IDEAS home Printed from https://ideas.repec.org/a/inm/ortrsc/v35y2001i3p215-237.html
   My bibliography  Save this article

An Analytic Stochastic Model for the Transit Vehicle Holding Problem

Author

Listed:
  • Mark D. Hickman

    (Department of Civil Engineering and Engineering Mechanics, The University of Arizona, Tucson, Arizona 85721-0072)

Abstract

This paper describes an analytic model that determines the optimal vehicle holding time at a control stop along a transit route. This model is based on a stochastic transit service model presented by Andersson and Scalia-Tomba (1981) and enhanced by Marguier (1985). The use of a stochastic service model allows greater realism in the analytic modeling. Making use of these results, the paper presents an analytic model that may be used to determine the optimal holding time for a vehicle at a control stop. As it is formulated, the single vehicle holding problem is a convex quadratic program in a single variable, and is easily solved using gradient or line search techniques. The analytic holding model overcomes two noted problems in the literature: it includes stochastic service attributes of vehicle running times and passenger boarding and alighting processes, and the model may be used for real-time control purposes. The use and potential benefits of the model are illustrated in a simple example. This model may be useful in developing a computerized decision support system to enhance the effectiveness of transit operational decision-making.

Suggested Citation

  • Mark D. Hickman, 2001. "An Analytic Stochastic Model for the Transit Vehicle Holding Problem," Transportation Science, INFORMS, vol. 35(3), pages 215-237, August.
    • Handle: RePEc:inm:ortrsc:v:35:y:2001:i:3:p:215-237
    DOI: 10.1287/trsc.35.3.215.10150
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/trsc.35.3.215.10150
    Download Restriction: no
    File URL: https://libkey.io/10.1287/trsc.35.3.215.10150?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Arnold Barnett, 1974. "On Controlling Randomness in Transit Operations," Transportation Science, INFORMS, vol. 8(2), pages 102-116, May.
    2. G. F. Newell, 1974. "Control of Pairing of Vehicles on a Public Transportation Route, Two Vehicles, One Control Point," Transportation Science, INFORMS, vol. 8(3), pages 248-264, August.
    3. Warren B. Powell & Yosef Sheffi, 1983. "A Probabilistic Model of Bus Route Performance," Transportation Science, INFORMS, vol. 17(4), pages 376-404, November.
    4. Philippe H. J. Marguier & Avishai Ceder, 1984. "Passenger Waiting Strategies for Overlapping Bus Routes," Transportation Science, INFORMS, vol. 18(3), pages 207-230, August.
    5. E. E. Osuna & G. F. Newell, 1972. "Control Strategies for an Idealized Public Transportation System," Transportation Science, INFORMS, vol. 6(1), pages 52-72, February.
    6. Arnold I. Barnett, 1978. "Control Strategies for Transport Systems with Nonlinear Waiting Costs," Transportation Science, INFORMS, vol. 12(2), pages 119-136, May.
    7. J. K. Jolliffe & T. P. Hutchinson, 1975. "A Behavioural Explanation of the Association Between Bus and Passenger Arrivals at a Bus Stop," Transportation Science, INFORMS, vol. 9(3), pages 248-282, August.
    8. Adamski, Andrzej & Turnau, Andrzej, 1998. "Simulation support tool for real-time dispatching control in public transport," Transportation Research Part A: Policy and Practice, Elsevier, vol. 32(2), pages 73-87, February.
    9. Adamski, Andrzej, 1992. "Probabilistic models of passengers service processes at bus stops," Transportation Research Part B: Methodological, Elsevier, vol. 26(4), pages 253-259, August.
    10. R. A. Chapman & J. F. Michel, 1978. "Modelling the Tendency of Buses to Form Pairs," Transportation Science, INFORMS, vol. 12(2), pages 165-175, May.
    11. Andersson, Per-Åke & Scalia-Tomba, Gian-Paolo, 1981. "A mathematical model of an urban bus route," Transportation Research Part B: Methodological, Elsevier, vol. 15(4), pages 249-266, August.
    12. Adebisi, O., 1986. "A mathematical model for headway variance of fixed-route buses," Transportation Research Part B: Methodological, Elsevier, vol. 20(1), pages 59-70, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hall, Randolph & Dessouky, Maged & Zhang, Lei & Singh, Ajay & Patel, Vishal, 1999. "Evaluation of ITS Technology for Bus Transit Systems," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt2nq1824t, Institute of Transportation Studies, UC Berkeley.
    2. Mohammad Reza Amin-Naseri & Vahid Baradaran, 2015. "Accurate Estimation of Average Waiting Time in Public Transportation Systems," Transportation Science, INFORMS, vol. 49(2), pages 213-222, May.
    3. Andres, Matthias & Nair, Rahul, 2017. "A predictive-control framework to address bus bunching," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 123-148.
    4. Dessouky, Maged & Hall, Randolph & Zhang, Lei & Singh, Ajay, 2003. "Real-time control of buses for schedule coordination at a terminal," Transportation Research Part A: Policy and Practice, Elsevier, vol. 37(2), pages 145-164, February.
    5. Sánchez-Martínez, G.E. & Koutsopoulos, H.N. & Wilson, N.H.M., 2016. "Real-time holding control for high-frequency transit with dynamics," Transportation Research Part B: Methodological, Elsevier, vol. 83(C), pages 1-19.
    6. Jiamin Zhao & Maged Dessouky & Satish Bukkapatnam, 2006. "Optimal Slack Time for Schedule-Based Transit Operations," Transportation Science, INFORMS, vol. 40(4), pages 529-539, November.
    7. Xuan, Yiguang & Argote, Juan & Daganzo, Carlos F., 2011. "Dynamic bus holding strategies for schedule reliability: Optimal linear control and performance analysis," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1831-1845.
    8. Adamski, Andrzej & Turnau, Andrzej, 1998. "Simulation support tool for real-time dispatching control in public transport," Transportation Research Part A: Policy and Practice, Elsevier, vol. 32(2), pages 73-87, February.
    9. Bian, Bomin & Zhu, Ning & Meng, Qiang, 2023. "Real-time cruising speed design approach for multiline bus systems," Transportation Research Part B: Methodological, Elsevier, vol. 170(C), pages 1-24.
    10. Xuan, Yiguang & Argote, Juan & Daganzo, Carlos F., 2011. "A Dynamic Holding Strategy to Improve Bus ScheduleReliability and Commercial Speed," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt0jp7c8k8, Institute of Transportation Studies, UC Berkeley.
    11. Zhang, Shuyang & Lo, Hong K., 2018. "Two-way-looking self-equalizing headway control for bus operations," Transportation Research Part B: Methodological, Elsevier, vol. 110(C), pages 280-301.
    12. Carey, Malachy & Kwiecinski, Andrzej, 1995. "Properties of expected costs and performance measures in stochastic models of scheduled transport," European Journal of Operational Research, Elsevier, vol. 83(1), pages 182-199, May.
    13. Gkiotsalitis, K. & Cats, O., 2021. "At-stop control measures in public transport: Literature review and research agenda," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 145(C).
    14. Gkiotsalitis, K. & Alesiani, F., 2019. "Robust timetable optimization for bus lines subject to resource and regulatory constraints," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 128(C), pages 30-51.
    15. Pilachowski, Joshua Michael, 2009. "An Approach to Reducing Bus Bunching," University of California Transportation Center, Working Papers qt6zc5j8xg, University of California Transportation Center.
    16. Vismara, Luca & Chew, Lock Yue & Saw, Vee-Liem, 2021. "Optimal assignment of buses to bus stops in a loop by reinforcement learning," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    17. Klumpenhouwer, W. & Wirasinghe, S.C., 2018. "Optimal time point configuration of a bus route - A Markovian approach," Transportation Research Part B: Methodological, Elsevier, vol. 117(PA), pages 209-227.
    18. Alexander Webb & Pramesh Kumar & Alireza Khani, 2020. "Estimation of passenger waiting time using automatically collected transit data," Public Transport, Springer, vol. 12(2), pages 299-311, June.
    19. Berrebi, Simon J. & Crudden, Sean Óg & Watkins, Kari E., 2018. "Translating research to practice: Implementing real-time control on high-frequency transit routes," Transportation Research Part A: Policy and Practice, Elsevier, vol. 111(C), pages 213-226.
    20. Dessouky, Maged & Singh, Ajay & Hall, Randolph, 1997. "Transit ITS Simulator (TRANSITS): Design Document," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt49k184rv, Institute of Transportation Studies, UC Berkeley.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ortrsc:v:35:y:2001:i:3:p:215-237. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.