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Extensions to online delay management on a single train line: new bounds for delay minimization and profit maximization

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  • Sven Krumke
  • Clemens Thielen
  • Christiane Zeck

Abstract

We present extensions to the Online Delay Management Problem on a Single Train Line. While a train travels along the line, it learns at each station how many of the passengers wanting to board the train have a delay of δ. If the train does not wait for them, they get delayed even more since they have to wait for the next train. Otherwise, the train waits and those passengers who were on time are delayed by δ. The problem consists in deciding when to wait in order to minimize the total delay of all passengers on the train line. We provide an improved lower bound on the competitive ratio of any deterministic online algorithm solving the problem using game tree evaluation. For the extension of the original model to two possible passenger delays δ 1 and δ 2 , we present a 3-competitive deterministic online algorithm. Moreover, we study an objective function modeling the refund system of the German national railway company, which pays passengers with a delay of at least Δ a part of their ticket price back. In this setting, the aim is to maximize the profit. We show that there cannot be a deterministic competitive online algorithm for this problem and present a 2-competitive randomized algorithm. Copyright Springer-Verlag 2011

Suggested Citation

  • Sven Krumke & Clemens Thielen & Christiane Zeck, 2011. "Extensions to online delay management on a single train line: new bounds for delay minimization and profit maximization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(1), pages 53-75, August.
    • Handle: RePEc:spr:mathme:v:74:y:2011:i:1:p:53-75
    DOI: 10.1007/s00186-011-0349-2
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    Citations

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    Cited by:

    1. Twan Dollevoet & Dennis Huisman & Leo Kroon & Marie Schmidt & Anita Schöbel, 2015. "Delay Management Including Capacities of Stations," Transportation Science, INFORMS, vol. 49(2), pages 185-203, May.
    2. Schön, Cornelia & König, Eva, 2018. "A stochastic dynamic programming approach for delay management of a single train line," European Journal of Operational Research, Elsevier, vol. 271(2), pages 501-518.
    3. Dollevoet, T.A.B. & Huisman, D. & Schöbel, A. & Schmidt, M.E., 2012. "Delay Management including Capacities of Stations," Econometric Institute Research Papers EI 2012-22, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    4. Li, Wenxin & Peng, Qiyuan & Wen, Chao & Wang, Pengling & Lessan, Javad & Xu, Xinyue, 2020. "Joint optimization of delay-recovery and energy-saving in a metro system: A case study from China," Energy, Elsevier, vol. 202(C).
    5. Anita Schöbel & Silvia Schwarze, 2013. "Finding delay-resistant line concepts using a game-theoretic approach," Netnomics, Springer, vol. 14(3), pages 95-117, November.
    6. König, Eva & Schön, Cornelia, 2021. "Railway delay management with passenger rerouting considering train capacity constraints," European Journal of Operational Research, Elsevier, vol. 288(2), pages 450-465.
    7. Eva König, 2020. "A review on railway delay management," Public Transport, Springer, vol. 12(2), pages 335-361, June.

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