Vehicle Capacity-Aware Rerouting of Passengers in Delay Management

Authors Matthias Müller-Hannemann , Ralf Rückert, Sebastian S. Schmidt

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Matthias Müller-Hannemann
  • Institut für Informatik, Martin-Luther-Universität Halle-Wittenberg, Von-Seckendorff-Platz 1, D 06120 Halle (Saale), Germany
Ralf Rückert
  • Institut für Informatik, Martin-Luther-Universität Halle-Wittenberg, Von-Seckendorff-Platz 1, D 06120 Halle (Saale), Germany
Sebastian S. Schmidt
  • Institut für Informatik, Martin-Luther-Universität Halle-Wittenberg, Von-Seckendorff-Platz 1, D 06120 Halle (Saale), Germany


The authors wish to thank Deutsche Bahn for providing test data.

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Matthias Müller-Hannemann, Ralf Rückert, and Sebastian S. Schmidt. Vehicle Capacity-Aware Rerouting of Passengers in Delay Management. In 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019). Open Access Series in Informatics (OASIcs), Volume 75, pp. 7:1-7:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


Due to the significant growth in passenger numbers, higher vehicle load factors and crowding become more and more of an issue in public transport. For safety reasons and because of an unsatisfactory discomfort, standing of passengers is rather limited in high-speed long-distance trains. In case of delays and (partially) cancelled trains, many passengers have to be rerouted. State-of-the-art rerouting merely focuses on minimizing delay at the destination of affected passengers but neglects limited vehicle capacities and crowding. Not considering capacities allows using highly efficient shortest path algorithms like RAPTOR or the connection scan algorithm (CSA). In this paper, we study the more complicated scenario where passengers compete for scarce capacities. This can be modeled as a piece-wise linear, convex cost multi-source multi-commodity unsplittable flow problem where each passenger group which has to be rerouted corresponds to a commodity. We compare a path-based integer linear programming (ILP) model with a heuristic greedy approach. In experiments with instances from German long-distance train traffic, we quantify the importance of considering vehicle capacities in case of train cancellations. We observe a tradeoff: The ILP approach slightly outperforms the greedy approach and both are much better than capacity unaware rerouting in quality, while the greedy algorithm runs more than three times faster.

Subject Classification

ACM Subject Classification
  • Applied computing → Transportation
  • Theory of computation → Discrete optimization
  • Mathematics of computing → Network flows
  • Delay management
  • passenger flows
  • vehicle capacities
  • rerouting


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