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Transit Service and Path Choice Models in Stochastic and Time-Dependent Networks

Author

Listed:
  • Mark D. Hickman

    (Texas A&M University, Department of Civil Engineering, College Station, Texas 77843)

  • David H. Bernstein

    (Princeton University, Department of Civil Engineering and Operations Research, Princeton, New Jersey 08544)

Abstract

This paper develops a new path choice model that incorporates both time-dependent and stochastic transit service characteristics, and allows passengers to update path choice decisions while waiting. To develop this model, a new transit service model is proposed that represents route segments using a shuttle model. Such a model balances requirements for stochastic and time-dependent service modeling with the ability to aggregate to a larger transit corridor or network. This service model leads to a dynamic model of transit path choice, in which the passenger may wait until a vehicle is about to depart before making a boarding decision. A formal definition of this dynamic path choice model is given, and its differences with previous path choice models are noted. Based on this definition, two mathematical formulations of the dynamic model are developed. The first formulation assumes that the passenger will use the dynamic model for all possible vehicle departure times in the future, and is formulated as an optimal control problem. It is shown mathematically that this problem formulation is a less-constrained version of previous path choice models. However, because of some analytic and behavioral difficulties with this first model, a more well-behaved constrained formulation is also presented. A small corridor example demonstrates the significant differences in path choices and travel times between the constrained dynamic model and more traditional path choice models. Limitations of these dynamic path choice models are also discussed.

Suggested Citation

  • Mark D. Hickman & David H. Bernstein, 1997. "Transit Service and Path Choice Models in Stochastic and Time-Dependent Networks," Transportation Science, INFORMS, vol. 31(2), pages 129-146, May.
    • Handle: RePEc:inm:ortrsc:v:31:y:1997:i:2:p:129-146
    DOI: 10.1287/trsc.31.2.129
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    Citations

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    Cited by:

    1. Mohamed Wahba & Amer Shalaby, 2014. "Learning-based framework for transit assignment modeling under information provision," Transportation, Springer, vol. 41(2), pages 397-417, March.
    2. Yang, Lixing & Zhou, Xuesong, 2017. "Optimizing on-time arrival probability and percentile travel time for elementary path finding in time-dependent transportation networks: Linear mixed integer programming reformulations," Transportation Research Part B: Methodological, Elsevier, vol. 96(C), pages 68-91.
    3. Nielsen, Lars Relund & Andersen, Kim Allan & Pretolani, Daniele, 2014. "Ranking paths in stochastic time-dependent networks," European Journal of Operational Research, Elsevier, vol. 236(3), pages 903-914.
    4. Liu, Yang & Blandin, Sebastien & Samaranayake, Samitha, 2019. "Stochastic on-time arrival problem in transit networks," Transportation Research Part B: Methodological, Elsevier, vol. 119(C), pages 122-138.
    5. Hamdouch, Younes & Lawphongpanich, Siriphong, 2008. "Schedule-based transit assignment model with travel strategies and capacity constraints," Transportation Research Part B: Methodological, Elsevier, vol. 42(7-8), pages 663-684, August.
    6. Ahmad Tavassoli & Mahmoud Mesbah & Mark Hickman, 2020. "Calibrating a transit assignment model using smart card data in a large-scale multi-modal transit network," Transportation, Springer, vol. 47(5), pages 2133-2156, October.
    7. Hänseler, Flurin S. & van den Heuvel, Jeroen P.A. & Cats, Oded & Daamen, Winnie & Hoogendoorn, Serge P., 2020. "A passenger-pedestrian model to assess platform and train usage from automated data," Transportation Research Part A: Policy and Practice, Elsevier, vol. 132(C), pages 948-968.
    8. Giulio Cantarella & Pietro Velonà & David Watling, 2015. "Day-to-day Dynamics & Equilibrium Stability in A Two-Mode Transport System with Responsive bus Operator Strategies," Networks and Spatial Economics, Springer, vol. 15(3), pages 485-506, September.
    9. Khani, Alireza, 2019. "An online shortest path algorithm for reliable routing in schedule-based transit networks considering transfer failure probability," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 549-564.
    10. Leng, Nuannuan & Corman, Francesco, 2020. "The role of information availability to passengers in public transport disruptions: An agent-based simulation approach," Transportation Research Part A: Policy and Practice, Elsevier, vol. 133(C), pages 214-236.
    11. Ichoua, Soumia & Gendreau, Michel & Potvin, Jean-Yves, 2003. "Vehicle dispatching with time-dependent travel times," European Journal of Operational Research, Elsevier, vol. 144(2), pages 379-396, January.
    12. Ahmad Tavassoli & Mahmoud Mesbah & Mark Hickman, 2018. "Application of smart card data in validating a large-scale multi-modal transit assignment model," Public Transport, Springer, vol. 10(1), pages 1-21, May.
    13. Yang, Lixing & Zhou, Xuesong, 2014. "Constraint reformulation and a Lagrangian relaxation-based solution algorithm for a least expected time path problem," Transportation Research Part B: Methodological, Elsevier, vol. 59(C), pages 22-44.
    14. Tarun Rambha & Stephen D. Boyles & S. Travis Waller, 2016. "Adaptive Transit Routing in Stochastic Time-Dependent Networks," Transportation Science, INFORMS, vol. 50(3), pages 1043-1059, August.

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