Effect of road width and traffic volume on vehicular interactions in heterogeneous traffic

Transcription

1 JOURNAL OF ADVANCED TRANSPORTATION J. Adv. Transp. 2014; 48:1 14 Published online 2 March 2012 in Wiley Online Library (wileyonlinelibrary.com)..196 Effect of road width and traffic volume on vehicular interactions in heterogeneous traffic Karuppanagounder Krishnamurthy 1 * and Venkatachalam Thamizh Arasan 2 1 Department of Civil Engineering, National Institute of Technology Calicut, Calicut, Kerala , India 2 Department of Civil Engineering, IIT Madras, Chennai, Tamil Nadu, India SUMMARY Highway traffic flow phenomena involve several complex and stochastic variables with high interdependencies. The variations in roadway, traffic and environmental factors influence the traffic flow quality significantly. Capacity analysis of road sections under different traffic and geometric conditions need to quantify the vehicles of widely varying characteristics to a common and universally acceptable unit. Passenger car unit (PCU) is the universally adopted unit of traffic volume, keeping the passenger car as the standard vehicle with reference to its static and dynamic characteristics; other vehicles are expressed to its equivalent number in terms of PCUs. The studies carried out in this aspect represent the dynamic nature of impedance caused by a vehicle while moving through a traffic stream. The PCU values recommended by the Highway Capacity Manual are widely applied in many countries; however, their applicability is highly under debate because of the variations in prevailing local traffic conditions. There are several factors that influence the PCU values such as traffic, roadway, vehicle, environmental and control conditions, etc. Apart from vehicular characteristics, the other two major factors that influence the PCU of vehicles are the following: (i) road width and (ii) traffic volume. In this study, estimation of PCU values for the different types of vehicles of a highly heterogeneous traffic on 7.5- and 11.0-m-wide roads, using micro-simulation technique, has been dealt with. It has been found that the PCU value of a vehicle type varies significantly with variation in road width and traffic volume. The results of the study indicate that the PCU values are significantly influenced by the said two factors. Copyright 2012 John Wiley & Sons, Ltd. KEY WORDS: flow; headway; traffic safety capacity; transport planning; transportation analysis 1. INTRODUCTION Road capacity, in general, can be understood as the maximum possible volume of traffic that can pass through a given road section. Thus, the knowledge of traffic volume is an important basic input required for accurate estimation of road capacity. Expressing traffic volume as the number of vehicles passing a given section of road or traffic lane per unit time will be inappropriate when several types of vehicles with widely varying static and dynamic characteristics are comprised in the traffic. The problem of measuring the volume of such heterogeneous traffic has been addressed by converting the different types of vehicles into equivalent passenger cars and expressing the volume in terms of passenger car unit (PCU) per hour. PCU is the universally adopted unit of measurement of traffic volume derived by keeping the passenger car as the standard vehicle. Under fairly homogeneous traffic conditions, the vehicles follow traffic lane, and the volume or capacity under such conditions is expressed in terms of passenger cars per hour per lane. The vehicles of highly heterogeneous traffic with widely varying physical and operational characteristics, such as the one prevailing on Indian roads, occupy on the basis of the availability of space any convenient lateral position on the road without any lane discipline. Under such conditions, expressing traffic volume in terms of PCU per hour per lane is irrelevant, *Correspondence to: Karuppanagounder Krishnamurthy, Department of Civil Engineering National Institute of Technology Calicut, Calicut, Kerala , India. kk@nitc.ac.in Copyright 2012 John Wiley & Sons, Ltd.

2 2 K. KRISHNAMURTHY AND V. T. ARASAN and the volume of traffic has to be expressed by taking the whole width of roadway into consideration. The interaction between moving vehicles under such heterogeneous traffic condition is highly complex. The present study is aimed at quantifying the vehicular interactions in heterogeneous traffic under different roadway and traffic conditions. A micro-simulation technique has been used to model the heterogeneous traffic flow observed on Indian roads, and the vehicular interaction has been quantified in terms of PCU. 2. LITERATURE REVIEW With the aim of the study being the quantification of the interaction of different vehicle types with other vehicles in heterogeneous road traffic, it was first decided to identify the major factors influencing the extent of interaction so that the relevant literature can be identified and reviewed. Apart from vehicular factors, the other major factors influencing the extent of the interaction are road geometry and volume of traffic (the environmental factors and driver behaviour, which may also influence the extent of interaction, are held as invariants for the purpose of this study). As this study is focused on vehicular interaction at the micro level, as the first step, a straight stretch of road on level terrain is considered. Thus, the width of the road way is the only geometric aspect considered for this study. The literature review is thus focused on aspects related to the effect of traffic volume and road width on vehicular interaction. The search for literature on effect of traffic volume on vehicular interaction revealed that most of the studies conducted in this regard are related to lane-based and fairly homogeneous traffic (e.g. [1,3] and Srinivas et al. 2004). A few studies conducted under heterogeneous traffic conditions (e.g. [4 6]) deal only with macro-level aspects of vehicular interactions, either on the basis of field observed data or with the use of mathematical techniques. The literature review on impact of road width on vehicular interaction revealed that the studies are all related to lane-based traffic conditions (e.g. [7 10]), and no studies pertaining to lane-less heterogeneous traffic condition, dealing with this aspect, have been reported. Thus, the available literature provided only a limited base for the present study. 3. OBJECTIVES The general objective of the work reported here is to study the effect of road width and traffic volume, on the level of interaction between vehicles under heterogeneous traffic conditions prevailing on Indian roads. The specific objectives of this study are the following: (i) to quantify the vehicular interactions in heterogeneous traffic in terms of PCU, using micro-simulation technique, and (ii) to study the effect of road width and traffic volume on PCU values of vehicles. 4. SIMULATION FRAMEWORK On Indian roads, as mentioned earlier, because of the high level of heterogeneity of traffic, the vehicles, while manoeuvring, occupy any lateral position on the road, on the basis of space availability. In view of this, while modelling the heterogeneous traffic flow, appropriate vehicle movement logics need to be developed to simulate the stated conditions of traffic flow. As per the adopted methodology for this study, the entire road space is considered as a single unit. The road space is then considered to be a surface made of small imaginary squares (cells), thus transforming the entire space into a matrix. The vehicles will be represented, with dimensions, as rectangular blocks occupying a specified number of cells, whose coordinates are defined in advance with reference to a fixed origin. This technique will facilitate identification of the type and position of vehicles on the road stretch at any instance of time during the simulation process [11]. For the purpose of simulation, the time-scan procedure is adopted. The scan interval chosen for the simulation is 0.5 s. To address the problem of arrival of more than one vehicle within the scan interval of 0.5 s at higher volume levels, we have adopted a 0.05-s precision for generation of time headway. This 0.05-s precision facilitates generation of a maximum of 20 vehicles per second when the traffic volume is very high. Accordingly, a check will be made for every 0.05 s for vehicle arrivals and the arrived vehicles, if any, will be put on to the entry point of the study stretch of the road, on a first-come-first-served basis. The simulation process, which is intended to model traffic

3 TRAFFIC OPERATIONS AND MANAGEMENT 3 flow through mid-block sections of urban roads, basically, consists of the following three modules: (i) vehicle generation; (ii) vehicle placement; and (iii) vehicle movement. The flow chart shown in Figure1 depicts the major logical steps involved in the overall simulation process Vehicle generation In a stochastic traffic simulation process, the vehicles arrive randomly, and they may have varying characteristics (e.g. speed, vehicle type, etc.). Traffic simulation models therefore require randomness to be incorporated to take care of the stochasticity. This is easily performed by generating a sequence of random numbers. For generation of headways, free speed, etc., the model uses several random number streams, which are generated by specifying seed value. Whenever a vehicle is generated, the associated headway is added to the sum of all the previous headways generated to obtain the cumulative headway. The arrival of a generated vehicle occurs at the start of the warm-up road stretch when the cumulative headway equals the simulation clock time. At this point of time, after updating the positions of all the vehicles on the road stretch, the vehicle placement module is invoked Vehicle placement Any generated vehicle is placed at the beginning of the simulation stretch, considering the safe headway, which is based on the free speed assigned to the entering vehicle, lateral gap and the overall width of the vehicle with lateral clearances. If the longitudinal gap in front is less than the minimum required safe gap, the entering vehicle is assigned the speed of the leading vehicle, and once again the check for safe gap is made. If the gap is still insufficient to match the reduced speed of the entering vehicle, it is Start Inputs, Initialization and Generate first vehicle headway Is cumulative precision step = scan Yes Move all vehicles No Is current time = No Current time = current time + precision Add vehicle Yes Headway to output Generate headway for next vehicle No Is simulation time over? Yes End Figure 1. Simulation framework.

4 4 K. KRISHNAMURTHY AND V. T. ARASAN kept as backlog, and its entry is shifted to the next scan interval. During every scan interval, the vehicles remaining in the backlog will be admitted first, before allowing the entry of a newly generated vehicle Vehicle movement This module of the program deals with updating the positions of all the vehicles in the study road stretch sequentially, beginning with the exit end, using the formulated movement logic. Each vehicle is assumed to accelerate to its free speed or to the speed limit specified for the road stretch, whichever is minimum, if there is no slow-moving vehicle immediately ahead. If there is a slow-moving vehicle in front, the possibility for overtaking the slow-moving vehicle is explored. If possible, the fast-moving vehicle will overtake the slow-moving vehicle. If overtaking is not possible, the fast-moving vehicle decelerates to the speed of the slow-moving vehicle in front and follows it. The model is also capable of showing the animation of simulated traffic flow over the road stretch for better understanding of the system. 5. MODEL VALIDATION The validation problem arises because various approximations to reality are made in creating the model. The goal of the validation process is to produce a model that represents true system behaviour closely enough for the model to be used as a substitute for the actual system for the purpose of experimenting with the system. Validation is usually achieved through the calibration of the model an iterative process of comparing the model with actual system behaviour and using the discrepancies between the two and the insights gained to improve the model. This process is repeated until model accuracy is judged acceptable. Accordingly, the model of heterogeneous traffic flow was validated using field observed traffic data Model input The complexity of heterogeneous traffic flow increases because of the presence of several categories of vehicles with widely varying performance characteristics in the traffic stream. The different types of vehicles, commonly observed on urban roads of India, can be grouped into eight different categories: (1) buses; (2) trucks; (3) cars including jeeps and small vans; (4) light commercial vehicles comprising large passenger vans and small four-wheeled goods vehicles; (5) motorised three-wheelers, which includes auto-rickshaws, which are three-wheeled motorised vehicles that carry a maximum of three passengers and three-wheeled motorised vehicles that carry small quantities of goods; (6) motorised two-wheelers, which include motor cycles, scooters and mopeds; (7) Bicycles; and (8) tricycles, which include cycle-rickshaw, which are three-wheeled pedal-type paratransit vehicles that carry a maximum of two passengers and three-wheeled pedal-type vehicles that carry a small amount of goods over short distances. The motorised three-wheelers constitute a significant proportion in the total traffic because of their advantages in higher maneuverability at congested traffic conditions [12]. The operational characteristics of vehicles are influenced by their physical dimensions and mechanical capability. The ability to respond to the traffic stream environment depends upon the manoeuvring capabilities of the vehicles, governed by the engine power, acceleration/deceleration and turning capabilities, etc. The average overall dimensions of the different vehicle types and the field observed lateral clearances between vehicles are shown in Table I. The lateral clearance share values are used to calculate the actual lateral clearance between vehicles on the basis of the type of the subject vehicle and the vehicle by the side of it. For example, at zero speed, if a bus is beside a motorised three-wheeler, then the minimum clearance between the two vehicles will be = 0.5 m. The longitudinal clearance at zero speed, based on field observations, is taken as 0.5 m for all combinations of vehicles. The acceleration rate of a vehicle varies over operating speed and between vehicle types. The field-observed acceleration rates of the different types of vehicles, for three different speed ranges, are given in Table II.

5 TRAFFIC OPERATIONS AND MANAGEMENT 5 Table I. Vehicular dimensions and field-observed lateral clearances. Vehicle type Average overall dimension (m) Minimum lateral clearance share (m) Length Breadth At zero speed At a speed of 60 km/h Buses Trucks Light commercial vehicles Cars Motorised three-wheelers Motorised two-wheelers Bicycles Tricycles Table II. Acceleration characteristics of the different categories of vehicles. Vehicle type Rate of acceleration at various speed ranges (m/s 2 ) 0 20 (km/h) (km/h) Above (40 km/h) Buses Trucks Light commercial vehicles Cars Motorised three-wheelers Motorised two-wheelers Bicycles Tricycles Study stretch of road The credibility of the simulation model needs to be established through a comparison of simulated values of traffic flow characteristics with its corresponding values observed in the field. Hence, a road section, on a straight and level stretch of a four-lane divided road with raised curbs, in Chennai city, India, was considered for model validation. The width of the road space available for each direction of traffic flow on the road is 7.5 m. Out of the total width of 7.5 m, a 1.5-m-wide road space, adjacent to the curb, is reserved for bicycles by making paint markings on the pavement surface. The road surface intended for bicycles, when found free, is also used by motorised vehicles if required. The traffic flow on the stretch was measured for 1 h by video capturing the traffic and making classified count of vehicles after transferring the video data to a computing work station. A total of 3704 vehicles were observed to pass in one direction, through the section, during the observation period of 1 h. It was found during the traffic volume count that the number of trucks and tricycles was very small, constituting about 0.4% and 0.2%, respectively, of the total traffic. Hence, these vehicles, for the purpose of analysis, were treated to be equivalent to suitable other categories of vehicles with similar characteristics. With the static and dynamic characteristics of trucks being more or less the same as that of buses, the trucks were considered to be equivalent to buses. Also, each tricycle was treated to be equivalent to two bicycles. The observed composition of the traffic, after the said modifications in composition, is depicted in Figure 2. The simulation model requires the free-speed parameters of vehicles to fix limiting speeds for vehicles in the simulation process. The free-speed values of the different vehicle types, obtained through field measurement on the study stretch, during lean traffic periods are shown in Table III Representation of input variables A number of probability distributions are available to represent the occurrence of events in modelling stochastic systems. In simulation models, the governing variables pertaining to various input

6 6 K. KRISHNAMURTHY AND V. T. ARASAN Bicycle 9.6% Bus and Truck 2.5% L.C.V. 3.3% M.T.W. 40.9% Car 27.8% M.Th.W. 15.9% Figure 2. Field-observed traffic composition. L.C.V., light commercial vehicle; M.T.W., motorised two-wheelers; M.Th.W., motorised three-wheelers. Table III. Free-speed parameters of the different types of vehicles. Vehicle type Free-speed parameters (km/h) Mean Minimum Maximum Standard deviation Buses and trucks Light commercial vehicles Cars Motorised three-wheelers Motorised two-wheelers Bicycles parameters, which are stochastic in nature, are represented through appropriate probability distributions. In the traffic flow phenomenon, vehicle arrivals and headways are random in nature and hence are to be represented using probability distributions. The arrival and headway data were obtained by running the video of the traffic flow at a slower speed ( one-eighth of the actual speed) to enable recording of all the vehicle arrivals manually by observing the details displayed on the monitor of the computer. The number of vehicle arrivals, in successive 5-s intervals, was recorded, covering the whole of the hourly volume of traffic. The data, thus obtained, after grouping into classes, were used to represent the vehicle arrivals through suitable distributions. In this study, it was found, through chi-squared test, that the observed arrival pattern has a significant fit with Poisson distribution (calculated value of chi-squared was against the critical value of 16.92). Similarly, for the observed traffic volume of 3704 vehicle per hour, the inter-arrival time between successive vehicles was measured by noting down the time gap between successive vehicle arrivals by playing the video of the traffic flow at one-eighth of the original speed. Because the measurement pertains to the total width of road space and because the traffic had a considerable number of smaller vehicles like motorised two-wheelers, a significant proportion of the observed headways was very small, resulting in a mean headway, t, of 1.03 s. The headway data, classified over a time interval of 0.8 s, were found to fit into the negative exponential distribution. The goodness of fit was tested using a chi-squared distribution. The calculated chi-squared value is against the critical value from a chi-squared table, for seven degrees of freedom at a 5% level of significance, of Thus, the observed headway data fitted well into the assumed negative exponential distribution. For a depiction of the goodness of fit of the headway data, cumulative frequency distribution of the observed and theoretical headways (inter-arrival time) were plotted on the same set of axes, as shown in Figure 3. It can be seen that the distribution of observed and theoretical headways match with each other to a large extent, corroborating the inference obtained through the chi-squared test. The vehicles generated during the simulation process will be placed at the start of the simulation stretch of road after assigning free speeds corresponding to the vehicle types. The free speeds of the

7 TRAFFIC OPERATIONS AND MANAGEMENT 7 Cumulative % Frequency Observed Headway Theoretical Headway Headway in Seconds Figure 3. Observed and theoretical headways. different categories of vehicles were considered to follow normal distribution [13]. The average reaction time of drivers was taken as 0.7 s [14] Comparison of observed and simulated values The model was validated by simulating the field-observed traffic flow and comparing the characteristics of the simulated traffic with those of the observed traffic. For the purpose of simulation, a 7.5-m-wide, 1400-m-long road stretch was considered. The middle 1000 m was the observation stretch, the initial 200-m length at the entry point was used as a warm-up zone and a 200-m length at the exit point was also excluded from the analysis to ensure a fairly uniform flow of traffic being observed. To ensure stable flow condition during the measurement of flow characteristics, we set the simulation clock to start only after the first 50 vehicles crossed the exit end of the road stretch. During the simulation process, the time taken by each vehicle to traverse the specified simulation stretch is observed to estimate the speed maintained by each vehicle. Road geometry and vehicle characteristics were the fixed inputs to the simulation model. Traffic volume and composition were the variable inputs. It was decided to validate the model by comparing a derived output of the simulation model with the corresponding field-observed value. Accordingly, the traffic flow was simulated for 1 h, and the average speed maintained by the different categories of vehicles was obtained as the output of the model. The simulation was run with three random number seeds, and the average of the three values was taken as the final output of the model. The average speed of different vehicle types was observed using video survey data collected on the stretch. A comparison of the simulated and observed speeds is given in Table IV. It can be seen that the two values match with each other on the basis of t-test, to a significant extent, implying the satisfactory level of validation of the model Study of speed flow relationship As an additional validation of the simulation model, it was decided to develop speed flow relationship for the heterogeneous traffic and check whether the relationship follows the well-established trend. For developing the speed flow relationship, we considered a heterogeneous traffic stream on a 7.5-m-wide road space (for the simulation), with the field-observed traffic composition (depicted in Figure 2). The simulation experiments were carried out starting from a very low traffic volume-to-capacity level. The traffic volume, at different traffic flow levels, was measured in terms of the number of vehicles. The traffic speed is the mean traffic stream speed. To get the stream speed, we first obtained the exit volume of each category of vehicles, with its average speed, for all volume levels. Then, the traffic stream speed was obtained as the weighted average of the speeds of the different categories of vehicles in the traffic steam. Also, the model was used to simulate the heterogeneous traffic flow on an 11.0-m-wide road space over a wide range of traffic volume, and measurement of flow and speed was made following the procedure adopted for the 7.5-m-wide road. The two speed flow curves, plotted on the same set of axes, are shown in Figure 4. It can be seen that the relationship follows the well-established trend in both the cases, thus confirming the validity of the model to simulate heterogeneous traffic flow under

8 8 K. KRISHNAMURTHY AND V. T. ARASAN Table IV. Model validation based on observed and simulated speeds. Vehicle type Observed average speed (km/h) Simulated average speed (km/h) Difference (deviation) Squared deviation Bus and truck Light commercial vehicle Car Motorised three-wheeler Motorised two-wheeler Bicycles Total d mean = mean of observed difference = 7.29/6 = t statistic, t o = d mean /(S d / K), where K = number of data sets = 6. S d 2 = 10.51/5 = 2.102, where S d is the standard deviation; S d = t o = 1.21/(1.449/ 6) = The critical value of t statistic for 0.05 level of significance and five degrees of freedom, obtained from standard t-distribution table, is It can be seen that the value of t statistic calculated from the observed data (t o ) is less than the corresponding value from the t table. Therefore, it is corroborated that the formulated null hypothesis H 0 : m s m o = 0 (there is no significant difference between the simulated and observed means speeds) may be accepted. Stream speed in km/h 7.5 m road space 11.0 m road space Volume in number of vehicles per hour Figure 4. Speed flow relationship for the heterogeneous traffic. varying roadway and traffic conditions. It can also be seen that the capacity values for the traffic composition considered are about 4300 and 6800 vehicles per hour for 7.5- and 11.0-m-wide road spaces. 6. ESTIMATION OF PASSENGER CAR UNIT After a careful study of the various approaches adopted for the estimation of PCU of vehicles, it was found that the methodology of approach of the Transport and Road Research Laboratory [15], London, UK, may be appropriate for the heterogeneous traffic being dealt with. The PCU has been defined by TRRL as follows: on any particular section of road under particular traffic conditions, if the addition of one vehicle of a particular type per hour will reduce the average speed of the remaining vehicles by the same amount as the addition of, say x cars of average size per hour, then one vehicle of this type is equivalent to x PCU.This definition has been taken as the basis for derivation of PCU values in this study. The PCU value for the different types of vehicles, at various volume levels, was estimated by taking the average stream speed as the measure of performance. Accordingly, the stream speed of the

9 TRAFFIC OPERATIONS AND MANAGEMENT 9 heterogeneous traffic of chosen composition (Figure 2), for a chosen volume, was first determined. Then, a certain percentage (50%) of cars was replaced by the reference vehicle type (for which the PCU value is to be estimated) in the traffic stream, such that the average stream speed remained the same as before. This was achieved by varying the number of the reference vehicles introduced to substitute the removed cars until the original speed of the traffic was obtained by simulation. Then, the number of cars removed divided by the number of reference vehicle type introduced will give the PCU value of that vehicle type. To account for the possible variation due to randomness, three random number seeds (three seeds were found to be optimal in this case after trying with more number of seeds) were used for the simulation, and the average of the three values was taken as the PCU value. This procedure was repeated for different volume levels, falling over a wide range. The trends of variation of PCU values for the different types of vehicles, obtained as per the said procedure, for 7.5- and 11.0-m-wide road spaces are shown in Figures 5 9. It may be noted that the traffic volume has been m road space 11.0 m road space Bus PCU Value Volume to capacity ratio Figure 5. Passenger car unit value for buses and trucks. 7.5 m road space 11.0 m road space LCV PCU Value Volume to capacity ratio Figure 6. Passenger car unit (PCU) value for light commercial vehicles (LCV). 7.5 m road space 11.0 m road space Auto PCU Value Volume to capacity ratio Figure 7. Passenger car unit (PCU) value for motorised three-wheelers.

10 10 K. KRISHNAMURTHY AND V. T. ARASAN Two-Wheeler PCU Value 7.5 m road space 11.0 m road space Volume to capacity ratio Figure 8. Passenger car unit (PCU) value for motorised two-wheelers. Bicycle PCU Value 7.5 m road space 11.0 m road space Volume to capacity ratio Figure 9. Passenger car unit (PCU) value for bicycles. indicated as the ratio over capacity (capacity values taken from Figure 4) for ease of perception of the traffic volume levels considered for making the plots. 7. RESULTS AND DISCUSSIONS 7.1. Effect of traffic volume It is clear from Figures 5 9 that the PCU values of the different types of vehicles change significantly with change in traffic volume. Hence, for the heterogeneous traffic conditions, it is appropriate to treat the PCU of a vehicle type as a dynamic quantity rather than a constant. The variation of PCU values over volume for the different types of vehicles (Figures 5 9) shows an increasing trend at low volume levels and then a decreasing trend at higher volume levels to reach its lowest value at capacity level. The reason for the trend can be explained as follows. At low volume levels, with the spacing (both longitudinal and lateral spacing) between vehicles being more, cars (which are the reference vehicles) are able to manoeuvre through the gaps easily, which facilitates fast movement. Hence, at low volume levels, the presence of other vehicles with low free speeds may not become a severe deterrent in reducing the speed of the cars. The longitudinal and lateral space available at low volume levels facilitate the cars to have high maneuvering freedom and maintain higher speeds. Although a significant speed difference exists between cars and other vehicles at low volume levels, cars can perform overtaking manoeuvres without much reduction in their speeds. An increase in traffic volume at this stage significantly reduces the spacing between vehicles, resulting in a steep rate of reduction in the speed of cars. Also, on multilane roads, an increase in traffic volume increases the lateral friction, and overtaking manoeuvres become difficult. This trend continues up to a certain volume level, at which the speed of the traffic as a whole gets reduced and, consequently, the speed difference between cars and other vehicle types gets reduced. When the traffic volume becomes high enough to bring down the speed of cars equal to the average stream speed, the relative speed differences tend to vanish, and the physical dimensions of vehicles play a major role in determining PCUs. At this stage, a further increase in volume results in a lesser rate of change (decreases) in the speed of cars, resulting in lesser impact

11 TRAFFIC OPERATIONS AND MANAGEMENT 11 due to the introduction of the subject vehicle. When the traffic volume levels are near the capacity level of the given roadway section, the vehicles are forced to move with smaller relative speed differences between a car and other subject vehicles. At this condition, the static characteristics (physical dimensions) of the subject vehicle play a major role in the impedance offered by the vehicle, when compared with their dynamic characteristics, which play a significant role at lower volume levels. This results in the decreasing trend of the PCU value of the subject vehicle at higher volume levels. The lateral distribution of vehicles on the given roadway section is found to be influenced by the traffic composition and volume [16 18] Effect of road width It is observed from Figures 5 to 9 that it is clear that the PCU value of all the vehicles in the heterogeneous traffic is higher on the 11.0-m-wide road when compared with the values on the 7.5-m-wide road. The variation in the width of pavement, which governs the lateral clearance available between two vehicles, significantly influences the capacity, speed and safety of the roadway sections [19,20]. It would be useful to know the reason for the higher PCU values on wider roads. As the first step in this regard, plots connecting the volume (volume-to-capacity ratio) and the speed of the different types of vehicles were made for the 7.5- and 11.0-m-wide roads. It was found from the plots that in all the cases, for a given volume-to-capacity ratio, the speed of a vehicle type is higher in the case of the 11.0-m-wide road when compared with the 7.5-m-wide road. The plots for cars and buses and trucks are shown in Figures 10 and 11, respectively, as examples. The reason for this may be attributed to the fact that when vehicles do not follow traffic lanes and occupy any lateral position on the road space, while manoeuvring forward, the manoeuvring process becomes easier on wider roads, facilitating faster movement of vehicles. As all the vehicles are able to move faster on wider roads, the reason for higher PCU values on wider roads cannot be explained using the speed data in its raw form. Hence, it was decided to calculate the percentage increase in speeds of all types of vehicles so that the increase in car speed can be compared with the increase in the speed of other vehicles. The details of the calculation are shown in Table V. It can be seen from the table that at all the chosen volume-to-capacity levels, the percentage increase in the speed of cars is higher than the percentage increase in the speeds of all the other categories of vehicles. This implies that for a given volume-to-capacity ratio, the speed difference between a car and any subject vehicle is higher in the case of the 11.0-m-wide roads when compared with the speed differences on the 7.5-m-wide roads. Hence, the PCU values of the vehicles are higher on 11.0-m-wide roads compared with those on 7.5-m-wide roads Check for accuracy of the passenger car unit estimates The check for the accuracy of the PCU estimates was carried out by simulating homogeneous (carsonly) traffic and the heterogeneous traffic flows on the same road space. For this purpose, first, the cars-only traffic flow was simulated on the 7.5-m-wide road space, and the road capacity was obtained as 3250 cars per hour by making the speed flow curve. Then, the flows in cars per hour corresponding to a set of volume capacity ratios were determined. The capacity of the 7.5-m-wide road under the heterogeneous traffic (composition as in Figure 2) condition is 4300 vehicles per hour (Figure 4). With 7.0 m Road 11.0 m Road Cars Speed in km/h Volume-to-Capacity ratio Figure 10. Speed flow relationship for cars on the 7.5- and 11.0-m-wide road spaces.

12 12 K. KRISHNAMURTHY AND V. T. ARASAN 7.5 m road space 11.0 m road space Buses and Trucks speed in km/h Volume to capacity ratio 7.0 m Road 11.0 m Road Buses and Trucks speed in km/h Volume-to-Capacity ratio Figure 11. Speed flow relationship for buses and trucks on the 7.5- and 11.0-m-wide road spaces. Table V. Comparison of speed variation on and 7.5-m-wide roads. Vehicle type Volume-tocapacity ratio Speed of the vehicle type (km/h) On 7.5-m-wide road On 11.0-m-wide road Percentage increase in speed* Cars Buses and trucks Light commercial vehicle Motorised three-wheeler Motorised two-wheeler Bicycle *Percentage increase in speed is calculated as speed on the 11.0-m-wide road minus speed on the 7.5-m-wide road divided by the speed on the 7.5-m-wide road and the whole multiplied by 100. the knowledge of the composition of the heterogeneous traffic, it is possible to know the number of vehicles of each category present in the traffic stream at the capacity flow level of 4300 vehicles per hour. The PCU values of the different vehicle categories, at capacity flow condition, were obtained from Figures 5 to 9. Then, the number of vehicles in each category multiplied by the corresponding PCU value gives the PCU equivalents of each category of vehicles. The sum of the equivalent values then gives the capacity flow of heterogeneous traffic in PCU per hour. On the same lines, the flow in

13 TRAFFIC OPERATIONS AND MANAGEMENT 13 Volume in PCU Homogeneous Traffic y = 2816x R² = Heterogeneous Traffic 0 Volume-to-Capacity ratio Figure 12. Traffic volumes in passenger car unit (PCU) on 7.5-m-wide road space under homogeneous and heterogeneous traffic. Volume in PCU Homogeneous Traffic y = x R² = Volume-to-Capacity ratio Heterogeneous Traffic Figure 13. Traffic volumes in passenger car unit (PCU) on 11.0-m-wide road space under homogeneous and heterogeneous traffic. PCU per hour of the heterogeneous traffic, for the selected set of volume capacity ratios, was estimated. Then, plots relating the set of volume-to-capacity ratios and the corresponding flow were made for the cars-only and heterogeneous traffic. The two plots, made on the same set of axes, are depicted in Figure 12. It can be seen that both the plots are closely related to each other, indicating that the PCU estimates made are fairly accurate at all volume levels. To explain the accuracy of estimates on statistical basis, we performed a t-test by relating the flow in the number of cars per hour for the selected set of volume-to-capacity ratios and the corresponding heterogeneous traffic flows expressed in PCU per hour. The calculated value of t (t 0 ) is 2.06 against the critical value (from t table) of This implies that the traffic flow estimates made in PCU per hour significantly represent the simulated flows of the cars-only traffic. Hence, it can be said that the PCU estimates are fairly accurate. The results of a similar check performed in the case of the 11.0-m-wide road are depicted in Figure 13. The results (the calculated value of t is 1.98 against the critical value of 2.17) indicate that the PCU estimates are fairly accurate in the case of the 11.0-m-wide roads also. 8. CONCLUSIONS The following are the important conclusions of this study: (1) The validation results of the simulation model of heterogeneous traffic flow indicate that the model is capable of replicating the heterogeneous traffic flow on mid-block sections of urban roads to a highly satisfactory extent. The validity of the model is further confirmed by the speed flow relationships developed using the simulation model for 7.5- and 11.0-m-wide road spaces, which are found to follow the well-established trend of the speed flow curves. (2) The PCU estimates, made through simulation, for the different types of vehicles of heterogeneous traffic, for a wide range of traffic volume levels indicate that the PCU value significantly changes

14 14 K. KRISHNAMURTHY AND V. T. ARASAN with changes in traffic volume. Thus, for the traffic condition considered for this study, there is a reason to treat the PCU value for a vehicle type as a dynamic quantity rather than as a constant. (3) It is found that, by virtue of the complex nature of interaction between vehicles under the heterogeneous traffic condition, at low volume levels, the PCU value of vehicles increases with increases in traffic volume, whereas under higher volume conditions, the PCU value decreases with an increase in traffic volume. (4) The results of the simulation experiment to study the effect of road width on PCU values indicate that for any vehicle type in heterogeneous traffic, the PCU value increases with increase in the width of road space. (5) The check performed to ascertain the accuracy of the PCU estimates by comparing the flow of cars-only traffic and the PCU equivalent of heterogeneous traffic on 7.5- and 11.0-m-wide road spaces indicates that the estimates are fairly accurate. REFERENCES 1. Van Aerde M, Yagar S. Volume effects on speeds of 2-lane highways in Ontario. Transportation Research Part A 1983; 17A(4): Al-Kaisy AF, Younghan J, Rakha H. Developing passenger car equivalency factors for heavy vehicles during congestion. Journal of Transportation Engineering 2005; 131(7): Srinivas PZ, Weimin Z, Pengcheng Z. Modelling and mitigation of car truck interactions on freeways. Transportation Research Board 2004-Annual meeting Kadiyali LR. A study of the problems of single-lane pavements in India and their improvements. Indian Roads Congress Journal 1973; 296: Justo CEG, Tuladhar SBS. Passenger car unit values for urban roads. Indian Roads Congress Journal 1984; 362: Chandra S, Sikdar PK. Factors affecting PCU in mixed traffic situations on urban roads. Road and Transport Research 2000; 9(3): Armour M. Effect of road cross section on vehicle lateral placement. AustralianRoadResearchBoard1985; 15(1): Evans L, Charlton SG. Explicit and implicit process in behavioural adoption to road width. Accident Analysis and Prevention 2006; 38: Tang TQ, Wong SC, Huang HJ, Zhang P. Macroscopic modeling of lane-changing for two lane traffic flow. Journal of Advanced Transportation 2009; 43(3): Zhang JW, Dai WM, Xiugang Li. Developing passenger car equivalents for China highways based on vehicle moving space. Transportation Research Board Annual Meeting Arasan VT, Kashani SH. Modelling platoon dispersal pattern of heterogeneous road traffic. Transportation Research Board, Annual Meeting 2003; 1852: Shimazaki T, Rahman M. Physical characteristics of paratransit in developing countries of Asia. Journal of Advanced Transportation 1996; 30(2): Arasan VT, Koshy R. Methodology for modeling highly heterogeneous traffic flow. Journal of Transportation Engineering 2005; 131(7): Mukherjee SK, Rao SK, Raichowdhury ML. Fitting a statistical distribution for headways of approach roads at two street intersections in Calcutta. Journal of Institutions of Engineers (India) 1988; 69: Transportation and Road Research Laboratory (TRRL), London, Traffic H.M.S.O. Research on Road Traffic Chunchu M, Ramachandra Rao K, Satishkumar NV. Analysis of microscopic data under heterogeneous traffic conditions. Transport 2010; 25(3): Hidas P. Modelling lane changing and merging in microscopic traffic simulation. Transportation Research Part-C 2002; 10: Hidas P. Modelling vehicle interactions in microscopic simulation of merging and weaving. Transportation Research Part-C 2005; 13: Gunay B. Car following theory with lateral discomfort. Transportation Research Part-B 2007; 41(7): Gunay B. A methodology on the automatic recognition of poor lane keeping. Journal of Advanced Transportation 2010; 42(2):