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The Holding Problem at Multiple Holding Stations

In: Computer-aided Systems in Public Transport

Author

Listed:
  • Aichong Sun

    (Pima Association of Governments)

  • Mark Hickman

    (University of Arizona)

Abstract

Inherent stochasticity within the transit operating environment suggests there may be benefits of holding vehicles at more than one holding station on a route. In this paper, the holding problem at multiple holding stations considers holding vehicles at a given subset of stations on the route. By approximating the vehicle dwell time as the passenger boarding time, the holding problem at multiple holding stations can be modeled as a convex quadratic programming problem, with the objective function as a convex quadratic function subject to many linear constraints. This particular problem can be solved by a heuristic that decomposes the overall problem into sub-problems which can be solved to optimality. Also, a hypothetical numerical example is presented to illustrate the effectiveness of the problem formulation and heuristic.

Suggested Citation

  • Aichong Sun & Mark Hickman, 2008. "The Holding Problem at Multiple Holding Stations," Lecture Notes in Economics and Mathematical Systems, in: Mark Hickman & Pitu Mirchandani & Stefan Voß (ed.), Computer-aided Systems in Public Transport, pages 339-359, Springer.
    • Handle: RePEc:spr:lnechp:978-3-540-73312-6_17
    DOI: 10.1007/978-3-540-73312-6_17
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    Citations

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    Cited by:

    1. Hadas, Yuval & Shnaiderman, Matan, 2012. "Public-transit frequency setting using minimum-cost approach with stochastic demand and travel time," Transportation Research Part B: Methodological, Elsevier, vol. 46(8), pages 1068-1084.
    2. Liang, Shidong & Zhao, Shuzhi & Lu, Chunxiu & Ma, Minghui, 2016. "A self-adaptive method to equalize headways: Numerical analysis and comparison," Transportation Research Part B: Methodological, Elsevier, vol. 87(C), pages 33-43.
    3. 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.
    4. Khan, Zaid Saeed & Menéndez, Mónica, 2023. "Bus splitting and bus holding: A new strategy using autonomous modular buses for preventing bus bunching," Transportation Research Part A: Policy and Practice, Elsevier, vol. 177(C).
    5. Delgado, Felipe & Munoz, Juan Carlos & Giesen, Ricardo, 2012. "How much can holding and/or limiting boarding improve transit performance?," Transportation Research Part B: Methodological, Elsevier, vol. 46(9), pages 1202-1217.
    6. Sun, Yanshuo & Schonfeld, Paul, 2016. "Holding decisions for correlated vehicle arrivals at intermodal freight transfer terminals," Transportation Research Part B: Methodological, Elsevier, vol. 90(C), pages 218-240.
    7. Ibarra-Rojas, O.J. & Delgado, F. & Giesen, R. & Muñoz, J.C., 2015. "Planning, operation, and control of bus transport systems: A literature review," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 38-75.
    8. 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).

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