MEASURING PASSENGER CAR EQUIVALENTS (PCE) FOR LARGE VEHICLES AT SIGNALIZED INTERSECTIONS

MEASURING PASSENGER CAR EQUIVALENTS (PCE) FOR LARGE VEHICLES AT SIGNALIZED INTERSECTIONS Md. Mizanur RAHMAN Doctoral Student Graduate School of Engineering Department of Civil Engineering Yokohama National University 79-5, Tokiwadai, Hodogaya-ku Yokohama 240, Japan Fax: +81-045-331-1707 E-mail: mmr1971@yahoo.com Fumihiko NAKAMURA Associate Professor Graduate School of Engineering Department of Civil Engineering Yokohama National University Hodogaya-ku, Yokohama 240, Japan Fax: +81-045-331-1707 E-mail: nakamura@cvg.ynu.ac.jp Izumi OKURA Professor Graduate School of Engineering Department of Civil Engineering Yokohama National University 79-5, Tokiwadai, Hodogaya-ku Yokohama 240, Japan Fax: +81-045-331-1707 E-mail: okura@cvg.ynu.ac.jp Abstract: This study introduces a new method for estimating passenger car equivalents (PCE) for large vehicle at signalized intersections based on increased delay caused by the large vehicle. In this study PCE value for large vehicles is estimated as a unit value plus the ratio of the increased delay due to the presence of large vehicle in the queue to the base delay of a passenger car when the queue is composed of all basic vehicles or passenger cars. Based delay and increased delay due to large vehicles are calculated from observed headways data, collected from various intersection approaches of Yokohama city. This method includes the effects of large vehicle s position in the queue to estimate the PCE value. Most of the previous studies considered the percentage of heavy vehicles in the queue to estimate the PCE value. However, for the same percentage of heavy vehicles if the position of large vehicle in the queue varies, the PCE value varies considerably. It is necessary to include this concept to estimate PCE value at signalized intersections, as delay caused by the large vehicle varies significantly among different position in the queue. Key Words: Passenger car equivalents (PCE), large vehicles, signalized intersections, queue position, increased delay 1. INTRODUCTION The signalized intersection is the most serious capacity constraint along an urban street. The effect of traffic factors on the capacity of a intersection approach is usually allowed for by the use of weighting factors, referred to as Passenger Car Equivalents, assigned to differing vehicle categories. Signalized intersections represent an unavoidable impedance to traffic flow. No matter how well a signal is timed and no matter how well that timing is maintained and adapted instantaneous conditions, some vehicles arrive during the red interval. These vehicles form a queue that must be dissipated during the ensuing green interval. The presence of large vehicle (heavy vehicle) in the traffic stream adversely affects vehicular performance and reduces the actual capacities of the highway facilities. This adverse effects are sever at signalized intersections as all vehicles have to stop at signalized intersections when signal turn to red. The presence of large vehicles in the queue increases the headway as well as delay of others vehicles.

The term passenger car equivalent (PCE) was introduced in the 1965 Highway Capacity Manual. Since 1965, considerable research effort has been directed toward the estimation of PCE value for various roadway types. However, at present, there is neither a commonly accepted nor clearly defined theoretical basis for the concept of passenger car equivalent. There have been many researchers to estimate PCE at signalized intersection based on microscopic as well as macroscopic approach, giving different numerical results. Importance of these result lies on the purpose of application and the way PCE value is used. This study introduces a new methodology for estimating the effects of large vehicles on traffic performance at signalized intersections. Effects of large vehicles are quantified based on the delay caused by large vehicles considering each queue position of vehicles. Concept of new PCE estimation method is introduced and PCE values for large vehicles at signalized intersection are suggested for different proportion of large vehicles. 2. PCE MEASURING METHODS AT SIGNALIZED INTERSECTIONS The concept of estimating passenger car equivalent (PCE) is to estimate the number of passenger cars displaced by each heavy vehicle in the traffic flow. The term passenger car equivalent was first used in 1965 Highway Capacity Manual (HCM) and defined as the number of passenger cars displaced in the traffic flow by a truck or a bus, under the prevailing roadway and traffic conditions. Since the 1965 HCM, much research has been done in this area. Headway ratio method is currently the most commonly used method for PCE estimation. Greenshields et al. (1947) estimated PCE value by following equation. This method is known as basic headway method. PCE i = H i / H c (1) Where: PCE i = passenger car equivalent of vehicle class i H i = Average headway of vehicle class i, (sec) H c = Average headway of passenger car, (sec) Miller (1968) developed PCE values for through traffic at intersections based on the additional headway a heavy vehicle would require over a passenger car. He used the concept of basic headway method and determined that the PCE value of a truck was 1.85. Carstens (1971) also using the headway approach, developed a PCE value of 1.63 for a truck, where a truck was defined as a vehicle with more than four tires. The 1985 and the 1994 Highway Capacity Manual did not include direct use of PCE values for heavy vehicles for analysis of signalized intersection. It considered the effects of heavy vehicles using an adjustment factor for saturation flow rate. S = S i * f HV * (2) Where: S = saturation flow rate under prevailing condition, (vphg) S i = ideal saturation flow rate, (pcphgpl) f HV = adjustment factor for heavy vehicle The adjustment factor for heavy vehicles depends on the percentage of heavy vehicles in the traffic flow. Although not directly mentioned, the PCE values used in HCM are derived from

the following equations. 100 fhv = 100 + Phv( PCE 1) (3) PCE 100 100 = + 1 fhv * Phv Phv (4) Where: P hv = percent of heavy vehicles, (%) The 1985 HCM used a uniform PCE value of 1.5 and in the 1994 HCM this value is 2.0. The uniform values suggested that no difference on the impacts of heavy vehicles with respect to type of vehicles and proportion of heavy vehicles. No assumption is made in this regard and no adequate documentation was provided for this change. Based on the headway method Molina (1987) developed a method to estimate the PCE value of large trucks at signalized intersections based on the increased headways caused by the large truck. Monila estimate PCE using following equation. dh PCE k = 1 + (5) Where: hb PCE k = passenger car equivalents of vehicle type k dh = the total increased headway of the queue caused by the vehicle type k. This is equal to the difference of total headway of a queue with vehicle type k and total headway time of a passenger car queue h b = saturation flow headway of passenger car The authors found that truck type affects the size of the PCE. Position of the vehicle in the queue did not significantly affect the PCE value for the two- and three-axle, single-unit trucks, however, position of vehicle in queue has a very pronounced effect on the PCE value of large five-axle combination of trucks. In this study proportion of trucks and position of trucks in queue are not considered. The authors suggested that PCE values of 3.7 and 1.7 should be used for heavy and light vehicles, respectively. Zhao (1998) proposed a delay-based passenger car equivalents method for heavy vehicles at signalized intersections. The author used the headway data and estimate PCE value by following equation. di D PCEi = 1 + (6) do Where: D PCE i = delay-based PCE for vehicle type i d i = additional delay caused by a vehicle type i d o = average delay of passenger car queue The author found that PCE values are highly correlated with traffic volumes and percent of heavy vehicles. D-PCE value increases with the rise of traffic volume and percentage of heavy vehicles. From a limited sample, the author recommended PCE values for single unit trucks and combination of trucks for various percentages of trucks and traffic volume in tabular form. In this study effect of heavy vehicle s position in queue are not taken into considerations. Based on the basic headway method, Molina s method include the additional headway caused by the heavy vehicles. It still does not reflect the total delay that experiences by the vehicle in

the queue when heavy vehicles present in the queue. Zhao s method include the effect of total delay experiences by the vehicle but not include the effect of queue position of the vehicles which is utmost important to calculate the total delay. An overall review of the studies suggested that past efforts on determining the effects of heavy vehicles at signalized intersections has concentrated on adjusting the saturation flow rate. Very few studies considered the total delay to estimate the PCE value for heavy vehicles. Furthermore, no study was considered the effects of large vehicle s position in the queue to estimate the PCE value for large vehicles at signalized intersections. This paper estimated the PCE of large vehicles based on not saturation flow rate but increased delay due to following reasons: the PCE value at signalized intersections has so far been taken as the equivalent number of passenger cars that a large vehicle physically displaced in the queue. The delay due to large vehicles on the queued vehicles has not taken into consideration. Vehicular delay is a level of service (LOS) measures at signalized intersections, so it is required to consider the delay due to large vehicles to estimate PCE value at signalized intersections. 3. COLLECTION AND PROCESSING OF DATA All data were collected from the signalized intersections located in Yokohama city of Kanagawa prefecture of Japan. Fifteen approaches of seven signalized intersections (fixedtimed) are selected for this study. All locations were through lanes, and they were carefully selected so that there was no obvious deficiency of roadway or traffic condition that would affect the PCE value. Vehicle movements were recorded by using a portable digital video camera system for all the selected sites. All fields videotaping of traffic movements were conducted in August to October of 2002. Within the filming period, only interested lane traffic movements data were recorded. In all, more than 20 hours of traffic data were recorded on videotapes for this study. The tapes were first examined in the laboratory to screen out the cases that were not suitable for this study, including the followings: platoons within whom vehicles did not stop before entering an intersection; platoons with turning vehicles; and platoons in which movements of vehicle were impede by pedestrians, cross traffic, or turning vehicles. In other words, only platoons containing unimpeded, straight-through vehicles stopped before entering an intersection were considered as valid cases for the study. The valid cases were later viewed on a television screen to extract the headways of queued vehicle. Time Code (TC) reader software was used to estimate the headways of vehicles entering the intersections. For the first vehicle of a queue, its entering headway was taken to be the time elapse between the start of a green indication and the time at which the rear bumper of the vehicle cleared the stop line of the intersection. For other vehicles in the queue, the entering headways were taken to be the elapsed time, rear bumper to rear bumper, as successive vehicles passed an intersection stop line. From the data reduction phase, a total of 450 singlelane vehicular platoons (450 cycles) were found to be valid for this study. This headways data were later used to calculate the total delay and estimate PCE values. 4. EFFECTS OF LARGE VEHICLE S POSITION IN QUEUE ON TOTAL DELAY Delay of a vehicle in a given queue position is not linearly related to the queue discharge headway for that position. In this study it is assumed that delay experienced by each vehicle

started when signal changes to green. For first vehicle delay is equal to the headway of first vehicle, and for second vehicle delay is equal to the sum of headway of first and second vehicle and so on. This delay calculation is based on the study of Gerhart (1976). If H i is the discharge headway for the i th queue position, then the total delay (D i ) occurring to a vehicle in that position is given by equation (7). This delay calculation does not include stopping delays at red signal. Stopping delay is affected by arrival patterns of vehicles at intersections not affected by the vehicle type. j i = = = Di Hj The total delay (D t ) accrued by a queue of length m is then given by j 1 j k Dt D (7) = = ( m) j (8) = j 1 or D t(m) = mh 1 +(m-1)h 2 +.. +2H m-1 +H m (9) Using equation (9) and observed headways data it was estimated that total delay accrued by a queue of length 10 passenger cars is 122.7 sec. The effects of large vehicle s position in queue on the total delay with different percentage of large vehicles are shown in the following figures based on the observed data. Where, Q1 means 1 st vehicle of the queue is large vehicles and others vehicles are passenger car, Q2 means 2 nd vehicle of the queue large vehicle and so on. As shown in figure 1, total delay caused by large vehicle is significant at the beginning of the queue and this value decreases as position of large vehicle in the queue increases. Average total delay caused by large vehicle for a queue length of 10 vehicles with 10% large vehicles are 147.3 sec and 128.3 sec for first queue position and tenth queue position of large vehicle respectively. These values indicated that there is a huge difference between the total delay due to the position of large vehicle in the queue and this difference is as high as 15%. This is the reason why the effect of large vehicle s position in the queue is taken into consideration to measure the PCE value. 150 Total delay (sec) 145 140 135 130 125 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Position of large vehicle in queue Figure 1: Effect of position of large vehicle in queue on delay (10% large vehicles)

Position of large vehicles in queue Q110/Q210 Q19/Q29 Q18/Q28 Q17/Q27 Q16/Q26 Q15/Q25 Q14/Q24 Q13/Q23 Q12 Total delay for queue position 2nd and others Total delay for queue position 1st and others 140 145 150 155 160 165 170 Total delay (sec) Figure 2: Effect of position of large vehicle in queue on delay (20% large vehicles) Position of large vehicles in queue Q1210/Q2310 Q129/Q239 Q128/Q238 Q127/Q237 Q126Q236 Q125/Q235 Q124/Q234 Q123 140 145 150 155 160 165 170 Total delay (sec) Total delay for queue position 1st, 2nd and others Total delay for queue position 2nd, 3rd and others Figure 3: Effect of position of large vehicle in queue on delay (30% large vehicles) As shown in figure 2 maximum delay occurred when first two vehicles is large vehicle, not only that for other combinations greater delay occurred when leader of the queue is large vehicle. Figure 2 shows the comparison of total delay for first and second queue position with different combination of large vehicles position. In figure 2, Q12 means that 1 st and 2 nd vehicles of the queue belong to large vehicle and others vehicles are passenger cars. Q23 means that 2 nd and 3 rd vehicles are large vehicles and remaining vehicles are passenger cars and so on. Figure 3 shows the similar effects for 30% large vehicles in the queue. In figure, Q123 means that 1st, 2 nd and 3 rd vehicle of the queue is large vehicles and others are passenger cars and so on. From the above three figures one thing is clear and it is common for all percentage of large vehicles, maximum delay occurred when large vehicle stand at the beginning of the queue. It is also suggested by the analysis that total delay increase with the increases of percentage of large vehicles in the queue and this increase is sharp for small percentage of large vehicles and reaches almost constant value at higher percentage of large vehicles. This is shown in figure 4.

Total delay (sec) 200 190 180 170 160 150 140 130 120 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Percentage of large vehicles in queue Figure 4: Relationship between total delay and proportion of large vehicles in queue 5. PCE OF LARGE VEHICLES In this study large vehicles are defined as those vehicles which have more than four tires (example: truck, bus etc). This study introduces a new method for estimating passenger car equivalents (PCE) for large vehicle at signalized intersections based on increased delay caused by the large vehicle. In this study PCE values for large vehicles are estimated as a unit value plus the ratio of the increased delay due to the presence of large vehicle in the queue to the base delay of a passenger car when the queue is composed of all basic vehicles or passenger cars. PCE LVj = 1+ (d LGj /D o ) (10) Where: PCE LVj = Passenger car equivalents for a large vehicle at j th queue position d LGj = increased delay due to the large vehicle at j th queue position D o = base delay of a passenger car when all the queued vehicles are passenger car Based delay and increased delay due to large vehicles are calculated from observed headways data, collected from various intersection approaches of Yokohama city. Increased delay due to large vehicle is calculated by comparing the total delay of a mixed queue (queue composed of both passenger cars and large vehicles) and base queue (queue composed of passenger cars only) for a given number of queue lengths. This method includes the effects of large vehicle s position in the queue to estimate the PCE value. Most of the previous study only considered the percentage of heavy vehicles in the queue to estimate the PCE value at signalized intersection. However, for the same percentage of heavy vehicles if the position of large vehicle in the queue varies, the increased delay caused by large vehicle also varies and PCE value varies considerably, as estimation of PCE value is related with increased delay caused by large vehicle. So it is utmost important to include this concept to estimate PCE value at signalized intersections, as delay caused by the large vehicle varies significantly among different position in the queue. Using equation (10), PCE values are estimated for 10%, 20% and 30% large vehicles considering the all possible combination of large vehicles position in the queue from the observed headways data. The estimated PCE values are given in Table 1, Table 2 and Table 3 respectively.

Table1. PCE value for different position of large vehicle (10% large vehicles) Queue position 1 2 3 4 5 6 7 8 9 10 PCE 1.20 1 1.163 1.148 1.123 1.118 1.097 1.081 1.065 1.055 1.005 Table 2. PCE value for different positions of large vehicle (20% large vehicles) Queue position 2 3 4 5 6 7 8 9 10 1 1.317 1.289 1.273 1.250 1.239 1.220 1.209 1.198 1.187 2 1.249 1.234 1.216 1.204 1.193 1.175 1.163 1.153 3 1.219 1.217 1.202 1.191 1.173 1.161 1.150 4 1.194 1.183 1.175 1.161 1.150 1.139 5 1.165 1.146 1.132 1.121 1.110 6 1.134 1.113 1.104 1.095 7 1.107 1.089 1.081 8 1.082 1.065 9 1.062 As shown in Table 1, PCE value for large vehicle decreases as position of large vehicles in the queue increases. This has a similar tendency as we observed in case of total delay calculation. As shown in Table 1 large vehicle has a very little impact on the PCE value when it stands at the end of the queue. So it is utmost important to include the concept of large vehicle s position in the queue to PCE estimation and capacity analysis of signalized intersections because signal design is directly related to capacity or saturation flow of signalized intersections. If the position of large vehicles in the queue is say 2 nd and 5 th, then we have to read the PCE value of row 2 and column 5 (1.216) from Table 2 and so on. Cross ( ) sign means that this PCE value already mentioned, this is also true for Table 3. As shown in Table 2, PCE value (for 20% large vehicles) is maximum 1.317 when large vehicle s position in the queue is first and second, and this value is 1.062 when large vehicle s position in the queue is nine and ten. So there is a big difference in PCE value for same percentage of large vehicles due to the change of the position of the large vehicles in the queue. As shown in Table 3 (for 30% large vehicles) maximum PCE value is 1.368 and minimum PCE value is 1.066 and this occurred when lager vehicle s position is first-second-third and eight-nine-ten in the queue respectively. Another important observation from the tables is that when the queue position increases the PCE values decreases sharply and percentage of large vehicles in the queue does not significantly impact the PCE values at the end of the queue. This seems to us occur due to at the end of the queue vehicles reached their saturation flow and there is a very little difference in headway between vehicles and delay difference is also low. For other percentage of large vehicles it is also possible to estimate the PCE values for all possible combination of large vehicle s position in the queue. It is evidenced from previous tables that the maximum PCE value of large vehicles occurred when large vehicles stand at the beginning of the queue, so for other percentage of large vehicles PCE values are estimated for leading position of the large vehicles in the queue. However, in real case the position of large vehicles in the queue is random, not constant. For this reason, to use the PCE values for

practical purposes average effects of large vehicles rather than maximum effects are taken into consideration. The estimated PCE values for various proportions of large vehicles are given in Table 4 (considering queue length of 8 vehicles to 17 vehicles). Table 3. PCE value for different queue positions (30% large vehicles) Queue position 1 2 3 4 5 6 7 8 9 10 1,2 1.368 1.351 1.337 1.323 1.308 1.288 1.282 1.271 2,3 1.304 1.285 1.272 1.259 1.247 1.237 1.228 3,4 1.359 1.268 1.265 1.257 1.243 1.233 1.224 4,5 1.333 1.299 1.239 1.230 1.217 1.209 1.202 5,6 1.289 1.231 1.228 1.176 1.166 1.158 1.150 6,7 1.255 1.213 1.204 1.182 1.123 1.118 1.111 7,8 1.218 1.185 1.174 1.157 1.139 1.093 1.086 8,9 1.184 1.162 1.155 1.139 1.121 1.108 1.066 9,10 1.176 1.145 1.147 1.127 1.115 1.103 1.092 1.079 10,1 1.258 1.239 1.227 1.215 1.206 1.192 1.182 2,4 1.295 1.289 1.277 1.266 1.257 2,5 1.234 1.219 1.209 1.200 2,6 1.202 1.193 1.185 2,7 1.173 1.167 2,8 1.152 3,5 1.316 1.219 1.208 1.199 1.191 3,6 1.310 1.189 1.183 1.175 3,7 1.285 1.167 1.159 3,8 1.281 1.152 3,9 1.272 4,6 1.295 1.175 1.167 1.159 4,7 1.279 1.157 1.149 4,8 1.264 1.135 4,9 1.254 5,7 1.261 1.139 1.132 5,8 1.249 1.119 5,9 1.239 6,8 1.235 6,9 1.225 7,9 1.214 For capacity analysis or signal design, from field observations we have to estimate the average queue length and proportion of large vehicles in the queue. Then PCE value of the table 4 will be used to convert the mixed flow into basic flow. The PCE values of Table 4 are applicable for queue size 8 to 17 vehicles to convert the mixed flow into basic flow for signal timing design. As shown in Table 4 PCE value increases as percentage of large vehicles in the queue increases, and after some value (60% large vehicles) increase rate is almost constant. Capacity reduction resulted from the PCE value (this study) is compared with that from constant PCE values of 1.5 and 2.0 used in 1985 and 1994 HCM respectively. Capacity

reduction factor is calculated from the equation (3), where percentage of large vehicles and PCE values of Table 4 are used. For 1985 and 1994 HCM, PCE value is constant for all percentage of large vehicles. Figure 5 show the amount of reduction applied to the saturation flow rate (or capacity) due to the presence of large vehicles in the queue at signalized intersections considering the effect of large vehicle s position in the queue. As shown in figure 5, 1994 HCM overestimates the capacity reduction factor for each percentage of large vehicles and this overestimation is high in case of higher percentage of large vehicles. In case of 1985 HCM, capacity reduction factor is almost similar to this study although there is some underestimation for small percentage of large vehicles. Table 4: PCE value for different proportion of large vehicles considering the average effects of large vehicle s position in queue % of large 10 20 30 40 50 60 70 80 90 vehicles PCE value 1.183 1.302 1.344 1.396 1.435 1.501 1.523 1.547 1.564 Capacity reduction factor 1.00 0.90 0.80 0.70 0.60 0.50 85 HCM 94 HCM This study 0 10 20 30 40 50 60 70 80 90 100 Proportion of large vehicles (%) Figure 5: Capacity reduction comparison 5. CONCLUSIONS This study looked at the effect of large vehicle s position in the queue on total delay estimation and developed PCE values for large vehicle at signalized intersections considering this effect. Based on the results of this study, the following can be concluded: Total delay caused by large vehicle is significant at the beginning of the queue and this value decreases as position of large vehicle in the queue increases. Maximum delay occurred when large vehicle stand at the beginning of the queue. Total delay increase with the increases of percentage of large vehicles in the queue and this increase is sharp for small percentage of large vehicles and reaches almost constant value at higher percentage of large vehicles. For the same percentage of large vehicles if the position of large vehicle in the queue varies, the increased delay caused by large vehicle also varies. PCE value for large vehicle decreases as position of large vehicles in the queue increases. Large vehicle has a very little impact on the

PCE value when it stands at the end of the queue. There is a big difference in PCE value for same percentage of large vehicles due to the change of the position of the large vehicles in the queue. PCE value increases as percentage of large vehicles in the queue increases. In this study queue length of 8 vehicles to 17 vehicles used to develop PCE values at signalized intersections. Further study will required for larger queue length, as queue length affects the discharge headways as well as total delay. a) Books and Books chapters b) Journal papers REFERENCES Carstens, R. L. (1971) Some Traffic Parameters at Signalized Intersections, Traffic Engineering, Vol. No. 41, No. 11, August, 33-36. Gerhart, F. K. and Wilkinson, M. (1976) Relationship of Signal Design to Discharge Headway, Approach Capacity, and Delay, Transport Research Record 615, Transport Research Board, Washington D.C. Molina,C.J. (1987) Development of Passenger Car Equivalencies for Large Trucks at Signalized Intersections, ITE Journal, November,Vol. 57, 33-37 c) Papers presented to conferences Zhao, W. (1998) Delay-Based Passenger Car Equivalents for Heavy Vehicles at Signalized Intersections. Proceedings of ICTTS 98. d) Other documents Greenshields, B.D., Shaspior, D. and Erickson, E.L. (1947) Traffic Performances at Urban Intersections, Bureau of Highway Traffic, Technical Report No. 1, Yale University, New Haven, Conn. Miller, A.J. (1968) The Capacity of Signalized Intersections in Australia, Australian Road Research Board Bulletin, No. 3. March. Transportation Research Board, National Research Council, (1985), Highway Capacity Manual, Special Report 209, Washington D.C. Transportation Research Board, National Research Council, (1994), Highway Capacity Manual, Special Report 209, Washington D.C.