distribution is carried out to check the suitability using the Kolmogorov-Smirnov test. The statistical results obtained from K-S statistical analysis explains that the discharge headways distribution at each queue position pursue a log-normal distribution shown in figure 6.

12 Figure 6: PDF of vehicles headway at each queue position

13 The basic function of a log-normal distribution is mentioned as follows: 1 ln( x) µ 2 2 σ 1 f ( x) = e, x>0 (3) xσ 2π Where σ and μ stand for scale and location parameter respectively. The statistical result obtained for the log-normal distribution for each queue position enlisted in table 4. Thus, the null hypothesis can be accepted as per statistical significance. Table 4: Result of the statistical test of discharge headway Position Sample size Kolmogorov-Smrinov Statistics P value Critical value (α=0.05) Variation of Discharge Headway: A Multilinear Regression Approach A number of influencing factors affecting the discharge headway was brought out by the various researchers in previous studies (16, 17, 20). Models were developed based on their prevailing roadway, traffic and control conditions. This study is proposed to analyze the variation of discharge headway with signal timing (green time) and vehicle type that is traveling through the intersection (Right turn and through movements) during the green time. Box plot is generated for the discharge headway as shown in figure 7. It shows two distinctive regimes: (a) the headway values show a decreasing trend until it becomes stabilized level and (b) at the end it shows an increasing trend due to less number of vehicles used that green time, increases the end lost time. Also, the drivers traveling through the intersection at the end of green have not much exact idea about the remaining time of green due to the non-countdown

14 signal system. Most of the previous studies have analyzed the discharge headway until it reaches the stabilized level (up to 10 to 12 vehicles in a queue). But the second regime shows that the discharge headway may increase at the end of the green due to the absence of vehicles. It implies that longer green time has a significant impact on discharge headway and may consider in the modeling of discharge headway. Figure 7: Variation of discharge headway with green time The linear regression model is fitted with both the regimes and results are shown in figure 7. Values given in brackets are the p-value and t statistic of the coefficient at 95% level of confidence. In the first regime, the headway value decreases at a rate of times with per unit change in green time. Whereas the next regime shows an increasing trend at a rate of times. The effect of vehicle type is also analyzed within the regimes using multi-linear regression analysis where discharge headway is considered as dependent variable and green time, and vehicle types are considered as independent variables. Eq. 4 shows the generalized form of the regression analysis between the dependent and independent variable. D = Intercept + GT + TW + M W + Car + BC (4) s αgt αtw αm 3W 3 αcar αbc Where Ds is the departure headway, GT stands for green time (sec), TW, M3W, and BC represent vehicle type Two Wheeler, Motorized Three Wheeler and Big Car respectively. The values of the intercept and the coefficient of the independent variables are determined at a higher coefficient of regression and lower standard error of estimation. Bus and LCV show a

15 statistical insignificant to the discharge headway, therefore in the modeling, they are considered as independent variables. Table 5 shows the result of multilinear regression analysis for both the regimes. Table 5: Multilinear regression modeling for both the regimes Regime 1 (R2 = 0.43, SEE = 0.84) Regime 2 (R2 = 0.49, SEE= 1.02) Factor Coefficient p value t-stat Coefficient p value t-stat Intercept E E Green time E E TW E E M3W E E Car E E Big Car E E The intercept value in regime 1 indicates that value of headway of a vehicle type standing at the front of the queue at the initiation of the green light. The coefficient values of the independent variables in regime 1 show a negative impression on discharge headway as headway value is getting decreasing and stabilized at the end of the regime 1. In regime 2, the green time has a positive impact on discharge headway as longer green time may increase the headway value. Although, the negative coefficients for the vehicle types imply that the appearance of any vehicle type in that duration reduces the headway value. The proportional values of the coefficient are shown in figure 8. Figure 8: Proportional changes in coefficient values

16 Figure 8 shows the proportional values of the coefficients for individual variables for both the regimes. Among all the variables, green times shows an extensive change over both the regimes starting from a negative impact in regimes 1, implies that the headways are being decreased, to the positive effect in regime 2 indicates that headway is getting increasing towards the end of the green time. Also, the coefficients of vehicles are shown a significant result. In regime 1 the Two Wheeler (TW) has the highest coefficient as in Indian mixed traffic stream TWs commonly stand at the front of the queue and maintain a lower gap during the discharge time. Whereas, the big car has the lowest coefficient as big size vehicle keep the longer gap at the initiation of green light. But, in the case of regime 2 two-wheeler has the lowest coefficient and big car has the highest coefficient. At the end of the green vehicles are traveling with higher acceleration and speed. Therefore, the presence of a four-wheeled vehicle type can pursue a lower headway value due to higher acceleration speed characteristics concerning two-wheeler or motorized three-wheeler. Few studies have analyzed discharge headway characteristics at signalized intersection especially for mixed traffic stream. Most of them recommended certain distribution functions i.e. Gumbel, Lognormal, Weibull, Gamma and Exponential for discharge headway analysis based on the traffic situations (25, 26, 10, 27). The present study also adopts various continuous distribution functions and finds that Lognormal distribution is the most suited model to represent the discharge headway distribution at each queue position (up to 10 th queue position). The present study also develops a model to find the discharge headway value using green time and vehicle type as these two parameters have a major significant effect on headway value. Radhakrishnan and Ramadurai (2015) formulated discharge headway model incorporating various influencing parameters such as vehicle type, lateral position (median, middle and nearkerb) and green time using linear mixed effect regression for Indian mixed traffic stream (28). But in a traffic stream where vehicles do not follow the lane discipline, it is difficult to

17 identify its position due to the haphazard movements. Therefore, the developed model in the present study may be efficient to analyze the headway characteristics at the signalized intersection for non-lane based mixed traffic stream.. 7. Conclusions The present study focuses on the comprehensive analysis of discharge headway at the signalized intersection under mixed traffic conditions. Data were collected from five different signalized intersection from 3 different cities of India. The discharge headway value of vehicles is analyzed after the onset of green while the initial queue departs through the intersection. A box-and-whisker plot is generated for discharge headway of vehicles to quantify its equitable profile. The diagram delineates that headway of vehicle decreases with the initial queue dispersion. Although, the differences between vehicle s headway are almost immutable after the 5 th queue position, gives a saturation headway of 2.05 sec/veh. The headway distribution at each queue position is also evaluated using various continuous distribution models. The Kolmogorov-Smirnov test is performed to define the adequate distribution model. The statistical results obtained from K-S statistical analysis explains that the distribution of discharge headways at each queue position pursue a log-normal distribution. The multi regime is fitted with the headway distribution during the entire green period. Vehicle type and green time are found more significant factors affecting discharge headway. Multilinear regression analysis was utilized to develop a model of discharge headway by considering the vehicle type and green time as independent variables. The result shows that in regime 1 the headway value decreases with an increase in green time and presence of a vehicle type. Although in regime 2, the headway value increases with an increase in green time, it may reduce due to the appearance of a vehicle type. The outcomes of the study may be beneficial in the microsimulation model development for the signalized intersection to assess the performance of the intersection.

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