Modelling travel time distribution and its influence over stochastic vehicle scheduling
Abstract
Due to the paucity of well-established modelling approaches or well-accepted travel time distributions, the existing travel time models are often assumed to follow certain popular distributions, such as normal or lognormal, which may lead to results deviating from actual ones. This paper proposes a modelling approach for travel times using distribution fitting methods based on the data collected by Automatic Vehicle Location (AVL) systems. By this proposed approach, a compound travel time model can be built, which consists of the best distribution models for the travel times in each period of a day. Applying to stochastic vehicle scheduling, the influence of different travel time models is further studied. Results show that the compound model can fit more precisely to the actual travel times under various traffic situations, whilst the on-time performance of resulting vehicle schedules can be improved. The research findings have also potential benefit for the other research based on travel time models in public transport including timetabling, service planning and reliability measurement.
Keyword : public transit, travel time, distribution fitting, stochastic vehicle scheduling, AVL data
How to Cite
Shen, Y., Xu, J., Wu, X., & Ni, Y. (2019). Modelling travel time distribution and its influence over stochastic vehicle scheduling. Transport, 34(2), 237-249. https://doi.org/10.3846/transport.2019.8940
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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TRB. 2013. Transit Capacity and Quality of Service Manual. Transportation Research Board (TRB’s) Transit Cooperative Research Program (TCRP) Report 165, Washington, DC, US. https://doi.org/10.17226/24766
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Van Oort, N.; Boterman, J. W.; Van Nes, R. 2012. The impact of scheduling on service reliability: trip-time determination and holding points in long-headway services, Public Transport 4(1): 39–56. https://doi.org/10.1007/s12469-012-0054-4
Vu, N. H.; Khan, A. M. 2010. Bus running time prediction using a statistical pattern recognition technique, Transportation Planning and Technology 33(7): 625–642. https://doi.org/10.1080/03081060.2010.512225
Xu, J.; Shen, Y. 2012. Setting scheduled trip time based on AVL data, Journal of Transportation Systems Engineering and Information Technology 12(5): 39–45. https://doi.org/10.1016/S1570-6672(11)60222-5
Yan, Y.; Meng, Q.; Wang, S.; Guo, X. 2012. Robust optimization model of schedule design for a fixed bus route, Transportation Research Part C: Emerging Technologies 25: 113–121. https://doi.org/10.1016/j.trc.2012.05.006
Zhao, J.; Dessouky, M.; Bukkapatnam, S. 2006. Optimal slack time for schedule-based transit operations, Transportation Science 40(4): 529–539. https://doi.org/10.1287/trsc.1060.0170
Akaike, H. 1974. A new look at the statistical model identification, IEEE Transactions on Automatic Control 19(6): 716–723. https://doi.org/10.1109/TAC.1974.1100705
Bunte, S.; Kliewer, N. 2009. An overview on vehicle scheduling models, Public Transport 1(4): 299–317. https://doi.org/10.1007/s12469-010-0018-5
Ceder, A. 2007. Public Transit Planning and Operation: Theory, Modeling and Practice. Butterworth-Heinemann. 640 p.
Chakroborty, P.; Kikuchi, S. 2004. Using bus travel time data to estimate travel times on urban corridors, Transportation Research Record: Journal of the Transportation Research Board 1870: 18–25. https://doi.org/10.3141/1870-03
Dessouky, M.; Hall, R.; Nowroozi, A.; Mourikas, K. 1999. Bus dispatching at timed transfer transit stations using bus tracking technology, Transportation Research Part C: Emerging Technologies 7(4): 187–208. https://doi.org/10.1016/S0968-090X(99)00019-4
Furth, P. G.; Hemily, B.; Muller, T. H. J.; Strathman, J. G. 2006. Using Archived AVL-APC Data to Improve Transit Performance and Management. Transportation Research Board’s (TRB’s) Transit Cooperative Research Program (TCRP) Report 113, Washington, DC, US. 94 p. https://doi.org/10.17226/13907
Furth, P. G.; Muller, T. H. J. 2007. Service reliability and optimal running time schedules, Transportation Research Record: Journal of the Transportation Research Board 2034: 55–61. https://doi.org/10.3141/2034-07
Huisman, D.; Freling, R.; Wagelmans, A. P. M. 2004. A robust solution approach to the dynamic vehicle scheduling problem, Transportation Science 38(4): 447–458. https://doi.org/10.1287/trsc.1030.0069
Kieu, L.-M.; Bhaskar, A.; Chung, E. 2015. Public transport traveltime variability definitions and monitoring, Journal of Transportation Engineering 141(1). https://doi.org/10.1061/(ASCE)TE.1943-5436.0000724
Kuo, Y.; Luo, C.-M.; Wang, C.-C. 2013. Bus route design with limited travel time, Transport 28(4): 368–373. https://doi.org/10.3846/16484142.2013.865103
Li, R.; Rose, G.; Sarvi, M. 2006. Using automatic vehicle identification data to gain insight into travel time variability and its causes, Transportation Research Record: Journal of the Transportation Research Board 1945: 24–32. https://doi.org/10.1177/0361198106194500104
Mazloumi, E.; Currie, G.; Rose, G. 2010. Using GPS data to gain insight into public transport travel time variability, Journal of Transportation Engineering 136(7): 623–631. https://doi.org/10.1061/(ASCE)TE.1943-5436.0000126
Mori, U.; Mendiburu, A.; Álvarez, M.; Lozano, J. A. 2015. A review of travel time estimation and forecasting for advanced traveller information systems, Transportmetrica A: Transport Science 11(2): 119–157. https://doi.org/10.1080/23249935.2014.932469
Muller, T. H. J.; Furth, P. G. 2000. Integrating bus service planning with analysis, operational control and performance monitoring, in ITS America 10th Annual Meeting and Exposition: Revolutionary Thinking, Real Results, 1–4 May 2000, Washington, DC, US, 1–20.
Naumann, M.; Suhl, L.; Kramkowski, S. 2011. A stochastic programming approach for robust vehicle scheduling in public bus transport, Procedia – Social and Behavioral Sciences 20: 826–835. https://doi.org/10.1016/j.sbspro.2011.08.091
Ng, M.; Szeto, W. Y.; Waller, S. T. 2011. Distribution-free travel time reliability assessment with probability inequalities, Transportation Research Part B: Methodological 45(6): 852–866. https://doi.org/10.1016/j.trb.2011.03.003
Pu, W. 2011. Analytic relationships between travel time reliability measures, Transportation Research Record: Journal of the Transportation Research Board 2254: 122–130. https://doi.org/10.3141/2254-13
Salicrú, M.; Fleurent, C.; Armengol, J. M. 2011. Timetable-based operation in urban transport: run-time optimisation and improvements in the operating process, Transportation Research Part A: Policy and Practice 45(8): 721–740. https://doi.org/10.1016/j.tra.2011.04.013
Shen, Y.; Xu, J.; Li, J. 2016. A probabilistic model for vehicle scheduling based on stochastic trip times, Transportation Research Part B: Methodological 85: 19–31. https://doi.org/10.1016/j.trb.2015.12.016
Shen, Y.-D.; Zhang, T.-H.; Xu, J. 2014. Homogeneous bus running time bands analysis based on k-means algorithms, Journal of Transportation Systems Engineering and Information Technology 14(2): 87–93. (in Chinese).
Srinivasan, K. K.; Prakash, A. A.; Seshadri, R. 2014. Finding most reliable paths on networks with correlated and shifted log-normal travel times, Transportation Research Part B: Methodological 66: 110–128. https://doi.org/10.1016/j.trb.2013.10.011
Taylor, M. A. P.; Susilawati. 2012. Modelling travel time reliability with the Burr distribution, Procedia – Social and Behavioral Sciences 54: 75–83. https://doi.org/10.1016/j.sbspro.2012.09.727
TRB. 2013. Transit Capacity and Quality of Service Manual. Transportation Research Board (TRB’s) Transit Cooperative Research Program (TCRP) Report 165, Washington, DC, US. https://doi.org/10.17226/24766
Uniman, D. L.; Attanucci, J.; Mishalani, R. G.; Wilson, N. H. M. 2010. Service reliability measurement using automated fare card data: application to the London underground, Transportation Research Record: Journal of the Transportation Research Board 2143: 92–99. https://doi.org/10.3141/2143-12
Van Lint, J. W. C.; Van Zuylen, H. J.; Tu, H. 2008. Travel time unreliability on freeways: why measures based on variance tell only half the story, Transportation Research Part A: Policy and Practice 42(1): 258–277. https://doi.org/10.1016/j.tra.2007.08.008
Van Oort, N.; Boterman, J. W.; Van Nes, R. 2012. The impact of scheduling on service reliability: trip-time determination and holding points in long-headway services, Public Transport 4(1): 39–56. https://doi.org/10.1007/s12469-012-0054-4
Vu, N. H.; Khan, A. M. 2010. Bus running time prediction using a statistical pattern recognition technique, Transportation Planning and Technology 33(7): 625–642. https://doi.org/10.1080/03081060.2010.512225
Xu, J.; Shen, Y. 2012. Setting scheduled trip time based on AVL data, Journal of Transportation Systems Engineering and Information Technology 12(5): 39–45. https://doi.org/10.1016/S1570-6672(11)60222-5
Yan, Y.; Meng, Q.; Wang, S.; Guo, X. 2012. Robust optimization model of schedule design for a fixed bus route, Transportation Research Part C: Emerging Technologies 25: 113–121. https://doi.org/10.1016/j.trc.2012.05.006
Zhao, J.; Dessouky, M.; Bukkapatnam, S. 2006. Optimal slack time for schedule-based transit operations, Transportation Science 40(4): 529–539. https://doi.org/10.1287/trsc.1060.0170