Paper No.542 STUDY OF THE EFFECT OF TRAFFIC VOLUME AND ROAD WIDTH ON PCU VALUE OF VEHICLES USING MICROSCOPIC SIMULATION† V. THAMIZH ARASAN* AND K. KRISHNAMURTHY** ABSTRACT The knowledge of traffic volume is an important basic input required for planning, analysis and operation of roadway systems. Expressing traffic volume as 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 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. The vehicles of highly heterogeneous traffic with widely varying physical and operational characteristics such as the one prevailing on Indian roads, occupy based on the availability of space, any convenient lateral position on the road without any lane discipline. The interaction between moving vehicles under such heterogeneous traffic condition is highly complex. The results of the study, provides an insight into the complexity of the vehicular interaction in heterogeneous traffic. The PCU estimates, made through microscopic simulation, for the different types of vehicles of heterogeneous traffic, for a wide range of traffic volume and roadway conditions indicate that the PCU value of a vehicle significantly changes with change in traffic volume and width of roadway. 1. INTRODUCTION The information on traffic volume is an important input required for planning, analysis, design and operation of roadway systems. Highway capacity values and speedflow relationships used for planning, design and operation of highways, in most of the developed countries, pertain to fairly homogeneous traffic conditions comprising vehicles of more or less uniform static and dynamic characteristics. But the traffic scenario in developing countries like India differs significantly from the conditions of developed countries in many respects. In Indian road traffic, the heterogeneity is of high degree with vehicles of widely varying static and dynamic characteristics. Under this condition, it becomes difficult to make the vehicles to follow traffic lanes. Consequently, the vehicles tend to choose any advantageous lateral position on the road based on space availability. Under the said traffic conditions expressing traffic volume as number of vehicles passing a given section of road per unit time will be inappropriate and some other suitable base needs to be adopted for the purpose. The problem of measuring 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. The PCU is the universally * ** † adopted unit of measurement of traffic volume, derived by taking the passenger car as the ‘standard vehicle’. The interaction between moving vehicles in a traffic stream is highly complex and is influenced by a number of roadway and traffic factors. The accurate estimation of the magnitude of vehicular interaction for different roadway and traffic conditions is the prerequisite for better operation and management of roadway facilities in their prevailing conditions. Since the traffic flow phenomenon is influenced by several stochastic variables of random nature, microsimulation technique has been found to be a versatile tool to model complex traffic systems for study of their characteristics over a wide range of operating conditions. The present study is aimed at studying the vehicular interactions in heterogeneous traffic under different roadway and traffic conditions and hence check for the accuracy of the available PCU estimates for the different categories of vehicles on Indian roads for a range of traffic volume and roadway conditions. 2. LITERATURE REVIEW After the introduction of the term PCU in the Highway Capacity Manual (HCM), USA in the year 1965, considerable research effort has been made toward Professor E -mail:
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[email protected] Written comments on this Paper are invited and will be received upto 15th November, 2008. } } 134 ARASAN & KRISHNAMURTHY ON subject matter reveals that studies conducted are mostly related to fairly homogeneous traffic conditions, and the few studies conducted under heterogeneous traffic conditions are not comprehensive enough to replicate the field conditions accurately. Hence, it was decided to make an attempt to study the vehicular interaction in heterogeneous traffic in a comprehensive manner and derive PCU values for different vehicle types through this research work. 3. SCOPE AND OBJECTIVES the estimation of PCU values for different vehicle types under various roadway conditions. For example, Huber (1982); Krammes and Crowely (1986) suggested that the factors which are considered in evaluating the level of service may be taken as the variables to describe the impedance to travel in PCU estimation. Keller and James (1984) developed a procedure to estimate Passenger Car Equivalent (PCE) values for large vehicles moving over an urban network using TRANSYT simulation model. As per this procedure, the amounts of delay caused by different vehicle types were taken as the basis to estimate the PCE values. Srinivas Peeta et al. (2003) modelled the car-truck interactions on freeway sections using microscopic traffic flow models. The car-truck interactions were modelled by associating a “discomfort level” for every non-truck driver in the vicinity of the trucks. It was observed that this discomfort is affect by the driver socioeconomic characteristics, and situational factors such as time-of-day, weather, and ambient traffic congestion levels. Al-Kaisy et al. (2005) found that the HCM suggested PCU factors for heavy vehicles is applicable only under free-flow conditions and hence, attempted to derive passenger car equivalents for heavy vehicles during congestion. It is found from the review of the literature that several studies on estimation of PCU values of vehicles in heterogeneous traffic have been conducted. For example, Terdsak and Chanong (2005) studied the effect of motor cycles on traffic operations on arterial streets of Bangkok. They found that the derived PCU of motor cycles showed a decreasing trend with increase in share of motor cycles in the traffic stream. Zhang et al. (2006) adopted the vehicle moving space (VMS) as the measure to derive passenger car equivalents for vehicles of different categories for Chinese roadway and traffic conditions. Chandra and Sikdar (2000) through an empirical study found that for a given road width, an increase in volume level of heterogeneous traffic causes more density on the road resulting in reduced uniform speed of vehicles. The lower speed difference between cars and subject vehicles yield smaller PCU value for the vehicle type. Chandra and Kumar (2003) studied the effect of road width on PCU of vehicles on two-lane highways and found that the PCU value increased with increase in width of roadway. Justo and Tuladhar (1984) developed mathematical models to derive PCU values for vehicles on urban roads based on empirical data under mixed traffic flow. Ramanayya (1988) estimated the PCU factors for different vehicle types at different levels of services taking the Western car as the Design Vehicle Unit DVU. The review of literature on the The proposed research work aims at analyzing the characteristics of the heterogeneous traffic flow to identify appropriate theoretical distributions for various traffic variables influencing the traffic stream characteristics, and study of the flow characteristics and vehicular interactions at micro level. The specific objectives of the research work are as follows. 1. To quantify the impedance caused to traffic flow by the different categories of vehicles in heterogeneous traffic in terms of PCU, over a wide roadway and traffic conditions using simulation technique and 2. To study the effect of road width and traffic volume on PCU values of vehicles. 4. THE SIMULATION FRAMEWORK Simulation being a versatile tool for modelling traffic flow, the simulation technique has been used to study the heterogeneous traffic flow characteristics on Indian Roads by a few researchers in the past (e.g., Ramanayya (1988), Kumar and Rao (1996) and Marwah and Singh (2000)). These modelling attempts, however, are not comprehensive enough to replicate the field conditions fully due to various limitations of the studies. Research attempts made at IIT Madras (Arasan and Koshy, 2004 & 2005) to comprehensively model heterogeneous traffic flow has resulted in replication of the field conditions satisfactorily. This simulation model has been used to simulate the heterogeneous traffic flow over a wide range of roadway and traffic conditions. The model is capable of simulating the traffic flow for any specified composition and traffic volume on a given width of roadway over specified time duration. As the variables influencing the traffic flow are random and stochastic in nature, appropriate statistical distributions are used to represent them in the model. The inter-arrival times (time headways) of vehicles are randomly generated from STUDY OF THE EFFECT OF TRAFFIC VOLUME TH COUNCIL MEETING ON PCU VALUE OF HIGHLIGHTS OF THE 178 AND ROAD WIDTH VEHICLES USING MICROSCOPIC SIMULATION specified statistical distributions. As per the methodology, the entire road space is considered as single unit. The road space will be considered to be a surface made of small imaginary squares (cells of convenient size 100 mm in this case); 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 co-ordinates will be defined before hand. The front left corner of the rectangular block is taken as the reference point, and the position of vehicles on the road space is identified based on the coordinates of the reference point with reference to the origin chosen at a convenient location on the space. This technique will facilitate identification of the type and location of vehicles on the road stretch at any instant of time during the simulation process (Fig. 1). 135 this issue, an additional clock for scanning with a precision of 0.05s is provided, so that a maximum of 20 vehicles can be added in one second. The precision of 0.05s, decided based on field studies, is intended to account for the maximum possible number of smaller vehicles, like motorised two wheelers, auto-rickshaw, etc. that may arrive in large numbers in short periods on multilane highways. Thus, the logic formulated for the model also permit admission of vehicles in parallel across the road width, since it is common for smaller vehicles such as Motorised two-wheelers to move in parallel in the traffic stream without lane discipline. Vehicles admitted to the simulation road stretch are then allowed to move based on the various movement logics formulated. Various manoeuvre for a vehicle moving on the simulation road stretch include free forward movement with desired speed, acceleration manoeuvre, movements leading to lateral shifting and overtaking of slower vehicles, movements involving deceleration and following of the front vehicle for want of sufficient gaps for overtaking, etc. When the cumulative precision time is equal to the scan interval, the module for vehicle movement ‘Move All Vehicles’ will be activated to Fig. 1. Reference axes for representing vehicle positions The simulation process, which is intended to model traffic 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 Fig. 2 depicts the major logical steps involved in the overall simulation process involving the three modules. For the purpose of simulation, the time scan procedure is adopted. The scan interval chosen for the simulation is 0.5 second. The arrival of vehicles on the road stretch will be checked for every 0.5 second and the arrived vehicles will be put on to the entry point of the study stretch of the road, on first-come-first-served basis. In the vehicle-generation module, the first vehicle is generated after initialization of the various parameters required to simulate heterogeneous traffic flow. Then, the generated vehicle is added to the system when the current time (clock time) becomes equal to the cumulative headway. At this stage, the module for adding vehicles named ‘Add Vehicle’ will be activated to facilitate the process. At higher traffic flow levels, there is a chance of more than one vehicle arriving during each scan interval (0.5s). To address Fig. 2. Simulation framework move all the vehicles in the simulation road stretch, with their current parameter values. The above process will be continued until the clock time matches with the assigned total simulation time. 136 ARASAN & KRISHNAMURTHY ON 5. TRAFFIC CHARACTERISTICS TABLE 2. MINIMUM AND MAXIMUM LATERAL CLEARANCES The different types of vehicles present in the heterogeneous traffic, for the purpose of this study, were grouped into eight different categories as follows. 1. Motorized two-wheelers (M.T.W), which include motor cycles, scooters and mopeds, 2. Motorized threewheelers (M.Th.W), which include Auto-rickshaws – three wheeled motorized paratransit vehicles to carry a maximum of three passengers and tempos – three wheeled motorized vehicles to carry small quantities of goods, 3.Cars including jeeps and small vans, 4. Light commercial vehicles (LCV) comprising large passenger vans and small four wheeled goods vehicles, 5. Bus, 6. Truck, 7. Bicycle and 8.Tricycle, which includes cyclerickshaw- three wheeled pedal type paratransit vehicles to carry a maximum of two passengers and three wheeled pedal type vehicles to carry small amount of goods over short distances. As this study pertains to traffic flow on urban arterials, animal drawn vehicles were not considered as these vehicles are not permitted/present in negligible number on these roads. Each animal drawn vehicle, if present, was taken to be equivalent to two tricycles for the purpose of simulation. The average overall dimensions of the vehicle types and the field observed lateral and longitudinal clearances between the vehicles are as shown in Tables 1 and 2 respectively. The lateral clearance-share values are used to calculate the actual lateral clearance between vehicles based on the type of the subject vehicle and the vehicle by the side of it. For example, at zero speed, if an autorickshaw is beside a bus, then the clearance between the two vehicles will be 0.2 + 0.3 = 0.5 m. The longitudinal clearance, at zero speed can be calculated by the same procedure. The field observed acceleration rates of the different types of vehicles, for three different speed ranges, are shown in Table 3. TABLE 1. OBSERVED VEHICULAR DIMENSIONS Vehicle type (1) Buses Trucks LCV Cars M.Th.W. M.T.W. Bicycles Tricycles Lateral-clearance share (m) At zero speed At a speed of 60 km/h (2) (3) 0.3 0.3 0.3 0.3 0.2 0.1 0.1 0.1 0.6 0.6 0.5 0.5 0.4 0.3 0.3* 0.3* * Maximum speed of these vehicles is 20 km/h TABLE 3. ACCELERATION RATES OF DIFFERENT CATEGORIES OF VEHICLES Vehicle type (1) Buses Trucks LCV Cars M.Th.W. M.T.W Bicycles Tricycles Rate of acceleration at various speed ranges (m/s2) 0-20km/h 20-40 km/h Above 40 km/h (2) (3) (4) 0.89 0.79 0.82 1.50 1.01 1.35 0.10 0.07 0.75 0.50 0.45 1.10 0.45 0.80 0.67 0.43 0.35 0.95 0.30 0.60 - 6. MODEL VALIDATION 6.1 Data Collection Heterogeneous traffic flow, in one direction, on straight and level stretch of a four-lane divided road with raised curbs, in the southern part of Chennai city, India was considered for model validation. The width of the road space available for each direction of flow 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 marking on the pavement surface. The traffic flow on the stretch was measured for one hour by video capturing the traffic flow 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 through the section during the observation period of one hour. It was found during the traffic count that Vehicle type (1) Buses Trucks LCV Cars M.Th.W. M.T.W. Bicycles Tricycles Overall dimension (m) Length Breadth (2) (3) 10.3 2.5 7.5 2.5 5.0 1.9 4.0 1.6 2.6 1.4 1.8 0.6 1.9 0.5 2.5 1.3 STUDY OF THE EFFECT OF TRAFFIC VOLUME TH COUNCIL MEETING ON PCU VALUE OF HIGHLIGHTS OF THE 178 AND ROAD WIDTH VEHICLES USING MICROSCOPIC SIMULATION there were no animal drawn vehicles present on the study stretch. Also, trucks and tricycles constituted respectively 0.28 and 0.15 per cent of the vehicles. The percentages being very small for the purpose of simulation, the trucks which are close to buses in respect of size and speed, were considered as buses and each of the tricycles, which are close to bicycle in dynamic characteristics were considered to be two bicycles. The observed composition of the traffic after the above said modification is depicted in Figure 3. The simulation model requires the free speed parameters of vehicles to initialize and assign the speed during their placement in the simulation stretch. The free speed parameters obtained through field measurement during lean traffic periods on the study stretch, are shown in Table 4. The free speed of cars (for any vehicle) depends on the make of the car, the age of the car, the level of maintenance of the car, the age, sex and the behaviour of the driver. These factors fall over a wide range under Indian conditions. This is the reason for a wide range in the value of free speeds of cars. 6.2. Model Calibration 137 There are several probability distributions available to describe the vehicle arrival pattern and headway distribution of traffic flow. In this study Poisson distribution and Negative exponential distributions were found to fit well for vehicle arrival pattern and headway distribution respectively (Rao et al. (1988)). The Chisquare goodness of fit test shows that observed frequencies have significant fit with Poisson distribution for vehicle arrival pattern. The calculated chi-square value is 12.136 against the critical value from chi-square table for 9 degrees of freedom at 5 per cent level of significance of 16.92. Thus, it is found that, the calculated chi-square value is less than the table value as shown in Table 5. This confirms the goodness-offit. The Poisson arrival pattern is also pictorially depicted in Fig. 4. Fig. 4. Observed vehicle arrivals pattern Fig. 3. Composition of field observed traffic TABLE 4. FREE SPEED PARAMETERS OF VEHICLES OF DIFFERENT TYPES Free speed parameters in km/h Vehicle Mean type (1) (2) Bus LCV Car M.Th.W M.T.W. Bicycle 53 50 60 45 48 14 Minimum Maximum (3) 38 37 40 30 25 10 (4) 68 65 90 55 60 18 Standard Deviation (5) 7 7 14 7 12 3 For the observed traffic volume of 3704 vehicle/h the inter arrival time between successive vehicles, namely the time headway (λ) has been found to be 1.03 seconds. The grouped headway data with a class interval of 0.8s, was found, using chi-square test, to fit into Negative Exponential distribution. The calculated chi-square value is 12.19 which is less the critical value from chi-square table for 7 degrees of freedom at 5 per cent level of significance of 14.07 and thus confirms the goodness-of-fit. The details of the χ2 test are given in Table 6. The cumulative frequency of the field observed and theoretical headways, plotted on the same set of axes, is shown in Fig. 5. It can be seen that both are matching with each other well. 138 ARASAN & KRISHNAMURTHY ON TABLE 5. GOODNESS - OF - FIT TEST FOR VEHICLE ARRIVAL PATTERN No. of Veh. Arrivals ( r ) in 5 seconds (1) 0 1 2 3 4 5 6 7 8 9 10 11 12 & Above Observed No. of Arrivals (2) 2 12 60 89 117 136 105 71 48 28 14 10 8 Expected No. of Arrivals (3) 4 19 51 89 117 122 107 80 52 30 16 8 4 Theoretical Frequency in the Class (E) (4) 23 Observed Frequency in the Class (O) (5) 14 χ2 = (O − E)2 E (6) 3.606 51 89 117 122 107 80 52 30 16 12 60 89 117 136 105 71 48 28 14 18 1.622 0.000 0.000 1.561 0.028 0.996 0.364 0.204 0.246 3.508 χ2 Value at 5 per cent level of Significance for 9 degrees of freedom is = 16.92 12.136 TABLE 6. GOODNESS-OF-FIT TEST FOR HEADWAY DISTRIBUTION Class Interval (1) 0.0 – 0.8 0.8 – 1.6 1.6 – 2.4 2.4 – 3.2 3.2 – 4.0 4.0 – 4.8 4.8 – 5.6 5.6 – 6.4 6.4 – 7.2 7.2 & More Theoretical Frequency of headway >Lower class limit (2) 3704 1704 783 360 166 76 35 16 7 3 Theoretical Frequency in the class (E) (3) 2000 920 423 195 90 41 19 9 7 Observed Frequency in the Class (O) (4) 2055 944 395 175 72 32 18 5 8 χ2 = (O − E)2 E (5) 0.486 0.624 1.872 1.976 3.423 2.040 0.046 1.578 0.143 χ2 Value at 5 per cent level of significance for 7 degrees of freedom = 14.07 χ2 Value = 12.19 STUDY OF THE EFFECT OF TRAFFIC VOLUME TH COUNCIL MEETING ON PCU VALUE OF HIGHLIGHTS OF THE 178 AND ROAD WIDTH VEHICLES USING MICROSCOPIC SIMULATION 139 statistical basis, are shown in Table 7. It can be seen that the simulated speed values significantly replicate the field observed speeds of the different categories of vehicles. TABLE 7. DETAILS OF COMPARISON OF THE OBSERVED SIMULATED SPEEDS ON STATISTICAL BASIS Vehicle type Observed average speed in km/h 31.47 30.86 33.4 31.18 33.59 13.63 7.29 Simulated speedin km/h 30.39 30.50 32.31 32.31 35.12 15.73 10.51 Difference (Deviation) AND Squared deviation Buses & Trucks 1.08 0.36 1.09 -1.13 -1.53 -2.1 1.17 0.13 1.19 1.28 2.34 4.41 Fig. 5. Observed and theoretical headways LCV Cars M.Th.W M.T.W Bicycles Total 6.3. Model Validation It is desirable to validate simulation models based on traffic characteristics that are derived out of the simulation process. Accordingly, it was decided to compare the speeds of each categories of vehicles obtained through simulation with the corresponding observed values. The speed values were derived by simulating the traffic over a 7.5 m wide straight stretch of road of 1400 m length. 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 stable flow condition during the measurement, the simulation clock was set 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 was observed to estimate the speed maintained by each vehicle. Then, a histogram of simulated and observed speeds was made as shown in Fig. 6. It can be seen that the observed and simulated speeds are matching to a greater extent in all the cases. The details of the comparison of the simulated and observed speeds of different categories of vehicles on dmean = Mean of observed difference =7.29/6 = 1.21 t statistic, to = dmean /(Sd/√K), where K = Number of data sets =6 Sd2 = 10.51/5= 2.102, where Sd is the Standard Deviation; Sd =1.449 to = 1.21/(1.449/√6) =2.06 The critical value of t statistical for 0.05 level of significance and 5 degrees of freedom, obtained from standard t-distribution table, is 2.57. Thus, it can be seen that the value of t statistic calculated based on the observed data (to) is less than the corresponding Table value. This implies that the simulated speeds significantly represent the observed speeds 7. VEHICULAR INTERACTION Fig. 6. Comparison of observed and simulated speeds The study of vehicular interaction is intended to quantify the relative impact of the presence of each of the different types of vehicles on traffic flow. This can be achieved by estimating the PCU values for the different categories of vehicle in the traffic. After a careful study of the various approaches adopted for estimation of PCU of vehicles, it was found that the methodology of approach of Transport and Road Research Laboratory (TRRL), London, UK may be appropriate for the heterogeneous traffic being dealt with. The PCU has been defined by TRRL (1965) as follows: “on any particular section of road under particular traffic condition, 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 140 derivation of PCU values, in this study. ARASAN & KRISHNAMURTHY ON traffic for a set of selected volume levels were estimated by simulating the homogeneous traffic flow, starting from very low volume to capacity level. The impedance caused by a vehicle type, in terms of PCU, for a chosen volume level was estimated by replacing a certain percentage (the observed percentage composition of the subjectvehicle in the field- Fig. 3) of cars in the homogeneous traffic stream with the subject-vehicle type, such that, the average speed of cars remained the same as before the replacement of the cars. The number of subject vehicle can be adjusted on trial basis by observing the average speed of cars in each trial. If the average car speed is more, after replacement, than the average car speed under homogeneous traffic, it is to be inferred that, the introduced number of subject vehicles is inadequate to compensate for the removed cars. Similarly, if the average speed of cars, after replacement, is less than the average car speed under homogeneous traffic, it is to be inferred that the introduced subject-vehicle volume is more than the equivalent volume of cars. After regaining the original speed of cars by adjusting the number of subject vehicles, the PCU value of the vehicle type can be estimated using the relation, PCU Value of subject − vehicle type = Number of cars removed Number of subject − vehicle type added 7.1. Vehicular Interaction in Cars-only Traffic Though the prime objective of this study is to quantify the vehicular interactions in terms of PCU under heterogeneous traffic, it will be appropriate to estimate the PCU values of different vehicle types while moving with cars-only traffic stream to provide a set of basic PCU values of the different types of vehicles. This will provide information on the absolute amount of impedance caused by a vehicle type while moving in the traffic stream, which comprises of cars and the subject vehicles only. In this regard, the model was first used to simulate homogeneous traffic (100 per cent passenger cars) in one direction, on four-lane, divided urban road to develop the fundamental speed-flow diagram. Thus, the width of road space available for movement of traffic in one direction will be 7.5 m. The total length of road stretch considered for the experiments is 1400 m, with 200 m sections at the entry and exit excluded from output data collection as warm-up and stabilizing section. The central 1000 m stretch was considered as the observation stretch, the various traffic flow parameters were recorded while vehicles were moving through it. To account for the variation due to randomness, the simulation runs were repeated using three different-random number streams to check for the consistency of the results. Then a graphical relationship between average speed and traffic volume was developed as depicted in Fig. 7. Using the speed-flow curve, the capacity of 7.5 m wide road space under homogeneous traffic condition, with traffic flow in one direction, was then obtained to be about 3250 passenger cars per hour as shown in Fig. 7. Since, speed is the performance measure identified to estimate the PCU values, average speed of cars-only The logic behind the above approach is that, as stated in the definition of PCU, the introduced subject vehicle type creates more or less the same effect on the traffic stream that is equivalent to that of the cars removed from the stream. The PCU value of the subject-vehicle was determined, following the said procedure, for the same set of traffic volume levels selected for cars-only traffic. Then a plot relating the chosen traffic volume levels and the corresponding PCU values of the subject vehicle was made. Such plots made for the different vehicle categories are shown in Figs. 8 through 12. Fig. 7. Speed-flow relationship on 7.5 m wide road under homogeneous traffic condition Fig. 8. Variation of PCU values of buses STUDY OF THE EFFECT OF TRAFFIC VOLUME TH COUNCIL MEETING ON PCU VALUE OF HIGHLIGHTS OF THE 178 AND ROAD WIDTH VEHICLES USING MICROSCOPIC SIMULATION It can be seen that in all the cases (Fig. 8 through 12) that at lower volume levels, the PCU value of the subject vehicle increases with increase in traffic volume. Whereas, at higher volume levels, the PCU value of the subject vehicle decreases with increase in traffic volume. The reasons for these trends can be explained as follows. The lower magnitude of PCU values at the low-volume level may be attributed to the longer space headway between the vehicles at lower volume levels. Then, the presence of subject vehicles may not impose severe impedance to movement of cars, even though the free speed of subject vehicle is less than the free speed of cars. Due to the availability of larger gaps, cars can overtake the subject vehicle without considerable reduction in speed. As the volume of traffic increases, however, the headway between the vehicles tends to decrease, resulting in increased magnitude of impedance caused to the movement of cars. It was observed that, the relative difference between the average speeds of cars and the subject vehicles decreases as the traffic volume increases. At volumes near capacity level, the speed difference between cars and subject vehicles tends to vanish, due to reduced speed of the vehicles irrespective of their free speed and operational capabilities. This causes considerable reduction in the impedance caused by the subject vehicle to the movement of cars, which results in lesser PCU value for the subject vehicle. 141 Fig. 11. Variation of PCU values of motorised two-wheelers Fig. 12. Variation of PCU values of bicycles 7.2. Vehicular Interaction under Heterogeneous Traffic As a first step towards quantifying the vehicular interactions under heterogeneous traffic, speed-flow relationship for heterogeneous traffic flow was developed on 7.5 m wide road space by conducting simulation experiments taking the field observed traffic composition as the basis. The developed relationship is depicted in Fig. 13. The average stream speed for a traffic volume level was estimated by taking the weighted average speed of different vehicles obtained from the simulation output. It can be seen that, the developed speed-flow relationship under heterogeneous traffic follows the well established parabolic trend, indicating the validity of the model for simulating highly heterogeneous traffic flow. The capacity of 7.5 m wide road space under heterogeneous traffic, for the observed traffic composition, was estimated to be about 4150 vehicles per hour. Fig. 9. Variation of PCU values of light commercial vehicles Fig. 10. Variation of PCU values of motorised three-wheelers 142 ARASAN & KRISHNAMURTHY ON Fig. 13. Speed-flow relationship under heterogeneous traffic on 7.5 m wide road The PCU values for the different types of vehicles, at various volume levels, were estimated by taking the average stream speed as the measure of performance. Accordingly, the stream speed of the heterogeneous traffic for a chosen volume level was first determined by conducting simulation experiments with the specified traffic composition. Then certain percentage (50 per cent) of cars were replaced by the subject vehicle type in the mixed traffic stream, such that the average stream speed remained the same as before the introduction of the additional subject vehicles in the stream. This was achieved by varying the number of the subject 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 subject vehicles introduced will give the PCU value of that vehicle type. To account for the variation due to randomness, three random number seeds were used for 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, along with the variation of the traffic stream speed, over traffic volume, are shown in Figures 14 through 18. Fig. 15. Variation of PCU values of light commercial vehicles Fig. 16. Variation of PCU values of motorised three-wheelers Fig. 14. Variation of PCU values of buses Fig. 17. Variation of PCU values of motorised two-wheelers STUDY OF THE EFFECT OF TRAFFIC VOLUME TH COUNCIL MEETING ON PCU VALUE OF HIGHLIGHTS OF THE 178 AND ROAD WIDTH VEHICLES USING MICROSCOPIC SIMULATION 143 heterogeneous traffic conditions using the same set of axes, the traffic volume has been represented using volume-to-capacity ratio. Fig. 18. Variation of PCU values of bicycles It can be seen that the general trend of variation of the PCU values of vehicles over volume is the same as in the case of cars-only traffic. Hence, the explanation provided for the trend in the case of cars-only traffic is valid for heterogeneous traffic condition also, the only minor difference being the flattening of the curve at veryhigh-volume levels. This implies that the constrained condition of movement experienced by the vehicles at capacity-flow level in cars-only traffic is reached well before the capacity-flow level in the case of heterogeneous traffic. 7.3. Effect of Traffic Composition on PCU Values It is clear that the degree of heterogeneity of traffic stream affects the speed and other traffic flow parameters, and influences the magnitude of interaction between the moving vehicles significantly. The presence of a vehicle type, other than car, in the cars-only traffic stream, creates a traffic condition, which is totally different from the cars-only traffic condition. The change in the traffic condition make the vehicles to offer varying amount of impedance to the movement of adjacent vehicles in the traffic stream, depending upon the extent of variation of traffic stream from cars-only (homogeneous) traffic condition. In the light of the said fact, a comparison of the interactions of different vehicle types in cars-only traffic and in heterogeneous traffic, the amount of interaction having been measured in terms of PCU, will be useful. Figs.19 through 23 illustrate the comparison of PCU values of different vehicle type and their variations over traffic volume, in cars-only traffic and heterogeneous traffic flow conditions. It may be noted that, to facilitate plotting of the variation of PCU in homogeneous and Fig. 19. PCU values of buses on 7.5 m wide road Fig. 20. PCU values of light commercial vehicles on 7.5 m wide road Fig. 21. PCU values of motorised three-wheelers on 7.5 m wide road 144 ARASAN & KRISHNAMURTHY ON 7.4. Effect of Roadway Width on PCU Values As one of the objectives of this research work is to study the effect of roadway width on PCU values of vehicles, the PCU values of the different categories of vehicles were estimated, by simulating traffic flow on different widths of roads. For the purpose of this study heterogeneous traffic flow of a selected composition on three different widths of road, namely, 7.5 m, 11.0 m and 14.5 m (equivalent to the widths of 2,3 and 4 lane roadways of urban roads) was considered. The PCU values of the different types of vehicles were considered for a wide range of traffic-volume levels on the three roadways. Since the capacity of a roadway section varies with its width, the PCU values on these roads needs to be compared based on some common traffic flow criterion. For this purpose, volume-to-capacity ratio (v/c ratio) was selected as the traffic flow criterion common to different widths of roads. In order to make the above comparison, the PCU values of different vehicle types were estimated at the selected volume-to-capacity ratio levels. The plots relating the PCU values of a vehicle type and the selected volumeto-capacity ratios, made for the three roadway widths, on the same set of axes, are shown in Figs. 24 through 27. Fig. 22. PCU values of motorised two-wheelers on 7.5 m wide road Fig. 23. PCU values of bicycles on 7.5 m wide road It can be seen that, the magnitude of vehicular interactions measured in terms of (PCU), under cars-only traffic condition, are significantly higher for all the vehicle types, when compared to their corresponding values under heterogeneous traffic condition. Higher PCU values under cars-only traffic condition may be attributed to the higher speed difference between the cars and the subject vehicle speed in cars-only traffic than the difference between car speed and subject vehicle speed under heterogeneous traffic condition. For example, at volume-to-capacity ratio value of 0.75, under cars-only traffic condition, the average speed of cars is 53.94 km/h and buses is 48.36 km/h, with a speed difference of 5.58 km/h. Whereas under heterogeneous traffic condition, the average car speed for the same volumeto-capacity ratio is 30.95 km/h and the average bus speed is 28.40 km/h, resulting in a speed difference of 2.55 km/h. The PCU values of buses at this level of traffic flow under cars-only traffic and heterogeneous traffic conditions were 3.5 and 2.5 respectively. Fig. 24. Variation of PCU values of buses on 7.5 m, 11.0 m and 14.5 m wide roads Fig. 25. Variation of PCU values of light commercial vehicles on 7.5 m, 11.0 m and 14.5 m wide roads STUDY OF THE EFFECT OF TRAFFIC VOLUME TH COUNCIL MEETING ON PCU VALUE OF HIGHLIGHTS OF THE 178 AND ROAD WIDTH VEHICLES USING MICROSCOPIC SIMULATION 145 Fig. 26. Variation of PCU values of motorised threewheelers on 7.5 m, 11.0 m and 14.5 m wide roads Fig. 29. Speed-flow relationships for buses on 7.5 m, 11.0 m and 14.5 m wide roads Fig. 27. Variation of PCU values of motorised two wheelers on 7.5 m, 11.0 m and 14.5 m wide roads Fig. 30. Speed-flow relationships for light commercial vehicles on 7.5 m, 11.0 m and 14.5 m wide roads It is observed (Fig. 24 through 27) that the PCU value of a vehicle type, at a given volume-to-capacity level, increases with increase in width of roadway. There has been marginal increase in magnitude of PCU values on 14.5 m wide road when compared to the corresponding values on 11.0 m road. Similarly, there is marginal increase in the PCU values on 11.0 m wide road when compared with 7.5 m wide road spaces. 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 7.5 m, 11.0 m and 14.5 m wide roads as shown in Figs. 28 through 32. Fig. 31. Speed-flow relationships for motorised threewheelers on 7.5 m, 11.0 m and 14.5 m wide roads Fig. 28. Speed-flow relationships for cars on 7.5 m, 11.0 m and 14.5 m wide roads Fig. 32. Speed-flow relationships for motorised two-wheelers on 7.5 m, 11.0 m and 14.5 m wide roads 146 ARASAN & KRISHNAMURTHY ON TABLE 8. SPEEDS ON It can be found from the plots that in all the cases, for a given volume to capacity ratio, the speed of a vehicle type increases with increase in the width of road space. 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 relatively easier on wider roads facilitating faster movement of vehicles. As all the vehicles are able to move relatively faster on wider roads, the reason for higher PCU values on wider roads cannot be explained using the speed data shown in Figs. 29 through 34. The increase in width of roadway invariably provides relatively higher manouverability for all vehicle types on wider roads. The interaction between the vehicles is quantified in terms of PCU, which is the amount of impedance caused by a vehicle type in comparison with that of passenger cars as the reference vehicle. Comparing the change in performance of cars while increasing the width of roadway, with that of subject vehicle will be the appropriate way to investigate the PCU variation on different road widths. Hence, it was decided to calculate the percentage increase in speeds of all types of vehicles, with increase in road width, so that the increase in car speed can be compared with the increase in the speed of other vehicles. The comparison of speeds of different vehicles at selected volume-to-capacity levels between 7.5 m to 11.0 m and 11.0 m to 14.5 m wide road spaces are as shown in Tables 8 and 9 respectively. It can be seen from the tables 8 and 9 that at all the chosen volume-to-capacity ratio values, the percentage increase in speed of cars is higher than the percentage increase in speed of all the other categories of vehicles. The higher free speed, acceleration and other mechanical capabilities of cars facilitate cars to gain more speed with increase in the road width when compared to other vehicle categories. Hence, it is clear that the increase in speed difference between cars and other categories of vehicles with increase in width of road space, has resulted in increased PCU values with increase in the width of road space. 8. CHECK FOR ACCURACY OF PCU ESTIMATES 7.5 m AND 11.0 m WIDE ROAD SPACES Speed of the vehicle type (km/h) Vehicle Volume to type capacity ratio (1) (2) On 7.5 m wide road (3) On 11.0 m Percentage wide road increase in speed (4) (5) Cars Buses & Trucks LCV M.Th.W. M.T.W. 0.25 0.50 0.75 0.25 0.50 0.75 0.25 0.50 0.75 0.25 0.50 0.75 0.25 0.50 0.75 ON 53.20 41.60 30.95 46.50 36.90 28.40 45.90 38.00 29.00 42.80 38.00 31.50 45.20 41.20 34.60 11.0 m AND 56.95 47.50 35.70 49.40 42.00 31.50 48.60 42.40 32.50 43.50 42.00 35.50 45.80 44.00 38.50 7.0 14.2 15.3 6.2 13.8 10.9 5.9 11.6 12.1 1.6 10.5 12.7 1.3 6.8 11.3 TABLE 9. SPEEDS 14.5 m WIDE ROAD SPACES Speed of the vehicle type (km/h) Vehicle Volume to On 11.0 m type capacity wide road ratio (1) (2) (3) On 14.5 m Percentage wide road increase in speed (4) (5) Cars 0.25 0.50 0.75 56.95 47.50 35.70 49.40 42.00 31.50 48.60 42.40 32.50 43.50 42.00 35.50 45.80 44.00 38.50 64.90 54.00 37.70 56.00 46.20 33.10 54.00 47.00 34.00 46.40 44.50 36.60 51.50 49.25 40.45 14.0 13.7 5.6 13.4 10. 5.1 11.1 10.8 4.6 6.7 6.0 3.1 12.4 11.9 5.1 Buses & Trucks LCV 0.25 0.50 0.75 0.25 0.50 0.75 M.Th.W. 0.25 0.50 0.75 M.T.W. 0.25 0.50 0.75 The check for the accuracy of the PCU estimates was done by simulating homogeneous (cars-only) traffic STUDY OF THE EFFECT OF TRAFFIC VOLUME TH COUNCIL MEETING ON PCU VALUE OF HIGHLIGHTS OF THE 178 AND ROAD WIDTH VEHICLES USING MICROSCOPIC SIMULATION and the heterogeneous traffic flows on the same road space. For this purpose, first, the cars-only traffic flow was simulated on 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 7.5 m wide road, under the heterogeneous traffic condition is 4150 vehicles per hour. Knowing 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 4150 vehicles per hour. The PCU values of the different vehicle categories, at capacity-flow condition were obtained from Figures 24 through 28. 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 PCU per hour of the heterogeneous traffic, for the selected set of volume-capacity ratios were estimated. Then, plots, relating the set of volume to capacity ratios and the corresponding flow were made for cars-only and the heterogeneous traffic as shown in Fig. 33. 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, paired t test was performed by relating the flow in number of cars TABLE 10. STATISTICAL TEST FOR 147 Fig. 33. Traffic volumes in PCU on 7.5 m road space per hour for the selected set of volume-to-capacity ratios and the corresponding heterogeneous traffic flows expressed in PCU per hour. The details of t test conducted for 7.5 m wide road space is shown in Table 10. dmean = Mean of observed difference = 140 / 9 = 15.56 t statistic of observed speeds, to = dmean /(sd /√k), where k = Number of data sets = 9 sd2 = 481934.4/ (k-1) = 481934.4/8 = 60241.78, where sd is the standard deviation; sd = 245.44 Therefore, |to| = 15.56 / (245.44 / √9) =0.20 The critical value of t statistic for 0.05 level of significance and 9 degrees of freedom, obtained from ON PCU VALUES 7.5 m WIDE ROAD SPACE V/C Ratio Volume in PCU Homogeneous Heterogeneous traffic Traffic (2) 382 765 1147 1529 1912 2294 2676 3059 3250 (3) 369 766 1233 1845 2028 2357 2596 2778 2802 ∑= Difference Deviation from mean difference (5) -2.6 -16.6 -101.6 -431.6 -131.6 -78.6 64.4 265.4 432.4 - (1) 0.118 0.235 0.353 0.471 0.588 0.706 0.824 0.941 1.000 (4) 13 -1 -86 -416 -116 -63 80 281 448 140 Square of Deviation from mean difference (6) 6.9 276.7 10,329.4 186,307.8 17,327.5 6183.3 4143.0 704,19.2 186,940.4 481,934.3 148 ARASAN & KRISHNAMURTHY ON 5. The check performed to ascertain the accuracy of the PCU estimates by comparing the flow of carsonly and the PCU equivalent of heterogeneous traffic on 7.5 m, 11.0 m, and 14.5 m wide road spaces indicate that, the estimates are fairly accurate. 6. Thus, for the traffic condition considered for this study, there is reason to treat PCU value of a vehicle type as a dynamic quantity rather than treating it as a constant. REFERENCES standard t-distribution Table, is 2.26. Thus, it can be seen that the value of t statistic calculated based on the observed data (t0) is less than the corresponding table value. Based on the closeness of the plots made for homogeneous and heterogeneous traffic volumes at selected volume to capacity ratios, and based on the statistical test, it may be concluded that the estimated PCU values are accurate. The results of similar exercises done for 11.0 m and 14.5 m wide road spaces indicate that, in these cases too, the respective plots match with each other. To check for the statistical significance in this regard, paired t tests were conducted. The calculated values of t (t0) are 1.42 and 1.01 against the table values of 2.13 and 2.18 respectively for 11.0 m and 14.5 m wide road spaces indicating that there are no significant differences in the volumes of cars-only and heterogeneous traffic, measured in PCU, at the selected volume to capacity ratios, in both the cases. 9. CONCLUSIONS 1. Ahmed Al.Kaishy, Younghan Jung and Hesham Rakha. (2005), “Developing Passenger Car Equivalency Factors for Heavy Vehicles during Congestion”. Journal of Transportation Engineering, ASCE, Vol. 131, No. 7, pp. 514-523. 2. Arasan, V.T. andy Koshy, R. (2004), “Simulation of Heterogeneous Traffic to Derive Capacity and Service Volume Standards for Urban Roads.” Journal of Indian Roads Congress, Vol. 65-2, pp. 219-242. 3. Arasan, V.T. and Koshy, R. (2005), “Methodology for Modeling Highly Heterogeneous Traffic Flow”. 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