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Transportation Research Procedia 17 ( 2016 ) 428 – 437

11th Transportation Planning and Implementation Methodologies for Developing Countries, TPMDC 2014, 10-12 December 2014, Mumbai, India Study on Speed and Time-headway Distributions on Two-lane Bidirectional Road in Heterogeneous Condition

Akhilesh Kumar Mauryaa*, Sanhita Dasb, Shreya Deyb, Suresh Namab aAssociate Professor, Department of Civil Engineering, Indian Institute of Technology Guwahati, Guwahati, Assam,781039, India. bPost Graduate Students, Department of Civil Engineering, Indian Institute of Technology Guwahati, Guwahati, Assam,781039, India

Abstract

In the present paper an attempt has been made to have an idea about speed and headway distribution pattern in heterogeneous traffic condition comprising of various motorized and non-motorized vehicles having widely varying speed range. Distribution of speed and time headway has been studied for different density levels namely, 0-20 PCU/km, 20-40 PCU/km, 40-60 PCU/km and 60-80 PCU/km. Statistical validity of each distribution is evaluated by Kolmogorov-Smirnov (K-S) test. Results show that the speed and time headway follow different distribution patterns under different density levels. Moreover speed distribution profile is evaluated for different types of vehicle and time headway distribution profiles are also determined for different vehicle pairs. The findings can be used for developing simulation models for two-way, two-lane roads under heterogeneous conditions. © 20162015 The The Authors. Authors. Published Published by Elsevierby Elsevier B.V. B.This V. is an open access article under the CC BY-NC-ND license (Selectionhttp://creativecommons.org/licenses/by-nc-nd/4.0/ and peer-review under responsibility). of the Department of Civil Engineering, Indian Institute of Technology Bombay. Peer-review under responsibility of the Department of Civil Engineering, Indian Institute of Technology Bombay Keywords: Speed distribution; Headway distribution; Heterogeneous traffic; Bi-directional road

1. Introduction

In developing countries like India, traffic conditions are highly heterogeneous comprising vehicles of varying physical dimensions, axle configurations, weight, power-to-weight ratio and other dynamic characteristics such as braking power, acceleration, etc. Due to these characteristics, the vehicles do not follow lane discipline, and occupy any lateral position along the entire width of the roadway irrespective of lane markings. Studies on speed and time headway distributions of road traffic are important as the statistics provide a deeper insight into the aggregate behavior of vehicles and drivers. Speed is one of the most important fundamental parameters to describe the performance of any roadway system. Knowledge of speed and time-headway is very important and essential in traffic engineering as development of a good transportation system is completely dependent on it. It plays important role in many areas, starting from geometric design of road, speed is required in accident studies, regulation and control of traffic

* Corresponding author. Tel.: +91-361-258 2426; fax: +91-361-258 2440. E-mail address: [email protected]

2352-1465 © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Department of Civil Engineering, Indian Institute of Technology Bombay doi: 10.1016/j.trpro.2016.11.084 Akhilesh Kumar Maurya et al. / Transportation Research Procedia 17 ( 2016 ) 428 – 437 429 operations, ascertaining travel time, determining capacity, delay and queue analysis, level of service analysis etc. Knowing speed distribution is necessary to fix a proper posted in order to facilitate safe and efficient movement of drivers. Time headway is a fundamental microscopic parameter in traffic flow theories that is measured by the difference in the time interval between two successive vehicles as they pass a reference point on the roadway measured from the same common features of both the vehicles. But under mixed traffic condition definition of headway is modified as the time interval between two successive vehicles as they pass a reference line on the entire width of the roadway. If the traffic is more or less homogeneous, it is possible to predict the distribution from the previous available researches but when there is great variation in speed of slow and fast moving vehicles it does not always follow conventional distributions. Again three-wheeler rickshaw and motor cycle are having high maneuverability, so they creep through the gap between bigger vehicles and retard the free movement of them. They do not follow lane discipline even if there are proper lane markings. Again there are various types of car having different length, width, maneuverability and acceleration-deceleration capability. All these circumstances make the traffic condition very complex. The present paper attempts to study the speed and time-headway distribution under such conditions in a two-lane both way urban road stretch.

2. Literature Review

A number of literatures are available explaining speed distribution pattern in homogeneous traffic condition but still there are only a few demonstrated the distribution pattern under heterogeneous traffic. Zhang and Maher (1998) used normal distribution in the simulation study and lognormal distribution in the application of the matching-Furness method to estimate the real data trip matrix with platoon dispersion. Dixon et al. (1999) examined speed data in 12 sections in rural multilane highway and concluded the distribution of free flow speed was found to be normally distributed. Jungwook (2008) suggested that on certain roadway systems Gaussian mixture model using the EM algorithm could be used to properly characterize the severity and variability in speed distribution due to congestion under mixed traffic condition in interstate freeway. Hasim et al. (2011) carried out his study on two lane rural highway in Egypt and on conducting Kolmogorov–Smirnov one-sample test (1-sample K–S test) he found that the speed data were normally distributed. Filippo and Marinella (2011) studied low volume roads in Italy and observed that speeds are normally distributed. Zou and Zhang (2011) said that a single normal distribution cannot accurately accommodate the excess kurtosis present in the speed distribution and they proposed skew-normal and skew-t distribution to fit speed data. They suggested that these two distributions can be applied effectively for both homogeneous and heterogeneous traffic. Sacchi et al. (2012) developed a new operating speed model to predict speed in urban arterial and collector street and found that speed data in all sites are normally distributed. Wang et al. (2012) introduced truncated normal and lognormal distribution for modeling speeds and travel time. Chandra et al. (2013) conducted study on multilane divided urban road under mixed traffic condition and concluded that speed distribution will follow normal distribution if SSR (Speed Spread ratio) is between 0.86-1.11. Hastim and Ramli (2013) have studied speed distribution in two lane and four lane oneway road on heterogeneous traffic in Makassar, Indonesia and found that at few roads satisfy normality tests while rest sections failed in the same. In the field of time headway analysis, many authors gave their contribution on the development of a headway model and analysis of some statistical properties of time headway. Starting from Adams (1936) who formulated the idea of arrival as a Poisson process, he concluded that the negative exponential distribution would be the best fit for time headway distribution. Dawson and Chimni (1968) proposed Hyperlang model as a linear combination of a translated exponential function and translated Erlang function. Tolle (1971) concluded that the lognormal distribution provided good fit for the traffic in platoons. Cowan (1975) proposed four headway models, M1, M2, M3 and M4 yielding Poisson process, shifted exponential distribution, mixed and exponential distribution, and generalized M3 distribution respectively. Griffiths and Hunt (1991) considered double displayed negative exponential distribution as an appropriate distribution for modeling the vehicular headways in urban areas. Hossain and Iqbal (1999) reported that the headways followed exponential and lognormal distribution for the vehicles in Dhaka. Under homogeneous conditions, Al-Ghamdi (2001) suggested that negative exponential distribution fitted well for flow rate less than 400 veh/h, shifted exponential and gamma distribution for medium flows i.e. 400-1200 veh/h and Erlang distribution for high flows above 1200 veh/h. Chandra and Kumar (2001) reported hyperlang distribution as the best distribution to describe headways on urban roads under mixed traffic. Zhang (2007) reported that Doubly Displaced negative exponential distribution (DDNED) fitted well for flow levels of 400 veh/h and 1,400 veh/h. Riccardo and Massimiliano (2012) found that Inverse Weibull distribution fitted well for most flow rates ranges and Log Logistic, 430 Akhilesh Kumar Maurya et al. / Transportation Research Procedia 17 ( 2016 ) 428 – 437

Person 5 fitted well for high flow rates on two lane two way roads in the Province of Venice. Dubey et al. (2013) reported Weibull + Lognormal (WLN) and Weibull + Extreme value (WEV) models as the best mixture models to model time gaps at flows of 2300 veh/h and 1900 veh/h respectively under mixed traffic conditions in Chennai. As it is seen from the available literature, there have been many studies carried out to examine probability distribution pattern of vehicular speed and headway on both homogeneous and heterogeneous traffic condition. But still there is less study conducted on heterogeneous traffic to model speed and time headway distributions for different density ranges. Moreover, there is limited information available in literature in showing the variations in speed for different types of vehicles and time headway for different pair of vehicles. So, this paper is aimed to study speed and time headway distributions taking into consideration all these mentioned factors at different density levels.

3. Data collection and analysis

3.1. Data collection

Data collection was done on a two-lane two way highway (NH-31) near Saraighat Bridge in Guwahati. Video recording technique was used for collecting data, whereby predominantly accurate data were processed at 1/25 s. The data were collected on Thursday (15th May, 2014) for 10 hours which included both morning and evening peak and off peak hours. Location of data collection site on Google map and a snapshot of the traffic stream are presented in Figure 1.

(a) (b) Fig. 1. (a) Study location on Google map and (b) snapshot of captured traffic stream.

3.2. Characteristics of Traffic Data

The section was chosen such that it was free from any side hindrance such as lot, gradient, bus-stop, intersection etc. The road section was on a high embankment with earthen shoulder of 1.6 m on each side and crash barrier on one side at a distance of 2 m from road edge. The data were collected under sunny weather on a working day. The video camera was placed on the 15 ft. high vantage point at roadside so as to capture the moving traffic of the entire road width in both the directions. The data used in the analysis were extracted from the videos at a rate of 25 frames per second for achieving a higher degree of accuracy. Due to higher traffic volume over majority of the survey time, it is observed that by vehicles (except two wheelers) was restricted. Vehicles in both directions were moving in a queue as seen from Figure 1 (b). Therefore, lane (or direction) based vehicular speed and time headways are calculated in this study.

4. Properties of the collected data

4.1. Estimation of Speed and Time Headway Probability Density Function

In order to fit distributions to the speed and headway data collected, the following assumptions were made: x Speed and time headways are analyzed for bidirectional traffic. Akhilesh Kumar Maurya et al. / Transportation Research Procedia 17 ( 2016 ) 428 – 437 431 x For all analysis, stream characteristics (like speed, flow and density) are averaged over 15 minute intervals. It is to be noted that flow and density are represented over the entire road width instead of a single lane due to weak lane discipline. Passenger Car Unit (PCU) conversion is done according to Indian Roads Congress code IRC 106: 1990. x Time headway distribution is analyzed under four different density ranges (0-20 PCU/km, 20-40 PCU/km, 40-60 PCU/km and 60-80 PCU/km). Traffic composition of selected stretch consists of Cars 33%, Motorized Two wheelers 26%, Light Commercial Vehicles (LCV) 15%, Three Wheelers 12%, Trucks/Buses 14%. 2500 50 2000 40 1500 30 1000 20

500 Speed(km/h) 10 Flow (PCU/h) 0 0 50 050100 0 2000 40 Density (PCU/km) Flow (PCU/h) 30 (a) (b) Fig. 2. Fundamental diagrams for (a) flow versus density, (b) speed versus flow, 20 and (c) speed versus density.

Speed(km/h) 10 Significant amount of data exist under congested traffic conditions. This can 0 be seen in Figure 2.This is due to the presence of high traffic on the selected 0 100 highway during peak hour period. From Figure 2 (a), a maximum flow of 2300 Density (PCU/km) PCU/h is observed for density of approximately 60 PCU/km. Accordingly, four (c) density ranges are chosen for the study (0-20 PCU/km, 20-40 PCU/km, 40-60 PCU/km and 60-80 PCU/km) to capture variability in speed and time headway distributions. Figure 2 shows that observed free flow stream speed is lower than 50 km/h; due to the presence of a large proportion of slow moving vehicles (like three wheelers, trucks and buses) on the road.

4.2. Statistical Characteristics of Speed and Headway Data

The fundamental statistical properties of speed and headway data used in analysis are shown in Table 1.

Table 1. Statistical parameters of speed and headway data Speed (kmph) Headway(s) Density 0-20 20-40 40-60 60-80 0-20 20-40 40-60 60-80 (PCU/km) Mean 40.58 37.68 37.29 29.70 5.49 3.15 2.82 3.30 Median 39.04 38.3 36.44 28.27 4.2 2.6 2.2 2.2 Mode 38.57 42.86 36.0 22.5 3.4 1.8 1.8 2.2 85percentile 46.61 44.26 43.55 38.57 10.1 4.64 3.9 3.52 Std. deviation 10.10 11.12 10.93 12.97 3.93 2.54 2.16 1.95 Sample size 574 2731 5684 4331 337 2480 5788 4289

From Table 1, it is observed that for a given range of density, the values of mean and median follow a descending order, and that the median is closer to mean at lower density. At higher density, it is nearer to the mode. However, with the increase in density levels, the mean, median and 85 percentile values of headways also decrease, indicating that vehicles maintain a shorter headway and lesser speed when density increases. However, mean headway corresponding to 60-80 PCU/km increases as the flow is lower in this range of density. 432 Akhilesh Kumar Maurya et al. / Transportation Research Procedia 17 ( 2016 ) 428 – 437

5. Estimated speed and time headway distributions

A set of probability density functions (pdf) is evaluated for both time headway and speed data at different density ranges. Probability density functions are fitted to the frequency distributions by Easyfit Software which fits and ranks the frequency distributions depending on K-S test results. In K-S test the null hypothesis is considered as the data follows a specific distribution. Critical K-S values are calculated based sample size and z-value at the required significant level. Then K-S values are calculated as per observed frequency and expected frequency calculated obtained from a particular probability density function. If the calculated K-S value is greater than the critical K-S value then we accept the null hypothesis. In this study estimation of parameters and the goodness of fit tests for the models are conducted at 5 % significance level. Even though the distributions are ranked as per K-S value, p-values are also calculated. If the p-value comes out to be less than 0.05, null hypothesis is to be rejected. However, here only those distributions are presented which are having both K-S and p-values above the critical K-S and critical p-value respectively.

5.1. Speed and time headway distributions for all vehicles

Table 2(a) and Table 2(b) show the distribution profiles and corresponding statistical parameters of all vehicles combined at different density level. The best fitted distributions are ranked as per the K-S and p-values.

Table 2(a). Speed distribution profiles and corresponding parameters for different density ranges Density Type of K-S Critical K- p- value pdf (PCU/km) distribution value S value Probability Density Function 0-20 0.22 0.9864 0.2 Lognormal 0.1083 0.18 0.16 0.9802 0.14 Beta 0.1125 0.12 f(x) 0.9703 0.1 Gamma 0.1175 0.4042 0.08 0.06 0.8926 0.04 Normal 0.1398 0.02 0 0.8709 16 24 32 40 48 56 64 72 80 Weibull 0.1443 x Histogram Beta Gamma Lognormal Normal Weibull Weibull 0.1315 0.8941 Probability Density Function 20-40 0.24 0.8834 0.22 Normal 0.1336 0.2 0.18 0.8755 0.16 Beta 0.1351 0.38086 0.14 0.12 f(x) 0.6268 0.1 Gamma 0.1732 0.08 0.06 Lognormal 0.1977 0.4614 0.04 0.02 0 8 16 24 32 40 48 56 64 72 80 88 x Histogram Beta Gamma Lognormal Normal Weibull Probability Density Function 40-60 0.22 0.9616 0.2 Beta 0.180 0.18 0.16 0.9378 0.14 0.12

Gamma 0.1182 f(x) 0.37062 0.1 0.8861 0.08 Weibull 0.1295 0.06 0.04 0.8646 0.02 Normal 0.1335 0 8 16 24 32 40 48 56 64 72 80 88 0.7749 x Lognormal 0.1477 Histogram Beta Gamma Lognormal Normal Weibull 60-80 Probability Density Function 0.9795 0.16 Beta 0.1063 0.14 0.12 Gamma 0.1158 0.9564 0.1 0.38086 f(x) 0.08 Weibull 0.1171 0.9526 0.06 0.9500 0.04 Lognormal 0.1179 0.02 0 8 16 24 32 40 48 56 64 72 80 0.8686 x Normal 0.1364 Histogram Beta Gamma Lognormal Normal Weibull

Akhilesh Kumar Maurya et al. / Transportation Research Procedia 17 ( 2016 ) 428 – 437 433

Table 2(b). Time headway distribution profiles and corresponding parameters for different density ranges Density Type of p- value pdf (PCU/km) distribution

Log-Pearson 3 0.9999 Probability Density Function 0-20 0.064 0.056

0.048

Burr 0.9959 0.04

0.032 Weibull 0.9951 f(x) 0.024 Gamma 0.9932 0.016 0.008 0 987654321 151413121110 x Histogram Burr (4P) Gamma (3P) Weibull Log-Pearson 3 20-40 Burr 0.9925 Probability Density Function Pearson 5 0.9924 0.12 0.1

Inverse Gaussian 0.9841 0.08

f(x) 0.06 0.04 0.02 0 Log-logistic 0.9636 987654321 151413121110 x Histogram Burr (4P) Inv. Gaussian (3P) Log-Logistic (3P) Lognormal (3P) Pearson 5 (3P) Lognormal 0.9181 Pearson 6 (4P)

40-60 Inverse Gaussian 0.9826 Probability Density Function Burr 0.9798 0.14 0.12

0.1

Log-logistic 0.9744 0.08 f(x) Pearson 5 0.9646 0.06 Lognormal 0.8371 0.04 0.02

0 987654321 151413121110 x Histogram Burr (4P) Inv. Gaussian (3P) Log-Logistic (3P) Lognormal (3P) Pearson 5 (3P) Pearson 6 (4P) 60-80 Log-logistic 0.9884 Probability Density Function Burr 0.9868 0.12 Pearson 5 0.9728 0.1

0.08

Lognormal 0.9622 f(x) 0.06 Inverse Gaussian 0.7355 0.04 0.02

0 987654321 151413121110 x Histogram Burr (4P) Inv. Gaussian (3P) Log-Logistic (3P) Lognormal (3P) Pearson 5 (3P) Pearson 6 (4P)

Following conclusions can be drawn from Table 2: x For speed it is seen that at higher density level Beta distribution fits best followed by Gamma distribution. x It is also observed that at lower density levels the graphs are quite symmetric but at high range of density it is positively skewed. x Generalized log-logistic distribution (Burr) appears suitable for representing time headway distributions for all density ranges. x The histogram corresponding to 0-20 PCU/km shows that there is a large variation in the time headway, indicating that vehicles can maintain any headway for the low density range. 434 Akhilesh Kumar Maurya et al. / Transportation Research Procedia 17 ( 2016 ) 428 – 437

5.2. Speed distribution for different vehicle types

In case of heterogeneous traffic condition, along with studying overall speed distribution pattern, study of speed characteristics of individual class of vehicle at different density level is very important as well. Due to having widely varying physical and dynamic characteristics, their behavior changes to a large extent with the change in number of different types of vehicle present in traffic stream. Table 3 represents best fitted distributions, statistical parameters and statistical test results at different density ranges for five types of vehicles.

Table 3. Best fitted distributions and statistical parameters of speed data of different vehicles for different ranges of density levels Density Vehicle type Distribution K-S value Critical K-S p-value Sample Mean Median Mode (PCU/km) value size LCV Gamma 0.11368 0.48893 0.99739 119 39.17 38.57 34.47

Bus/Truck Beta 0.14152 0.54179 0.98931 168 37.75 37.67 38.57

Two-wheeler Gamma 0.10718 0.48893 0.99877 78 42.12 40.76 38.57 0-20 Three-wheeler Beta 0.16629 0.51332 0.93149 76 35.62 35.22 35.22 Car Gamma 0.09826 0.44905 0.99895 133 47.33 46.29 50.63 LCV Beta 0.13178 0.44905 0.96779 336 35.10 36.54 39.42 Bus/Truck Weibull 0.12435 0.43247 0.97303 278 35.32 36.29 42.86

Two-wheeler Beta 0.13323 0.40420 0.92092 641 41.51 40.91 42.86 20-40 Three-wheeler Beta 0.14339 0.43247 0.91757 244 35.64 36.94 42.86 Car Normal 0.12168 0.40420 0.95973 775 36.83 37.24 42.86 LCV Beta 0.10675 0.41762 0.99189 843 36.71 36.00 36.00

Bus/Truck Beta 0.12490 0.41762 0.96191 804 35.70 35.06 36.00

Two-wheeler Gamma 0.11180 0.37062 0.95931 1599 39.49 38.30 39.13 40-60 Three-wheeler Beta 0.13788 0.41762 0.91985 626 34.54 34.44 33.96 Car Beta 0.10119 0.38086 0.98759 1823 37.29 36.49 34.62 LCV Beta 0.10124 0.40420 0.99362 675 28.41 27.11 37.50 Bus/Truck Beta 0.10763 0.43247 0.99409 543 28.09 27.27 41.22

Two-wheeler Beta 0.10304 0.37062 0.98030 1056 33.70 32.34 45.00 60-80 Three-wheeler Beta 0.11556 0.43247 0.98681 556 27.32 25.56 17.14 Car Lognormal 0.11119 0.40420 0.98222 1505 28.99 27.07 33.33

It can be seen from Table 3 that for same vehicle type it gives different best fitting distribution as well as varying statistical parameters with the change in density level. It indicates that there is an impact of composition and percentage of other vehicles. Following points can also be observed from Table 3:

x It is observed that mean speeds of LCV are 39.17kmph, 35.10kmph, 36.71kmph and 28.41kmph at density levels 0-20 PCU/km, 20-40 PCU/km, 40-60 PCU/km and 60-80 PCU/km respectively. It means with the increase in density speed is reduced. x It is also seen that Beta distribution gives best fit for LCV at three density levels, 20-40 PCU/km, 40-60 PCU/km and 60-80 PCU/km. x Mean speed of Two-wheeler came to be 42.12kmph, 41.51kmph, 39.49kmph, 33.70kmph for density ranges 0-20 PCU/km, 20-40 PCU/km, 40-60 PCU/km and 60-80 PCU/km respectively which indicates that Two-wheeler’s speed is less affected with the change in density. With higher density level it is even more than car speeds. This may be due to high maneuvering ability of Two-wheelers. x At 0-20PCU/km, 20-40 PCU/km, 40-60 PCU/km and 60-80 PCU/km density levels trucks have mean speed as 37.75kmph, 35.32kmph, 35.70kmph, 28.09kmph respectively. There is considerable amount of speed reduction with increase in density. This may be due to bigger size of Buses and Trucks, speeds are restricted. x Mean speeds of Three-wheeler are 35.62kmph, 35.64kmph, 34.54kmph, 27.32kmph at density levels 0-20 PCU/km, 20-40 PCU/km, 40-60 PCU/km and 60-80 PCU/km respectively. Due to poor dynamic characteristics speed reduction is markable for Three-wheeler compared to other vehicle types at high density level. x It is seen that car speed drops by almost 10kmph from 47.33kmph to 36.83kmph, it is probably due to sudden increase in number of Two-wheeler and Three-wheeler. Akhilesh Kumar Maurya et al. / Transportation Research Procedia 17 ( 2016 ) 428 – 437 435 x Overall it is observed that Beta distribution comes to be best fit for most of the cases.

5.3. Time headway distributions for different vehicle pairs

The study of headway distributions for different vehicular pairs gives an insight into vehicle-pair interactions as well the driving behavior under heterogeneous conditions. Interactions of different vehicle pairs and effect of leading vehicles on the driving behavior of following vehicles are studied. Samples with headway data greater than 50 are only considered in this study as working with less data lead to inaccurate results. However, due to better maneuverability and complex behavior of two-wheelers, their interactions with other vehicles are not considered in Density Leading Following Best fit p-value Mean Median Mode Sample (PCU/km) vehicle vehicle (s) (s) (s) size Car Car Log-logistic 0.920 2.42 2.2 1.8 171 Truck Car Pearson 5 0.916 2.95 2.6 2.2 54 Car Three-wheeler Burr 0.985 3.36 2.6 1.8,2.6 57 20-40 Three-wheeler Car Burr 0.701 2.60 2.2 1.8 84 LCV Car Burr 0.944 2.79 2.2 2.2 81 Car LCV Log-logistic 0.903 2.60 2.6 2.2 102 Car Car Log-logistic 0.915 2.41 2.2 2.2 501 Truck Car Log-Pearson 2 0.874 2.71 2.6 1.8 123 Car Three-wheeler Inv. Gaussian 0.995 3.16 2.6 1.4,1.8 178 40-60 Three-wheeler Car Log-Logistic 0.883 2.71 2.6 2.2 184 LCV Car Log–logistic 0.946 2.56 2.2 1.8 240 Car LCV Log-Logistic 0.992 2.80 2.6 2.2 204 LCV LCV Burr 0.989 2.89 2.6 1.8 165 Car Car Log-Logistic 0.987 2.60 2.6 2.2 482 Car Three-wheeler Burr 0.988 2.83 2.6 2.2, 3 168 Three-wheeler Car Burr 0.875 2.35 2.2 1.8 162 Three-wheeler Three-wheeler Pearson 6 0.899 2.63 2.2 2.2 92 60-80 LCV Car Log-Logistic 0.992 2.74 2.6 2.2 212 Car LCV Burr 0.998 3.10 3.0 1.8, 3 190 Truck Car Erlang 0.984 3.09 3.0 3.0 73 Car Truck Log-logistic 0.839 4.29 3.8 3.8 70 Car Bus Burr 0.990 3.66 3.4 3.0 73 this study. Table 4 presents the statistical properties and evaluation results of time headway histograms for different pairs of vehicles.

Table 4. Histograms and Density Plots Using the Estimated Parameters for Different Density Ranges

From Table 4, it is observed that there is a change in headway distributions and statistical parameters for same vehicle-pair when leading vehicle interchanges. This implies that there is an impact of the leading vehicle in driving behaviour of following vehicle. In addition to that, following points can also be concluded- x For the vehicle pair car-car (i.e. leading vehicle–car and following vehicle–car), it is observed that cars maintain smaller headway at low density level due to higher speed. Moreover, for the same vehicle pair Log–logistic appears to fit well the headway data for all density levels. x It is observed that three-wheeler maintain larger time headway with leading vehicles (i.e. cars) for all density ranges which is due to poor dynamic characteristics of three-wheeler as compared to car. x For LCV-car interactions, it is noted that for density 20-40 PCU/km, time headway is higher when the following vehicle is car and for other densities, headway is higher when the following vehicle is LCV. x Mean time headway values for vehicle pair truck-car and car-truck imply that trucks maintain a larger time gap when the leading vehicle is car. Also, there is a change in headway distribution pattern for truck-car and car-truck. x Mean time headway is found to be 2.89 s for LCV-LCV interactions at40-60 PCU/km whereas it is found to be 2.63 s for three-wheeler-three-wheeler at density level of 60-80 PCU/km. Three-wheeler maintains lower time headway than LCV due to its smaller dimensions as compared to that of LCV. 436 Akhilesh Kumar Maurya et al. / Transportation Research Procedia 17 ( 2016 ) 428 – 437

6. Conclusions

This paper presented the speed and time headway distributions observed on a two-lane two-way highway (NH-31) at different density ranges. In this study, an attempt has been made to identify the suitable distributions for all possible density ranges (0-20 PCU/km, 20-40 PCU/km, 40-60 PCU/km and 60-80 PCU/km). Based on analysis and results of the study, following points can be concluded:

x Beta distribution is giving the best fit for speed in most of the cases at 5% significant level and for Three-wheeler, Beta distribution is giving best fit in all the cases. Along with Beta, Gamma also appears to be good fit. x It is observed that speeds of all vehicles reduce considerably with the increase in density which is quite natural. x Mean speeds of Two-wheeler came to be 42.12kmph, 41.51kmph, 39.49kmph, 33.70kmph for density ranges 0- 20PCU/km, 20-40 PCU/km, 40-60 PCU/km and 60-80 PCU/km respectively which indicates that Two-wheeler’s speed is less affected with the increase in density. This may be due to high maneuverability of Two-wheelers. x Burr appears to be suitable for representing time headway distributions for all density ranges on two lane bi- directional road under heterogeneous conditions. Further, Log-Pearson Type 3, Inverse Gaussian and log-logistic also found suitable to represent the time headway distribution for all ranges of density at 5% significance level. x For vehicular interactions of car-truck, car-LCV and car- three-wheelers, it is observed that average time headway maintained are higher when the following vehicles are truck, LCV and three-wheelers in comparison to cases when following vehicles are cars. Higher time headway is due to their poor braking efficiency and low acceleration capabilities. x Vehicles maintain higher time headway at low flow conditions irrespective of congested (high density) or free flow (low density) conditions. Driving behavior of different vehicles in low density regions can be further studied if larger amount of data are collected. These results are based on data collected in NH-31 only; in future more data needs to be collected from different types of roads for its generalization. Results of this research could be the implementation in micro simulation software with regard to vehicle generation on such highways.

Acknowledgements

The data collection under this research work was funded by CSIR - Central Road Research Institute (CRRI), New Delhi under the Supra Institutional Network Project (SINP) category as part of the 12th Five Year Plan Period (FYP).

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