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Online delay management on a single train line: beyond competitive analysis

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Abstract

We consider the Online Delay Management Problem (ODMP) on a network with a path topology that is served by one train. In this problem the number of delayed passengers who want to board the train is not known beforehand but revealed in an online fashion once the train arrives at the corresponding station. The goal is to decide at which station a train should wait in order to minimize the total delay of all passengers.

Competitive analysis has become one of the standard tools to evaluate the performance of algorithms in the presence of incomplete information from a theoretical point of view. The ODMP has been analyzed by means of classical competitive analysis, where one compares the output of an online algorithm with that of an optimal offline algorithm which has complete knowledge about the input data. In this paper we use different approaches to overcome the often criticized pessimism of standard competitive analysis: lookahead, comparative analysis and average-case analysis. Each of these approaches extends the classical worst-case approach of competitive analysis in different aspects. We complement these extensions by addressing the problem from the viewpoint of stochastic optimization. We discuss the theoretical benefits of the concepts and provide a case-study on real world data.

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Notes

  1. In the original paper Koutsoupias and Papadimitriou (2000), the authors speak of the “comparative ratio of \(\mathcal{A}\) and \(\mathcal{B}\)”. We use “with respect to” instead to emphasize the asymmetry in the definition.

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Acknowledgement

We thank the anonymous referees for making suggestions to make the paper more consistent and easier to read. In particular, the comments about the greater outline were very helpful. We also thank the LinTim team for providing the Athens data.

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Authors and Affiliations

  1. Institute for Numerical and Applied Mathematics, University of Goettingen, Lotzestraße 16-18, 37083, Göttingen, Germany

    Marco Bender

  2. Department of Mathematics, University of Kaiserslautern, Paul-Ehrlich-Str. 14, 67663, Kaiserslautern, Germany

    Sabine Büttner & Sven O. Krumke

Authors
  1. Marco Bender
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  2. Sabine Büttner
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  3. Sven O. Krumke
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Correspondence to Sven O. Krumke.

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Bender, M., Büttner, S. & Krumke, S.O. Online delay management on a single train line: beyond competitive analysis. Public Transp 5, 243–266 (2013). https://doi.org/10.1007/s12469-013-0070-z

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