Analytical Approach to Evaluating Transit Signal Priority

Transcription

1 JOURNAL OF TRANSPORTATION SYSTMS NGINRING AND INFORMATION TCHNOLOGY Volume 8, Issue, April 008 Online nglish edition of the Chinese language ournal Cite this paper as: J Transpn Sys ng & IT, 008, 8(, RSARCH PAPR Analytical Approach to valuating Transit Signal Priority LIU Hongchao, *, ZHANG Jie, CHNG Dingxin 3 Department of Civil and nvironmental ngineering, Texas Tech University, TX , USA KBR Inc., 444 Oak Lawn Ave, Suite 00, Dallas, TX7507, USA 3 Department of Civil ngineering, California State University, Chico, CA 9599, USA Abstract: Successful deployment of transit signal priority (TSP systems requires thorough laboratory evaluation before field implementation. Traffic simulation is a powerful tool in this regard; however, it requires tremendous efforts toward network coding, data collection, and model calibration. Besides, simulation models tend to be proect specific, and the models developed for one proect are often discarded upon the completion of that proect. In this paper, it is shown that the impacts of two fundamental TSP strategies (early green and extended green can be evaluated using an analytical approach. The impacts of the above two strategies on both the prioritized and the nonprioritized approaches are illustrated using graphical as well as analytical methods. A simulation study is then conducted for comparison analyses, followed by a statistical approach for the test of generality. Key Words: traffic signal system; bus priority; traffic simulation; signal timing Introduction The importance of public transportation in providing sustainable mobility is being recognized by researchers and transportation authorities as well as the traveling public in the United States. Transit signal priority (TSP has shown promise in improving the performance of in-service transit vehicles by ensuring schedule adherence and reducing delay and operational cost. The simulation approach has commonly been used for evaluating TSP strategies as well as their impacts on other vehicles [3]. However, the efforts required for network coding, data collection, and model calibration make the simulation approach extremely tedious and time consuming. Basic requirements for simulating TSP involve emulating the logic of fixed time/actuated traffic signals under normal operation and during transit signal priority, detection of a bus at the check-in and check-out points, priority generator, priority server, communication links between buses and traffic signals, bus movements in the traffic stream, and dwelling time at bus stops. Advanced features that need to be modeled include, but are not limited to adaptive signal control, Automatic Vehicle Location (AVL systems, bus arrival time predictor, and checking or monitoring bus schedule online [4,5]. As pointed out by Liu [6], most simulation models currently available lack most of the characteristics and capabilities for realistically modeling TSP systems. In addition, the development of TSP simulation models has been approached differently by researchers and traffic engineers on the basis of their specific needs, and the interpretations of simulation outputs vary significantly from proect to proect. Recent examples include the works of Balke, Davol, Shalaby, Dion, and Ngan et al. [6]. Unfortunately, these models could not be used by other users. Sunkari et al. [] has presented an interesting modeling approach, in which a simple evaluation model was developed using the delay equation from the 985 Highway Capacity Manual. However, this method was oversimplified and did not lead to practical application. In the latest report by ITS America [3] and Smith et al. [4], it is concluded that arly Green and xtended Green are the two most commonly applied operational strategies in such systems. These two strategies are identical in the sense that both rely on shortening the green time of the opposing approaches to obtain extra green time for the prioritized approach. A maor concern with regard to the s operation is the possible negative impact it might have on other vehicles. This paper presents the analytical fundamentals underlying the arly Green and xtended Green operations. The analytical approach provides a useful tool for predicting and evaluating the performance of a common TSP system in a Received date: Jan, 008; Revised date: Mar 6, 008; Accepted date: Mar, 008 *Corresponding author. -mail: hongchao.liu@ttu.edu Copyright 008, China Association for Science and Technology. lectronic version published by lsevier Limited. All rights reserved.

2 LIU Hongchao et al. / J Transpn Sys ng & IT, 008, 8(, 4857 systematic fashion. The advantages of an analytical approach also lie in its simplicity and generality. Most data (e.g., bus dwelling time, pedestrian demand, and vehicle speed required by simulation models become unnecessary for the analytical method. The tremendous time and effort spent on coding network geometries and calibrating simulation models can also be saved. Analytical fundamentals of transit signal priority The intersection delay is composed of uniform delay, random delay, and residual queue delay. The issue of concern toward TSP is often the additional delay it might bring to the general traffic, i.e., the delay. If we assume that operation of TSP does not significantly change the randomness of traffic flow, the random delay should remain unchanged before and after the TSP. Hence, attention can be focused on the delay changes in the uniform delay and the residual queue delay. This will be presented in the following sections with graphical illustrations.. arly green arly Green applies if the signal is in red phase at the time of detection for point detection based systems or will be in red phase at the time when the bus is predicted to arrive at the intersection for the zone and area detection based systems. First, the impact of arly Green on the prioritized and nonprioritized approaches is illustrated... Impact of early green on prioritized approach Figure shows graphically an undersaturated case where the approach arrivals do not exceed the capacity. When arly Green is not operational, the green phase is started at point A, and the corresponding deterministic delay can be easily calculated by the first term of Webster s formula. If arly Green is present, the actual start time is at point B because of the early start of the green interval. The small time interval T (in seconds in between A and B is the total amount of green T time obtained from the nonprioritized phases, i.e., t, where t is the green time borrowed from the phase. The reduced intersection delay is thus the area of the shaded part, which is it (Ri T i[ delay] ( ( i where, C=cycle length in second; i=the prioritized phase; R i =red interval of phase i in second; i =traffic demand on lane group i in vehicle/s; i =flow ratio of the lane group i, i i / si ; S i =saturation flow rate of lane group i in vehicle/s. And the delay reduction per vehicle is T (Ri T i[ ( delay ( C( i Cumulative vehicles Cumulative vehicles s t R C R C R C R C Fig. Impact of early green on prioritized approach t R C R C Fig. Impact of early green on nonprioritized approaches t B B T T A A time time.. Impact of early green on nonprioritized approaches The green interval T for the prioritized approach is obtained by shortening the green intervals of preceding phases. Its possible negative impact is one of the maor concerns of the traffic engineers regarding the TSP. This impact can also be quantified. As shown in Fig., when an otherwise undersaturated signal phase is truncated before the queue on the associated approach is cleared, the total increased delay is composed of three elements if the assumption that TSP would not change the randomness of traffic flows is valid. The small triangle represents the initial queue delay caused by the residual queue because of the truncation of the phase; whereas represents the additional delay caused by the increased traffic arrivals during the prolonged red interval in the subsequent cycle; and 3 is the delay under normal operation when there is no truncation. The average initial queue delay [ delay ] is calculated by s R ( C t ( [ delay] (3 ( The induced delay during the extended red interval is t (R t R (4 [ delay ] s [ ( C t ]( R t ( where t =the amount of green time borrowed from phase. Hence, the total increased delay because of the early termination is

3 LIU Hongchao et al. / J Transpn Sys ng & IT, 008, 8(, 4857 [ delay] [ delay] [ delay] (5 And the issue of concern, i.e., the increased delay per vehicle is approximately [ delay] [ delay (6 C The impact of the early green on minor approaches is sensitive to the flow ratio of the affected approach and the amount of green time taken from the associated phase. It is evident that [ delay] 0 gives the upper threshold of t, which is the maximum available green time that can be borrowed for the prioritized phase without causing cycle failure at the associated phase. The t (optimal yields R t ( optimal C (7 This provides an additional guidance in TSP planning while determining the extent to which a minor phase can be shortened under specific traffic and signal timing conditions. In practice, t should be kept less than but as close as possible to t (optimal so as to obtain maximum benefit for transit vehicles and at the same time, keeping the truncated phases undersaturated during and after the priority operation.. xtended green The strategy of xtended Green is usually implemented at the end of the requested phase when the check-out call from a bus has not been received during the normal green interval. A similar analysis is conducted in the following sections to illustrate the impact of xtended Green on both prioritized and nonprioritized phases... Impact of extended green on prioritized approach Consider the diagram shown in Fig. 3. If the approach is assumed to be undersaturated and a bus is able to pass through the intersection during the extended green interval, the actual delay of the bus can be reduced to almost zero. The same benefit can be obtained only by those vehicles traveling with the bus, and the vehicles that have traversed the intersection during the normal green interval will not benefit from the operation. Therefore, it is intuitive that the operation of Green xtension can bring maximum benefit to transit bus but will not bring as much benefit as the arly Green does to other vehicles on the same approach. The reduction in delay, thereby saving time, by the extended green for general vehicles can be approximately estimated by calculating the shaded area in Fig. 3, which is T i i[ delay] TRii ( i (8 The average reduction in delay per vehicle is obtained by dividing the total reduced delay by the number of vehicle arrivals during (C+T, i.e. ( C T. i i[ delay] i[ ( delay ( C T.. Impact of extended green on nonprioritized approaches In contrast to the operation of early green where the nonprioritized phases are treated before the start of the prioritized phase, the minor phases are shortened during either the priority cycle or the transitional/recovery cycle in the case of the extended green. The negative impact of the extended green on the affected approaches comes from two aspects, namely, the green time of the prolonged red interval and the truncation of the green phase. The former is the result of a lengthened red interval because of the extension of the green time of the prioritized green phase. The latter is because of the early termination of the green phase during the transition, which is similar to the operation in the early green. Figure 4 graphically depicts the two kinds of delay induced by the extended green. It is worthy to note that the two parts of the delay might not apply simultaneously to all affected phases. Some of the phases might experience only the second part of the delay, whereas some others might experience both. It depends largely on how the extended interval T is digested among the subsequent phases. Cumulative vehicles Cumulative vehicles R C R C Fig. 3 Impact of green extension on the bus approach T R C R C t Fig. 4 Impact of green extension on affected minor phases i (9 time time

4 LIU Hongchao et al. / J Transpn Sys ng & IT, 008, 8(, 4857 The delay caused by the prolonged red interval is represented by the shaded area of, which is ( t R t [ delay] ( i, t [ 0, T ] (0 ( The average increased delay per vehicle because of the enlarged green interval is t (R t [ ( delay ( i, t [ 0, T ] ( C( The delay caused by the early termination of the phase during the transition is depicted by the shaded area, which is '( ' t R t R [ delay ] s [ ( C t ']( R t ' ( ' ( i, t [0, g ] ( Where t =the amount of green time cut from phase (for return to coordination; g = the green interval of phase ; The increased delay per vehicle is [ delay] [ delay (3 C Hence, the issue of concern, i.e., the total increased delay per vehicle for phase because of the green extension is either [ delay/ veh] or [ delay, or [ delay + delay, depending on the specific TSP policy. [ 3 xample applications and simulation test 3. Analytical method The example uses a typical signalized intersection with common lead-lag phases. Signal priority applies to the coordinated phases and 6. As shown in Table, all one needs is the signal timing plan and the traffic demand. To begin with, let s consider the early green. The easiest but least effective way is to terminate all preceding minor phases right after their minimum green interval is processed. For illustrative purpose, the minimum green strategy is evaluated in this example. Note that the v/c ratios of phase 4 and 8 as well as phase 5 are already high and it is very likely that their associated approaches might become oversaturated after TSP operation. The quantitative results are summarized in Table. Table Traffic and signal timing information Green time (s Phases Movements (veh/h S (veh/h Cycle (secs Lost time (secs Degree of saturation Min Avg. Max (4, (3, a (, b (, c (, Phases Movements t (secs (optimal t (secs Table Impact of early green T (secs Increased delay/veh./cycle (secs Reduced delay/bus/cycle (secs Avg. delay/ veh. Degree of saturation (4, (3, a (, b (, c (,

5 LIU Hongchao et al. / J Transpn Sys ng & IT, 008, 8(, 4857 Phases Movements T (secs t (secs Table 3 Impact of extended green ' t (secs Increased delay/vehicle (secs* Reduced delay/bus (secs (4, =7.8 (3, =.9 3a (,5 3b (, c (, *: In the form of delay/ veh] [ delay/ veh] [ For a phase terminated at the time of minimum green, t is the difference between the phase length and the minimum green interval. The sum of t of each minor phase is T, which is 4 s in this case. It is shown from the result that when t is close to t (optimal, e.g., the phases (4, 8, the increased delay on the associated approach is very low. Otherwise, the delay might increase significantly (e.g., for the movements of the phase (3, 7 and phase 5. Assume that an 8-second-extended green was applied to the phase 6 during the priority cycle. As a result, the vehicles of the phase immediately next to the phase 6, i.e., phase (4, 8, experienced an additional 8 s for waiting the green light. Thus, t is 8 seconds in qs. ( and ( for the calculation of (4,8 (4,8. Unlike the case in the fixed-time control, where these 8 seconds is transferred to all subsequent phases, the extra waiting time induced to later phases depend on the duration of the preceding phases as well. For example, if the phase (4, 8 was shortened for 4 seconds during the transitional cycle, ' should also apply and t4,8 4 s. Consequently, the phase next to (4, 8, i.e., phase (3, 7 is subect to 4 s for the extended red interval (i.e., t 3,7 =4 s and should apply. Similarly, if the phase was also cut off for, say, 4 seconds, should apply as well and the transition could be finished at the end of this phase, which incurs no impact on the following phase 5. The result is summarized in Table 3. A simple examination of the result is conducted by observing the reduction of the bus delay. For an undersaturated approach, if there is no green extension, the bus is likely to be stopped by the signal and wait for a full red interval until the next green phase. Hence, it is intuitive that the reduced bus delay should be close to the red interval of the associated phase. In this case, the average bus intersection delay was reduced by 44.5 seconds, which is very close to the red interval of phase 6, which is 46 seconds. Compared to the 8 seconds delay reduction brought by the early green, it is obvious that the extended green is more efficient in terms of the time saving for buses. Note that the increased delay on the affected approaches is given in the form of [ delay [ delay for illustration. As previously stated, all of the minor phases except for the phase 5 and were subect to the delay of both types in this example. The increased delay by the prolonged red interval seems to be much smaller than that caused by the phase truncation. Given the amount of time it saved for the buses, it is fair to conclude that in general the operation of the extended green is more efficient than the early green in the case where buses can traverse the intersection during the extended green interval. 3. Simulation test VISSIM simulation [5] was used in the test. The check-out detectors are placed at the stop bar and the distance between the check-in and check-out detectors is 300 ft. The travel speed of the transit buses and passenger cars is 5 mph and 35 mph, respectively, which are changed later for the generality test. Default acceleration and deceleration rates are used for both passenger cars and transit buses, which is.5 ft /s and 9.0 ft /s, respectively. VISSIM simulates the operation of early green and green extension according to the travel time predetermined in the NMA editor on the basis of free flow speed. If the bus is predicted to arrive during the green and there is still enough time in the normal green phase, the TSP call is ignored. Similarly, a request for the green extension might be put on hold to the next cycle for the early green if there is no enough green for extension. In addition, the Basic Bus TSP function has a built-in re-service timer that prevents TSP from occurring too often. The re-service timer will prevent TSP calls from being placed after a previous TSP call until the zero point of the cycle has been crossed twice. The built-in TSP function in VISSIM is close to the control logic in the field as described in the previous sections, which makes the simulation test reliable.

6 LIU Hongchao et al. / J Transpn Sys ng & IT, 008, 8(, 4857 No TSP Table 4 Model calibration Delays of bus priority phase (phase 6 Mean simulated value No No No Average No TSP Delays of other phase (phase 4 and 8 Mean simulated value No No No Average No TSP Delays of other phase (phase 3 and 7 Mean simulated value No No No Average No TSP Delays of phase 5 Mean simulated value No No No Average The calibration of the simulation model was conducted by comparing the simulation result with that of the analytical approach. In accordance with the analytical analysis, the random delays were excluded from the simulation. As shown in Table 4, the uniform delay and the residual queue delay from simulation are close to the calculated values when there is no TSP. The average deviations for phase 6, phase (3, 7, and phase (4, 8 are., 0.0, and.7, which indicates a less than 6% range between the analytical calculation and simulation values. For phase 5, the deviation is 9., which is still acceptable. Statistical analysis was conducted to furthermore evaluate these results. The impact of early green was derived from simulation runs and compared with the calculation results in Table 5. The average deviations for phase 6, phase (3, 7, phase 8 and 5 are.5, 7.3, 7., and.8 secs. The most significant error is 7.3 sec in phase (4, 8, which is still in 8.% range. Table 6 gives the result for the simulated and calculated values with the Green xtension. Similar to the case of the arly Green, the results agree with each other fairly well. To evaluate the impact of the vehicle speed to the simulation result, the speed of the passenger cars was changed from 35mph to 45mph and the speed of transit buses from 5mph to 35mph, and no significant effect was found. 4 Statistical test T-test is used for the proof of generality for the same case with different random seeds. nough simulation runs were made by using different random seeds. Ten different random seeds are tested and the results are summarized in Table 7. For the prioritized phase (phase 6 and phase (4, 8, the hypothesis is accepted at the 95% confident level. For phase (3, 7 and phase 5, the hypothesis is reected. This is reasonable because the analytical method is more accurate for the undersaturated situation. The degree of saturation is.67 for phase (3, 7 and.48 for phase 5. Table 5 Comparison between the analytical method and simulation with early green arly green Delays of bus priority phase (phase 6 No No No Average arly green Impact to other phase (phase 4 and 8 No No No Average arly green Impact to other phase (phase 3 and 7 No No No Average arly green Impact to phase 5 No No No Average

7 LIU Hongchao et al. / J Transpn Sys ng & IT, 008, 8(, 4857 Table 6 Comparison between the analytical method and simulation with green extension Green extension Delays of bus priority phase (phase 6 Impact to minor phase (phase 4,8 Impact to minor phase (phase 3,7 5 Conclusions Traffic simulation is a useful tool for the evaluation of a transit signal priority system. However, it is well-known that the development of simulation models has been inconsistent and proect specific. This paper presented an analytical approach for the design and evaluation of a transit signal priority system with the arly Green and xtended Green operations. Through graphical illustration, it was shown that the impact of arly Green and xtended Green on buses and general traffic could be quantified using D/D/ queuing models if the issue of concern is the induced delay. A numerical example was also presented. The result shows that the proposed method is promising in that it requires very limited information and provides fairly reasonable results. The analytical approach can be used independently or as a supplementary tool to simulation models for complicated situations. Future researches might include a comprehensive comparison analysis of the analytical approach with field observation and theoretical or data proof that TSP does not change the randomness of traffic flows, and extend the analytical approach for analysis of other TSP treatments such as the queue umpers and transit phases. Random seed Time point (s Table 7 Simulation results with different random seeds Phase 6 (-W Phase 4, 8 (S-N Phase 3, 7 (S-W Phase 5 (W-N Cal. Sim. Cal. Sim. Cal. Sim. Cal. Sim Phase Cal. Table 8 Result of T-test 95% confident interval lower upper p-value Accept or reect Accept 4, Accept 3, Reect Reect

8 LIU Hongchao et al. / J Transpn Sys ng & IT, 008, 8(, 4857 References [] Rakha H, Zhang Y. Sensitivity analysis of transit signal priority impacts on operation of a signalized intersection. J. Transp. ng., 004, 30(6: [] Liu H, Skabardonis A, Zhang W B, et al. Optimal detector location for transit signal priority. Transportation Research Record 867, Transportation Research Board, Washington D.C., 004, [3] Head K L, et al. Improved Traffic Signal Priority for Transit, TCRP Proect A-6 Interim Report, 00, /trb /crp.nsf /All+Proects/TCRP+A-6A, 007, November. [4] Wadas Y, Furth P G. Transit signal priority along an arterial using advanced detection. Transportation Research Record 856, Transportation Research Board, Washington D.C., 003, [5] Furth P G, Hemily B J, Muller T, et al. Uses of archived AVL-APC data to improve transit performance and management: review and potential. Transit Cooperative Research Program Web Document 3 (Proect H-8: Contractor s Final Report, 003. [6] Liu H. Development of Adaptive Transit Signal Priority Systems B, Theoretical Approach. Institute of transportation studies, University of California, Berkeley, 005. [7] Balke K N, Dudek C L, Thomas Urbanik II. Development and evaluation of intelligent bus priority concept. Transportation Research Record 77, Transportation Research Board, Washington, D.C., 000, 9. [8] Davol A P. Modeling of Traffic Signal Control and Transit Signal Priority Strategies in a Microscopic Simulation Laboratory, Massachusetts Institute of Technology, 00. [9] Shalaby A, Abdulhai B, Lee J. Assessment of streetcar transit signal priority options using microsimulation modeling. Canadian Journal of Civil ngineering, 003, 30(6: [0] Dion F, Rakha H, Zhang Y. valuation of potential transit signal priority benefits along a fixed-time signalized arterial. J. Transp. ng., 004, 30(3: [] Ngan V, Sayed T, Abdelfatah A. Impacts of various traffic parameters on transit signal priority effectiveness. Journal of Public Transportation, 004, 7(3: [] Sunkari S R, Beasley P S, Urbanik T, et al. Model to evaluate the impacts of bus priority on signalized intersections. Transportation Research Record 494, Transportation Research Board, Washington, D.C., 995, 7 3. [3] ITS America. An overview of transit signal priority. Advanced Traffic Management System, Committee and Advance Public Transportation System Committees, Washington, D.C., 003. [4] Smith H R, Hemily B, Ivanovic M. Transit Signal Priority (TSP: A Planning and Implementation Handbook. ITS America, Washington D.C., 005. [5] PTV America. Vissim 4.0 User Manual, Karlsruhe, Germany, 005.