Abstract
Bus holding strategy is an effective way for alleviating inevitable disruptions along a bus route, including decisions on the control point locations and slack duration. However, at present, the locations of the control points and corresponding slack times are largely determined by engineering experience and therefore lack theoretical optimization. The aim of this study is to develop a model which can jointly optimize the locations of the control points and corresponding slack times under a given number of control points. As locations of the upstream control points will influence the downstream operation states, this optimization problem is modeled as a multi-stage decision process. To evaluate the stability and efficiency of a bus system, we calculate the punctuality rate and travel time at each stage by taking into account the uncertainty along the route and propose a reasonable stage-utilization cost combing these two factors. A numerical case study based on a real bus route in Harbin of China is carried out to demonstrate our approach. The impacts of the weighting factor and slack times on the optimal control point plan are also discussed.
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Altun, S. Z. and Furth, P. G. (2009). “Scheduling buses to take advantage of transit signal priority.” Transportation Research Record: Journal of the Transportation Research Board, Vol. 2111, pp. 50–59, DOI: 10.3141/2111-07.
Bie, Y., Gong, X., and Liu, Z. (2015). “Time of day intervals partition for bus schedule using GPS data.” Transportation Research Part C: Emerging Technologies, Vol. 60, pp. 443–456, DOI: 10.1016/j.trc.2015.09.016.
Bie, Y., Wang, D., and Qi, H. (2012). “Prediction model of bus arrival time at signalized intersection using GPS data.” Journal of Transportation Engineering, Vol. 138, No. 1, pp. 12–20, DOI: 10.1061/(ASCE)TE.1943-5436.0000310.
Cats, O., Rufi, F. M., and Koutsopoulos, H. N. (2014). “Optimizing the number and location of time point stops.” Public Transport, Vol. 6, No. 3, pp. 215–235, DOI: 10.1007/s12469-014-0092-1.
Chen, J., Wang, S., Liu, Z., and Chen, X. (2018). “Network-level optimization of bus stop placement in urban areas.” KSCE Journal of Civil Engineering, Vol. 22, No. 4, pp. 1446–1453, DOI: 10.1007/s12205-017-0075-2.
Chen, P., Zheng, F., Lu, G., and Wang, Y. (2016). “Comparison of variability of individual vehicle delay and average control delay at signalized intersections.” Transportation Research Record: Journal of the Transportation Research Board, Vol. 2553, pp. 128–137, DOI: 10.3141/2553-14.
Dou, X., Yan, Y., Guo, X., and Gong, X. (2016). “Time control point strategy coupled with transfer coordination in bus schedule design.” Journal of Advanced Transportation, Vol. 50, No. 7, pp. 1336–1351, DOI: 10.1002/atr.1404.
Fu, L. and Yang, X. (2002). “Design and implementation of bus-holding control strategies with real-time information.” Transportation Research Record: Journal of the Transportation Research Board, Vol. 1791, pp. 6–12, DOI: 10.3141/1791-02.
Furth, P. G. and Miller, T. H. J. (2009). “Optimality conditions for public transport schedules with time point holding.” Public Transportation, Vol. 1, pp. 87–102, DOI: 10.1007/s12469-008-0002-5.
Guo, X., Sun, H., Wu, J., Jin, J., Zhou, J., and Gao, Z. (2017). “Multiperiodbased timetable optimization for metro transit networks.” Transportation Research Part B: Methodological, Vol. 96, pp. 46–67, DOI: 10.1016/j.trb.2016.11.005.
Liu, G. and Wirasinghe, S. C. (2001). “A simulation model of reliable schedule design for a fixed transit route.” Journal of Advanced Transportation, Vol. 35, No. 2, pp. 145–174, DOI: 10.1002/atr.5670350206.
Liu, Z., Yan, Y., Qu, X., and Zhang, Y. (2013). “Bus stop-skipping scheme with random travel time.” Transportation Research Part C: Emerging Technologies, Vol. 35, pp. 46–56, DOI: 10.1016/j.trc.2013.06.004.
Lu, L., Gu, Z., Huang, D., Liu, Z., and Chen, J. (2017). “An evaluation framework for the public information guidance system.” KSCE Journal of Civil Engineering, Vol. 21, No. 5, pp. 1919–1928, DOI: 10.1007/s12205-016-0888-4.
Ma, X., Liu, C., Wen, H., Wang, Y., and Wu, Y. (2017). “Understanding commuting patterns using transit smart card data.” Journal of Transport Geography, Vol. 58, pp.135–145, DOI: 0.1016/j.jtrangeo.2016.12.001.
Ma, X., Tao, Z., Wang, Y., Yu, H., and Wang, Y. (2015). “Long short-term memory neural network for traffic speed prediction using remote microwave sensor data.” Transportation Research Part C: Emerging Technologies, Vol. 54, pp. 187–197, DOI: 10.1016/j.trc.2015.03.014.
Ma, X., Wu, Y. J., Wang, Y., Chen, F., and Liu, J. (2013). “Mining smart card data for transit riders’ travel patterns.” Transportation Research Part C: Emerging Technologies, Vol. 36, pp. 1–12, DOI: 10.1016/j.trc.2013.07.010.
Mazloumi, E., Mesbah, M., Ceder, A., Moridpour, S., and Currie, G., (2012). “Efficient transit schedule design of timing points: A comparison of ant colony and genetic algorithms.” Transportation Research Part B: Methodological, Vol. 60, No. 1, pp. 217–234, DOI: 10.1016/j.trb.2011.09.010.
Qu, X., Oh, E., Weng, J., and Jin, S. (2014). “Bus travel time reliability analysis: A case study.” Proceedings of the Institution of Civil Engineers-Transport, Vol. 167, No. 3, pp. 178–184, DOI: 10.5220/0006971003750378.
Verbas, I. Ö., Frei, C., Mahmassani, H. S., and Chan, R. (2015). “Stretching resources: Sensitivity of optimal bus frequency allocation to stoplevel demand elasticities.” Public Transport, Vol. 7, No. 1, pp. 1–20, DOI: 10.1007/s12469-013-0084-6.
Wang, S. and Qu, X. (2017). “Station choice for Australian commuter rail lines: Equilibrium and optimal fare design.” European Journal of Operational Research, Vol. 258, No. 1, pp. 144–154, DOI: 10.1016/j.ejor.2016.08.040.
Wang, S., Qu, X., and Yang, Y. (2015). “Estimation of the perceived value of transit time for containerized cargoes.” Transportation Research Part A: Policy and Practice, Vol. 78, pp. 298–308, DOI: 10.1016/j.tra.2015.04.014.
Wirasinghe, S. C. and Liu, G. (1995). “Determination of the number and locations of time-points in transit schedule design.” Annuals of Operations Research, Vol. 60, pp.161–191, DOI: 10.1007/bf02031945.
Wu, Y., Yang, H., Tang, J., and Yu, Y. (2016). “Multi-objective resynchronizing of bus timetable: Model, complexity and solution.” Transportation Research Part C: Emerging Technologies, Vol. 67, pp. 149–168, DOI: 10.1016/j.trc.2016.02.007.
Xuan, Y., Argote, J., and Daganzo, C. F. (2011). “Dynamic bus holding strategies for schedule reliability: Optimal linear control and performance analysis.” Transportation Research Part B: Methodological, Vol. 45, No. 10, pp. 1831–1845, DOI: 10.1016/j.trb.2011.07.009.
Yan, Y., Meng, Q., Wang, S., and Guo, X., (2012). “Robust optimization model of schedule design for a fixed bus route.” Transportation Research Part C: Emerging Technologies, Vol. 25, pp. 113–121, DOI: 10.1016/j.trc.2012.05.006.
Yu, B., Yang, Z., and Yao, J. (2009). “Genetic algorithm for bus frequency optimization.” Journal of Transportation Engineering, Vol. 136, No. 6, pp. 576–583, DOI: 10.1061/(asce)te.1943-5436.0000119.
Yu, B., Yao, J., and Yang, Z. Z. (2010). “An improved headway-based holding strategy for bus transit.” Transportation Planning and Technology, Vol. 33, No. 3, pp. 329–341, DOI: 10.1080/03081061003732417.
Zhao, J., Dessouky, M., and Bukkapatnam, S. (2006). “Optimal slack time for schedule-based transit operations.” Transportation Science, Vol. 40, No. 4, pp. 529–539, DOI: 10.1287/trsc.1060.0170.
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Wang, Y., Bie, Y. & Zhang, L. Joint Optimization for the Locations of Time Control Points and Corresponding Slack Times for a Bus Route. KSCE J Civ Eng 23, 411–419 (2019). https://doi.org/10.1007/s12205-018-1491-7
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DOI: https://doi.org/10.1007/s12205-018-1491-7