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1 0 0 0 NOVEL AREA OCCUPANCY BASED METHODOLOGY FOR PCU ESTIMATION ON MULTILANE URBAN ROADS UNDER HETEROGENEOUS TRAFFIC SCENARIO Raunak Mishra Former Post Graduate Student Department of Civil Engineering, Birla Institute of Technology and Science Pilani, Pilani, Rajasthan, India 0. id: raunakmishr@gmail.com Pallav Kumar Research Scholar Transportation Engineering and Planning Section, Civil Engineering Department, Sardar Vallabhbhai National Institute of Technology (SVNIT), Surat, Gujrat-00 id: pallav@gmail.com Shriniwas S. Arkatkar* Assistant Professor, Transportation Engineering and Planning Section, Civil Engineering Department, SVNIT-Surat, Gujrat-00 id: sarkatkar@gmail.com Ashoke Kumar Sarkar Senior Professor & Director, Department of Civil Engineering, Birla Institute of Technology and Science Pilani, Pilani, Rajasthan, India 0. id: aksarkar@pilani.bits-pilani.ac.in Word count: words text + tables/figures x 0 words (each) = words Submission Date: th November 0

2 Mishra, Kumar, Arkatkar, Sarkar ABSTRACT This research is aimed at developing an area-occupancy based methodology for estimation of PCU values for different category of vehicles under heterogeneous traffic conditions on multilane urban roads for a wide range of traffic flow levels. As a first step, PCU values of different vehicle categories are determined based on Transport and Road Research Laboratory (TRRL) definition, replacing commonly considered measure of performance speed with area-occupancy using simulation. The values of PCU obtained were found to be significantly different for different V/C ratios, which shows PCU is dynamic in nature. While dynamic nature of PCU values is well appreciated, practitioners may prefer single set of optimized PCU values (unique for each of the vehicle categories), keeping in view the ease of its application in real-world projects. Hence, a new methodology using matrix solution is proposed in this study, to estimate the optimized or unique set of PCU values using area occupancy as performance measure. This method is devised based on real-traffic data comprising of two traffic streams (cars-only as well as heterogeneous traffic conditions) at different flow levels and wide variation traffic composition. Further, to check the credibility of the proposed method, PCU values from existing guidelines regulated by India Roads Congress (IRC) were compared with the estimated values. In addition to this, PCU values were also compared with values estimated using widely-accepted dynamic PCU concept of speed-area ratio. The comparison of converted equivalent traffic flows (PCU/h) obtained using PCU values estimated using different methods (dynamic PCU values by area-occupancy and speed-area ratio and IRC-0 values) with cars-only traffic flow levels (obtained from validated simulation model expressed as passenger-cars/h) is made for same V/C ratios. The results show that the PCU values suggested by IRC and dynamic PCU concept using speed-area ratio, underestimates and overestimates the flows, respectively at different traffic volumes. However, the values obtained using area occupancy concept is found to be consistent with the traffic flow in cars-only traffic situation at different flow conditions. The derived set of optimized PCU values proposed in this study can be useful for traffic engineers, researchers and practitioners for capacity and level of service analysis under heterogeneous traffic conditions. Keywords: Traffic flow, Passenger Car Unit, Area Occupancy

3 Mishra, Kumar, Arkatkar, Sarkar INTRODUCTION Passenger Car Unit (PCU) has a crucial role in roadway infrastructure planning and its efficiency evaluation. It is used as a conversion factor to convert different sets of vehicles of mix traffic flow into hypothetical equivalent homogenous flow. In mixed-traffic stream, as that of prevailing in developing countries, vehicles of different dimensions and operational capabilities compete for the same road space without any set rules, such as lane discipline. Generally, car is considered as a standard vehicle category having better mechanical as well as operational properties in the traffic stream. Therefore, it is a usual practice to use car as a reference vehicle to convert mix traffic stream (vehicles/h) into homogenous equivalent traffic stream (PCU/h). The factor used for conversion is known as PCU. The concept of PCU was first introduced in Highway Capacity Manual. Thereafter, the accurate estimation of PCU value to quantify the impedance of different vehicle types to reference vehicle (cars) has always been an area of interest for researchers. However, the complexity increases with increase in the degree of heterogeneity in traffic stream. The Indian Road Congress (IRC) suggests the static set of PCU values in IRC: 0 (0) and IRC: (0) respectively for urban and rural highways in India based on limited empirical studies. Historically, the basis for estimation of PCU values is varied in different studies. PCU values were estimated based on density (Huber), delay (Cunagin et al.), headway (Krammes and Crowley), V/C ratio (Fan), average speed (Elefteriadou et al.), queue discharge flow (Al-Kaisy et al.) (-) in various studies. However, most of these studies limited towards the PCU estimation of only heavy vehicles in fairly homogenous conditions. Krammes and Crowley () suggested that the basis for estimation of PCU values should be same as that used to define level of service. The traffic density has been considered as an important parameter for defining the Level of Service on multi-lane highways. Therefore, in HCM (000), traffic density was considered to compute PCU values for freeways. However, under heterogeneous traffic conditions prevailing in India, density does not always reflect the concentration of traffic as vehicles of different dimensions use the highway. Moreover, lane discipline is poor in India and many times two small vehicles such as auto-rickshaw and two-wheeler might occupy the same lane. Also, the vehicles might travel without adequate lateral clearances side-by-side without strictly following the lanes. At many places, lane markings are not maintained properly and thus, the vehicles move without any discipline. In such a situation, the determination of lane-wise capacity may not be appropriate and also while studying the traffic flow characteristics, density may not be the true indicator of occupancy. In this view, the studies conducted by Chari and Badarinath (), Khan and Maini () suggested that the measure of concentration for heterogeneous traffic should consider the vehicle area and easy to measure on field. The concept of Area-occupancy of vehicles proposed by Mallikarjuna and Rao (), could be a more appropriate parameter, as it considers the horizontal projected area of the vehicle without any restriction on trap length and width of road (Arasan and Dhivya) (0). Arasan and Dhivya (0, ) validated the logical correctness of the area-occupancy concept by comparing area occupancy with the flow and speed under homogeneous traffic condition using simulation. Area occupancy was found to accurately determine the road space usage by vehicles and it gives consistent values, even if there is a change in traffic composition and roadway conditions. Also, from the simulated model, the authors observed that the measure of area occupancy could satisfactorily explain the concentration of homogeneous traffic flow. The relationships of area occupancy with speed and flow using simulated model, they arrived at similar trends, indicating that the concept is appropriate enough as an alternate to density measurement for heterogeneous traffic. Over the last three decades some noteworthy works carried out for the estimation of PCU values under

4 Mishra, Kumar, Arkatkar, Sarkar mix flow condition. Justo and Tuladhar () carried empirical studies under mix traffic flow and developed the mathematical model to derive PCU values. Ramanayya () modelled the traffic flow on urban roads of India by using Equivalent Design vehicle and shown that PCU values are not constant due to heterogeneous traffic condition. Chandra and Sikdar () developed a concept and proposed a mathematical equation () to estimate dynamic PCU values based on physical size of vehicle and speed. Later Chandra and Kumar () also studied the effect of roadway width on two lane road on PCU values and found that PCU value increases linearly with increase in width of carriageway. PCUi = () Where, PCUi = Equivalent Passenger Car unit of vehicle i, Vc = average speed of car in traffic stream km/h, Vi = average speed of vehicle i in traffic stream km/h, Ac = projected rectangular plan area of car (m ), Ai = projected rectangular plan area of vehicle i (m ). LITERATURE REVIEW Shedding light on the use of micro-simulation technique, it serves as a worthy tool for studying various real world traffic problems, which are difficult to study on field. In India, due to heterogeneous traffic conditions the automated vehicle detection technologies such as loop detectors are not yet much successful. The traffic data needed to explore the various aspects of traffic flow is difficult to collect and extract. In this context, micro-simulation technique proves as an effective tool to investigate various traffic conditions. Many researchers had used micro simulation model such as HETEROSIM, Cellular Automata and VISSIM for mix traffic conditions successfully (Arasan and Koshy, Lan and Chang, Mehar et al.) (-). The HETEROSIM simulation model (Arasan and Krishnamurthy, Arasan and Arkatkar,) (-0) was used to estimate the PCU value variation with traffic volume, composition and roadway width. These studies used average speed as an equivalence criterion for estimation of PCU values and concluded that the PCU values varies with traffic volume and roadway width. Bains et al. () used the simulation technique to model the traffic flow on Indian expressways and estimated the capacity of six-lane divided expressway. Puvvala et al. () used VISSIM for developing the fundamental traffic flow relationships for Delhi-Gurgaon eight-lane divided urban multi-lane road and determined the capacity in terms of vehicles per hour. Sharma et al. () used microsimulation for capacity estimation of multi-lane divided highways in India. Mehar et al. () performed micro-simulation study in VISSIM and suggested PCU value for different vehicles at different LOS and for different traffic compositions on four-lane and six-lane divided highways. Most of the studies, used the mathematical formulation (equation-) proposed by Chandra and Sikdar () to derive PCU values. The review of past studies, has led to the following observations related to the estimation of PCU values. There is considerable variation in PCU values estimated by various researchers, because of using different equivalency criteria, varying roadway and traffic conditions considered for the study and the uncertainties associated with mixed traffic and its characteristics. PCU values provided by code of practice in India (IRC 0:0) provide static set of PCU values for urban roads in India. However, it would be unfair to use these values in the field without conducting any analysis based on field data. Moreover, Chandra and Sikdar () proposed dynamic PCU concept of Speed-Area ratio, for heterogeneous traffic for varying roadway and traffic condition. Although, the method is widely accepted for PCU estimation in India, but difficulty lies in the calculation of PCU for every time-interval under consideration.

5 Mishra, Kumar, Arkatkar, Sarkar Moreover, data collection and extraction is added difficulty for this methodology. Also, the area ratio used (Ac/Ai) in equation- is a ratio of physical area of vehicles under consideration and not influencing areas. Hence, dynamically, what proportion of road (area) is not well-captured by the approach proposed by Speed-Area ratio method. The formulation to establish PCU for a vehicle type on a particular roadway should necessarily be based on the variables that reflect the combination of factors contributing to the overall influence of the type of vehicle on the quality of service provided by the roadway. Hence, change in area-occupancy of a given traffic stream by the addition of a specified number of vehicles of a particular type in replacement of the reference vehicle category (passenger-cars) can be considered as a satisfactory basis for estimating PCU value. It may be also noted that in the past, computer simulation models were advantageously used to estimate the PCU values of various categories of vehicles under varying heterogeneous road traffic environment. In the light of above, this study is focused on, first, demonstrating the appropriateness of area occupancy to be used as a measure of traffic concentration for different roadway and traffic conditions. For this purpose, empirical and micro-simulation techniques were used. Then, using area-occupancy as measure of equivalence criteria for PCU estimation, the impedance of different vehicle types on reference vehicle (car) was quantified for different traffic volumes using micro-simulation. The objective of this study is to propose set of PCU values for different vehicle categories on multi-lane urban roads in India using area occupancy as measure. The motivation behind using area-occupancy as measure is its consistency with variation in roadway and traffic composition. Further, study also suggests a methodology for finding optimized PCU values of different vehicle categories in the traffic stream applicable to different flow conditions solving area-occupancy based simultaneous equations using matrix solution. The obtained set of PCU values of different vehicle categories in this study are suggested for eight-lane and six-lane multi-lane divided urban roads. The study also examines the accuracy of optimized PCU values over different range of flow. It also compares the effectiveness of optimized PCU values by comparing with dynamic PCU concept. Simulation logic of VISSIM-.0 can reasonably take care of the dimensions of the vehicles, their free speeds, acceleration characteristics, space gap requirements (both in lateral as well as longitudinal directions) in a traffic stream, etc. on multilane urban roads. Therefore, it was decided to use VISSIM, as it facilitates representation of all the relevant characteristics of heterogeneous traffic and permits the variation of all the parameters over a wider range than what might have been possible with field observed data. RESEARCH FRAMEWORK The methodological path adopted in this paper for estimation of PCU values using areaoccupancy measure is illustrated in Figure. First step starts with selection of study sections. Two study sections are selected for study purpose in this study: Delhi-Gurgaon Expressway and GAN Marg, Delhi. Second step is to analyse traffic-flow parameters such as: traffic flow, speed characteristics, lateral and longitudinal gap, area-occupancy, etc. Third step is to develop simulation model for the study section on Delhi-Gurgaon expressway. Delhi-Gurgaon Expressway is popularly known as Expressway. But, in reality it operates as multilane urban road with higher speed limit (0 km/h). Significant proportion of motorised-two wheelers and motorised three wheelers are observed on this road. It is provided with fly-overs at locations with junctions, thereby allowing main traffic to maintain higher speeds. Several sub-steps involved in model calibration and validation are shown in Figure. Further, step-four develops relationship of area occupancy with macroscopic traffic parameters such as speed and flow, for both the study sections using observed data and also using simulation model for Delhi-Guragon Expressway. In

6 Mishra, Kumar, Arkatkar, Sarkar FIGURE Research framework for estimation of PCU value using Area Occupancy (AO) as performance measure. step five, area occupancy is used as measure for PCU estimation for Delhi-Gurgaon Expressway. For that purpose, PCU definition by Transport and Road Research Laboratory (TRRL), London, UK is as follows: on any particular section of road under particular traffic conditions, the

7 Mishra, Kumar, Arkatkar, Sarkar 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, for different types of vehicles, as one of the method in this study. Hence, the PCU values for the different types of vehicles, at various flow levels, were estimated by taking the area occupancy as the measure of performance instead of average stream speed using simulation model. Also, a new methodology for PCU estimation is proposed in this study, which is based on matrix solution of simultaneous equation developed for all-cars traffic stream and mixed traffic stream using area occupancy. Further, accuracy of PCU values proposed in this study is checked with dynamic PCU values (Chandra and Sikdar (000)) () and static PCU values of IRC-0 () for urban roads. The accuracy check of these PCU values are done by converting mixed traffic flow into PCU/hour and then validating the flow values obtained in terms of PCU/hour with all-cars traffic obtained using simulation model at different volume-tocapacity ratios. The accuracy of these PCU values is reported as conclusion of this study at last. AREA OCCUPANCY Mallikarjuna and Rao () proposed the measure of area occupancy to represent concentration of traffic under heterogeneous traffic in India. It is expressed as the proportion of time the set of observed vehicles occupy the chosen stretch of a roadway within time interval under consideration. Mathematically, it can be expressed as shown: AREA OCCUPANCY = () Where, ti = time during which a stretch of a roadway is occupied by vehicle i in sec (occupancy time); ai = area of the road space occupied by vehicle i during time ti in m ; A = area of the detection zone in m and T = total observation period in sec Referring Figure, consider a road stretch segment of length, L and width, W. R and R are the two reference lines. As a vehicle of area A approaches the first reference line, the time taken by vehicle to cross its own length from the first reference line is t. The instant, rear bumper leaves the first reference line to instant front bumper touches the second reference line is t and the time taken to cross its own length from the second reference line is t. Thus the time occupied will be summation of t, t and t. The actual time for which the vehicle area presents in detection zone is t. For time t and t, the vehicle is partially occupied and thus summation of t, t and t overestimates the occupied time. Assuming the speed of the vehicle remains same while passing detection zone, twill be equal to t. If the time interval, ti is considered as the elapsed time from the instant front/rear end of vehicle crosses the first reference line it crosses the second reference line the problem of overestimation of occupancy can be avoided (0).

8 Mishra, Kumar, Arkatkar, Sarkar (a) Vehicle touches the first reference line (b) Time taken by vehicle to cross its length from first reference line (c) Actual time for which the vehicle area (d) Time taken by vehicle to cross its present in the detection zone length from second reference line FIGURE Schematic pictorial representation of the principle involved in measurement of area-occupancy under heterogeneous traffic conditions. DATA COLLECTION AND EXTRACTION Data collection was done at two locations (i) Delhi Gurgaon expressway, which is an eight-lane divided road having m wide road space in each direction of traffic flow and (ii) Gamel Abdel Nasser (G.A.N) Marg near IIT Delhi, which is a combination of six-lane and eight-lane divided roadway, having effective road width of. m per direction, as shown in (Figure a). The digital video camera was mounted over the foot over bridge (FOB) at a vantage point for capturing the traffic flow movement with adequate visibility. Although, the videography method to study traffic flow is tedious and time consuming, every micro-level data can be extracted using this technique. The video graphic data was captured for the morning as well as afternoon hours in both the locations. The aforesaid road segments were so chosen for study such that the uninterrupted flow conditions were assured. The observed traffic flow is found to be varying between 00 to 00 vehicles/h for Delhi-Gurgaon expressway, whereas 00 to 00 vehicles/h for GAN Marg. The data extraction was done manually by converting video into images of frames per second to obtain accuracy of time up to 0.0 seconds. The trap length of m and. m was marked on the computer screen for Delhi Gurgaon expressway and GAN Marg, respectively. The occupancy time of each vehicle in the detection zone considering all lanes together in one direction was measured, from the instant the front bumper touches the first reference line to the instant it touches the second reference line. Thus, the entry and exit frame number of each vehicle was noted and occupancy time was calculated. Then, the area occupancy and weighted mean stream speed were calculated using equation () and () using measured occupancy time for every one-minute time interval and expressed on an hourly basis. In heterogeneous traffic stream, vehicles of different dimension and characteristics uses the same road space, therefore weighted space mean speed was used to represent the heterogeneous traffic stream speed given by equation (). The observed weighted mean speed for Delhi Gurgaon expressway and GAN Marg is about. km/h and. km/h, respectively. The classified traffic flow count

9 Mishra, Kumar, Arkatkar, Sarkar consisting of various vehicle categories such as car, bus, truck, motorised two wheeler, motorised three-wheeler and Light Commercial Vehicles (LCV) was also done. The traffic composition observed from the traffic flow data on Delhi Gurgaon expressway and GAN Marg are presented in (Figure b). Vm = () where, k = Total number of vehicle categories present in traffic stream Ni = Number of vehicles of category i Vi = Speed of vehicle of category i in (km/h) Vm = Weighted mean speed in (km/h) 0 (a) 0 (b) FIGURE (a) Snapshot of Delhi Gurgaon Expressway and Gamel Abdel Nasser (G.A.N.) Marg near IIT Delhi location; (b) Traffic composition of Delhi Gurgaon Expressway and GAN Marg. SIMULATION MODEL DEVELOPMENT The main purpose of micro-simulation model development is to study the various aspects of realworld traffic conditions. In the subsequent paragraphs, the efforts made to tackle the issues of calibration and validation is discussed. Out of the two study sections, simulation model is developed only for Delhi-Gurgaon Expressways to study PCU values using area occupancy as measure. Next subsection, presents the calibration and validation of simulation model on Delhi- Guragon Expressway.

10 Mishra, Kumar, Arkatkar, Sarkar Calibration and Validation The iterative procedure involved in simulation modelling to replicate the actual field condition is calibration. It is a key task in modelling micro-simulation traffic models. The various parameters like roadway geometry, traffic volume and composition, observed speed distribution of various vehicle categories, desired acceleration parameters and minimum lateral distance maintained by vehicles were entered as an input. Initially, some trial simulation runs were made using the default values, however, the model was unable to replicate local traffic conditions. In order to minimize the error between simulated and empirical data various parameters were modified. The cumulative speed distributions of various vehicle categories obtained from field data were decoded in VISSIM. The spread ratio (S.R.) calculated using equation () and shown in (Table a), indicates the speed is approximately normally distributed as SR is within range of 0. and. (Dey et al.) (). SR = () where V, V0 and V are th, 0 th and th percentile speeds respectively. Further, a different kind of driving behaviour was used to reproduce the heterogeneous traffic condition. The entire road width based simulation where, there was only one lane having an effective width of four lanes was considered in the simulation. Thus, each vehicle was free to choose any lateral position and overtake from any side during the simulation on this four-lane width without any lane-discipline, similar to observed site conditions. The input data pertaining to vehicular (category-wise) dimensions, physical areas, minimum to maximum lateral clearance share along with dynamic characteristics such as acceleration rates over different speed ranges were given as input to the model. Observed traffic flow values and traffic composition was also given as input. Subsequently, to measure the travel time of each vehicle in detector zone, traffic detector at specific location similar to trap length of site condition, were placed. The estimated output of the simulation model was occupancy time of each vehicle in detection zone and the classified traffic volume count per hour. Also, the weighted space mean speed was calculated using the estimated simulation outputs. All the simulations were run for a total time of 00 seconds, including a buffer time of 00 seconds, each at the start and end of a simulation run to ensure precise results. The estimated values and the observed values were then compared and the error was computed as presented in (Table c). For checking the statically validity of model, a two tail t-test was done giving significance value of 0. which was found to be greater than the p value 0.0, hence null hypothesis was accepted that the simulated data and field data do not differ. Further, the mean absolute percentage error (MAPE) for the simulated and observed data is presented in (Table c) and calculated by using equation (). Since the MAPE error for both speed and flow was less than 0 %, it was accepted that the simulation model significantly able to reproduce local conditions and traffic behaviour. MAPE = 00 () where = observed value of measure; = predicted value of measure and N = number of observations. The speed-flow relationship for mixed-traffic flow was developed after processing of traffic data collected from specific observation sections and simulated outputs as depicted in (Figure ). From (Figure ), it can be inferred that the simulated data follows the well-known

11 Mishra, Kumar, Arkatkar, Sarkar parabolic trend between speed and flow, indicating the validity of simulation model. It is noteworthy to mention that, at both locations the empirical data did not exceed to the congested oversaturated condition, hence, the study explores the traffic phenomenon under capacity only. 0 FIGURE Speed-flow relationship of Delhi Gurgaon Expressway. TABLE (a) Speed Statistics in km/h of Different Vehicle Types at Selected Study Stretches Vehicle Category Location Samples Mean S.D Max Speed V V 0 V SR Car GAN Marg Delhi Gurgaon Truck GAN Marg Delhi Gurgaon Bus GAN Marg Delhi Gurgaon Two wheeler GAN Marg Delhi Gurgaon Three wheeler GAN Marg Delhi Gurgaon LCV GAN Marg Delhi Gurgaon

12 Mishra, Kumar, Arkatkar, Sarkar 0 0 TABLE (b) Vehicular characteristics as input to simulation model Vehicle Category Average Dimensions (m) Projected Rectangular Area (m ) Minimum Lateral Distance Standing at 0 km/h (m) Minimum Lateral Distance Driving at 0 km/h (m) Acceleration value of various Speed Ranges (m/s ) km/h km/h Car Truck Bus Two wheelers Three wheeler LCV TABLE (c) Comparison of Simulated and Observed Traffic Volume and Speed Mean Absolute Percentage Error (MAPE) Vehicle category Traffic Volume (Vehicles/h) Speed (km/h) MAPE % Simulated Observed Simulated Observed Speed Volume Car Truck Bus Two-wheeler Three-wheeler....0 LCV...0. Above 0km/h RELATIONSHIP OF AREA OCCUPANCY WITH TRAFFIC FLOW PARAMETERS In order to further investigate the relationship of AO with traffic flow parameters, the developed micro-simulation model was used to analyse the traffic flow condition of Delhi Gurgaon expressway along with empirical studies carried out on both study sections. To incorporate randomness in the simulation model, three simulation runs were done with different seed values. Corresponding to each input volume, area occupancy was calculated and relationship of area occupancy with weighted mean speed and volume for Delhi Gurgaon expressways is presented in (Figure ). Also, using the collected field data the relationship between weighted mean speed and volume with area occupancy for GAN Marg was obtained and depicted in (Figure ). From the (Figure ), it can be inferred that, with increase in area occupancy the speed of traffic stream decreases whereas, traffic flow increases with increase in area occupancy. Hence, the trends obtained are logical and similar to the theoretical trends of fundamental relations of speed and traffic volume with density. Further, it can be noted that the traffic characteristics of both the study stretches are quite different on the basis of their traffic composition and speed characteristics, nevertheless, similar trends of area occupancy with flow parameters obtained at both the locations. Hence, it can be seen that area occupancy as a performance measure is good enough to represent concentration of traffic, which is also easy to measure on field rather than traffic density. In the next section, area occupancy as performance measure was investigated for estimation of PCU values under varying mixed-flow conditions. For this purpose, both

13 Mishra, Kumar, Arkatkar, Sarkar simulation technique as well as empirical studies were conducted over wide range of traffic flow conditions, prevailing on Delhi Gurgaon expressway. (a) 0 0 (b) FIGURE (a) Speed-area-occupancy (b) Flow-area- occupancy plots at Delhi-Gurgaon expressway and GAN marg under heterogeneous conditions ESTIMATION OF PCU VALUES USING AREA OCCUPANCY AS MEASURE Methodology based on definition For accomplishing main objective of this research, various scenarios were explored in the simulation model to estimate PCU values using Delhi-Gurgaon roadway and traffic conditions, as example. The definition of PCU by Transport and Road Research Laboratory (TRRL) (), London, UK was considered for estimation of PCU values and given as: 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. A slight modification to this definition i.e. in place of equal average speed, equal area occupancy was considered as the basis of estimation of PCU in this study.

14 Mishra, Kumar, Arkatkar, Sarkar Corresponding to nine different V/C ratios, three simulation runs with different seed values were run and the average value of area occupancy was calculated. The impedance caused by the subject vehicles to reference vehicle (car) was quantified by removing the certain percentage of cars (0%) and adding certain percentage of subject vehicle in the mix traffic stream, such that, the area occupancy remains same as before the introduction of additional subject vehicles. This was achieved by the trial-and-error process by varying the number of subject vehicles corresponding to a certain V/C ratio. In simulation output, the numbers of subject vehicles added were obtained. Thus, for each volume the number of cars removed divided by the number of subject vehicle added gives the PCU value of that subject vehicle. PCU Value of subject vehicle type = A quick examination of PCU variation over selected flow levels (Figure ), reveals two important trends. At lower volume levels, the PCU values of subject vehicles having dimension greater than car, increases with increase in traffic volume. After certain volume, the PCU values for the same, decreases with increase in traffic volume. The reason for the trend could be explained as: the heavier the subject vehicle, the lesser is its manoeuvrability, the greater its impedance to other vehicles and thus greater is its PCU. At lower volume level, under heterogeneous traffic conditions, reference vehicle (cars) can easily manoeuvre through the available road space by occupying any lateral position for easy overtake operations. As the traffic volume increases, the addition of an extra subject vehicle in traffic stream produces significant impedance to cars. However, the trend declines after a certain volume level. At higher volume levels, under heterogeneous traffic conditions, the freedom of movement/manoeuvre of cars decreases attributing to lesser space headways, desired speed and significant role of acceleration-deceleration cycle. Hence, the relative difference between the aforementioned attributes decreases with increase in volume between the car and subject vehicle. Thus low PCU values obtained as the traffic flow reached to constraint condition. Conversely, for the subject vehicles having dimensions lesser than car such as motorized two and three-wheelers, the PCU values first decreases and then increases marginally at higher volume levels. This can be explained as: At lower volume, due to smaller size, easy manoeuvrability, quick acceleration and high speed potential of these vehicles, not causes the significant impact to cars. However, at higher volumes, these small vehicles can easily weave through the available gaps in the traffic stream. While weaving through the gaps, these vehicles contribute to significant psychological and practical impact on nearby car drivers, thereby creating some impedance. Thus, the PCU value increases marginally as traffic flow increases and reaches to constraint conditions. A quite interesting trend can be observed in case of heavy vehicle classes of trucks and buses (Figure ). At low volume, the initial PCU value for buses was higher than the PCU value of trucks. This is due to the larger rectangular area of buses considered in this study. After certain volume at same V/C ratio the PCU value of buses decreases earlier compared to trucks. Also, the PCU values of buses are reported lower than the trucks. This is because of better operation capabilities of buses in terms of manoeuvrability and role of acceleration- deceleration cycles. Also, during empirical study it was observed that the desired speed maintained by buses as shown in (Table a) were quite high compared to trucks. Thus, the above observations reinforce and justify the appropriateness of area-occupancy measure to quantify the impendence caused by other vehicle classes to cars by accounting effect of both physical dimension as well as operational capabilities of vehicles, at different flow levels.

15 Mishra, Kumar, Arkatkar, Sarkar 0 0 FIGURE PCU variations of different classes of vehicle at different traffic volume levels. The current standards of practice like Indian Roads Congress (0) () and manuals like Highway Capacity Manual (00) in USA () and Indonesian Highway Capacity Manual () suggests static PCU values to be used on a given facility for entire traffic volume ranges under prevailing roadway and traffic condition. PCU values provided by code of practice in India (IRC 0:0) (), provides static PCU values for urban roads in India. However, it would be unfair to use these values in the field without conducting any analysis based on real field traffic data. The advantage of providing optimized static PCU value may get more acceptability from practitioner point-of-view. With this motivation, further in the present study, a novel attempt was made to propose static but unique PCU values based on area-occupancy based simultaneous equations developed using real-traffic data. The subsequent section describes the methodology adopted for obtaining static PCU values using area occupancy as the measure of performance using empirical data. Proposed Matrix Methodology of PCU estimation using area occupancy as Measure Huber () suggested a methodology to estimate PCU/PCE values based on all-cars traffic stream and mixed traffic stream considering some measure of performance for equating flow for all cars traffic and mixed traffic stream. Same concept is used here for development of equations for PCU estimation. Under this methodology, a flow rate of base stream (containing all-cars traffic) and a flow rate of mixed stream, containing a proportion of cars, of light commercial vehicle, proportion of Bus, proportion of truck, of motorized twowheeler and of motorized three-wheeler, with the same performance measure (in this case area occupancy) can be equated as: ()

16 Mishra, Kumar, Arkatkar, Sarkar Where,,,,, are PCU values for light commercial vehicle, bus, truck, motorized two-wheeler, motorized three-wheeler respectively. The measure of performance used for the purpose of PCU estimation is Area Occupancy for equating the flow on both side of equation (). While doing so, the intervals with all-cars traffic were sorted from field observed data, thereby, area occupancies were calculated. The allcars traffic was obtained from different traffic flow levels. Based on these area occupancy values, the mixed traffic stream with same area occupancy was also sorted. This procedure was adopted for development of simultaneous equations. These equations were then solved using matrix solution. The matrix solution provides optimized values of PCU for different vehicle categories based on these equations are given in Column () of Table (a). Also, average PCU values obtained over different flow ranges based on TRRL definition using area occupancy is given in Column () of Table (a). Further, PCU values of different vehicle categories in Indian Roads Congress () guidelines are given in Column () of Table (a). These values are used for converting flow in terms of PCU/hour in Table (b) at different V/C ratios. ACCURACY CHECK FOR PCU In order to measure the accuracy of optimized static PCU values (which is most likely to be appreciated by practitioners), the comparison was made between the converted mixed-traffic flow, expressed in terms of PCU/h and cars-only traffic passenger-cars/h at same V/C ratios, obtained using simulation model. The obtained absolute percentage errors (APE) as shown in Table b, are less than %, for optimised PCU, indicating robustness of optimised PCU values. In continuance, the optimized static PCU values were also compared with PCU values obtained by micro-simulation. The dynamic PCU values obtained by micro-simulation model (using areaoccupancy) at different V/C ratios were averaged and represented as static PCU value for different vehicle categories. These values are further compared with static optimised PCU values of corresponding vehicle categories, obtained by empirical study using matrix method. A two-tail paired t-test was done at level of significance % and degrees of freedom, indicating t-statistic value as -., which is less than t critical. and p-value 0. (more than 0.0). Hence, null hypothesis was accepted that the PCU values obtained by empirical study (optimised) and microsimulation (average of dynamic PCU estimated using area-occupancy) do not differ significantly. Further, the optimized PCU values obtained by empirical study were compared with the static PCU value suggested by IRC and the dynamic PCU values obtained using well-accepted speed-area ratio method (). A two-tail paired t-test for a level of significance of 0.0 and eight degree of freedom was done between the homogenous cars-only traffic (cars/h) and the equivalent converted heterogeneous traffic (PCU/h), (as depicted in Table b). Table c, indicates The t-statistic, in case of traffic volume estimated from PCU obtained by areaoccupancy measure was., which was less than the t-critical.0. Hence null hypothesis was accepted that, there is no significant difference in the cars-only traffic and the traffic volume estimated from area occupancy measure in terms of PCU/h at selected V/C ratios. However, the null hypothesis was rejected in case of volume estimated from PCU values suggested by IRC () (t-statistic.0 greater than t-critical.0) and dynamic PCU by speed-area ratio method () (t-statistic. greater than t-critical.0), indicating that there is a significant difference between cars only traffic and heterogeneous traffic obtained in PCU/h. It may be noted, from Table b, that traffic volume obtained in PCU/h using PCU values suggested by IRC-0 and speed-area ratio method () invariably, underestimates and overestimates the traffic volume, respectively at different V/C ratios.

17 Mishra, Kumar, Arkatkar, Sarkar 0 The optimized PCU values indicated in (Table a) are then used for development of fundamental relationship for both the study sections, as depicted in Figure. From (Figure ), the capacity estimated for the Delhi Gurgaon Expressway section having.0m wide road space for observed traffic composition is 00 PCU/h and for GAN Marg having effective road width of.m for observed traffic composition is about 00 PCU/h. It can be noted that a reduction of. percent in capacity was obtained for GAN Marg, this is due to the difference in effective roadway width, free flow speed and presence of road side friction at GAN Marg site. TABLE (a) PCU values of vehicle categories for Delhi-Gurgaon Expressway section Vehicle Category (b) Comparison of PCU values obtained at varying traffic volumes for Delhi Gurgaon Expressway V/C Ratio PCU Values Optimized PCU (Observed Traffic-data) Average PCU (Micro- simulation) Cars () () () () Car Truck..0.0 Bus...0 Two Wheeler Three Wheeler...0 Light Commercial Vehicles (LCV) Volume in PCU APE (%) Homogenous Heterogeneous Traffic traffic Cars/h PCU/h Optimised (Area- Occupancy) PCU/h (IRC- 0) PCU/h (Speed-area ratio method) * AO IRC Speed- Area ratio *Chandra and Sikdar (000) () IRC

18 Mishra, Kumar, Arkatkar, Sarkar 0 00 Greenshields Model Field Data DG Expressway Field Data GAN Marg Greenshields Model Simulated Data DG Expressway Speed (km/h) (a) Volume (PCU/h) 0 FIGURE (a) Speed-flow plots; (b) Flow-area-occupancy plots for both study stretches. CONCLUSION The heterogeneous traffic conditions prevailing in India constitutes different vehicle classes which uses the same available road-space with added complexity of loose lane-discipline. Representing concentration of traffic as density or occupancy, which are lane-based parameters might not be appropriate under such conditions. Practically, measuring density is a difficult task particularly under non-lane based mixed-traffic conditions. To overcome this, the concept of area occupancy was reinvestigated for its appropriateness under varying traffic conditions, which was proposed earlier by Mallikarjuna and Rao () and (Arasan and Dhivya) (0). Consequently, the characteristics of area-occupancy on urban multilane roads are determined for varying flow levels. A well calibrated and validated micro-simulation model was developed using VISSIM

19 Mishra, Kumar, Arkatkar, Sarkar with a commanding objective of estimating PCU for different vehicle classes. For this purpose, different scenarios were generated in micro-simulation model for Delhi Gurgaon expressway study section. The trends obtained using the simulation model and field data, indicate consistency with theoretical trends of density of traffic with other flow parameters such as speed and flow. From the results, it can be concluded that, because of variation in available road-space and traffic composition between two study sections, the boundary conditions are significantly different. However, functional forms obtained for speed-area-occupancy and flow-area occupancy are realistically modelled, indicating validity of area-occupancy measure. Further, area occupancy is used as an equivalence criterion for estimation of PCU values. 0 The variation of PCU values with traffic volume under mixed-flow conditions was investigated and explained using simulation model (VISSIM). Hence, area-occupancy as a measure of PCU estimation was found to be suitable, incorporating well the effect of both vehicle size as well as its operational capabilities. Moreover, from practitioner s point-of-view, the new approach of solving area-occupancy based simultaneous equations using matrix method, is developed. The proposed set of optimized PCU values are recommended for different vehicle classes based on this method. The comparison of converted equivalent traffic volume (PCU/h) is done with traffic flow levels (V/C ratios) generated using simulation model for cars-only traffic scenario. The conversion carried out using optimised PCU values only could qualify paired t-test. While comparing performance of different candidate methods for PCU estimation on uninterrupted 0 facility, it is systematically established that area-occupancy based matrix method is found to be performing well at all V/C ratios. Whereas, the constant PCU values suggested by IRC and dynamic PCU values by speed-area ratio method unvaryingly found to be underestimating and overestimating the traffic volume at corresponding V/C ratios. The present approach of using area-occupancy as measure for estimating PCU values can also be valid for traffic conditions in Asia-Pacific developing countries, having similar nature of traffic. This may be pertinent for traffic conditions prevailing in developed countries like USA, as well. However, keeping in view lane-based traffic conditions in USA, area-occupancy measure can be replaced with time occupancy as a measure of PCU estimation. 0 SCOPE AND LIMITATIONS The future scope of this work will be application of area occupancy concept for varying multilane roadway (based on varying geometry and function) and traffic condition. Moreover, the concept of area occupancy can also be explored for its effectiveness in establishing Level of Service (LOS) thresholds for multilane-roads. The limitation associated with the concept is that it requires the travel time of each and every vehicle in the traffic stream in a given time-interval. Its calculation using automated instrumentation may be difficult because the detectors are always subjected to vehicle detection based errors under heterogeneous traffic. Hence, the method demands more man-power and time for manual data extraction under heterogeneous traffic conditions. 0 REFERENCES. Huber, M. J. Estimation of Passenger-Car Equivalents of Trucks in Traffic Stream. Transportation Research Record, No.,, pp Cunagin, W., and C. Messer. Passenger Car Equivalents for Rural Highways. In Transportation Research Record: Journal of the Transportation Research Board, No. 0, TRB, National Research Council, Washington, D. C.,, pp. -.

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