Multi-Source Multi-Sink Nash Flows over Time

Authors Leon Sering, Martin Skutella

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Leon Sering
  • Institute of Mathematics, Technische Universität Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany
Martin Skutella
  • Institute of Mathematics, Technische Universität Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany

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Leon Sering and Martin Skutella. Multi-Source Multi-Sink Nash Flows over Time. In 18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018). Open Access Series in Informatics (OASIcs), Volume 65, pp. 12:1-12:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


Nash flows over time describe the behavior of selfish users eager to reach their destination as early as possible while traveling along the arcs of a network with capacities and transit times. Throughout the past decade, they have been thoroughly studied in single-source single-sink networks for the deterministic queuing model, which is of particular relevance and frequently used in the context of traffic and transport networks. In this setting there exist Nash flows over time that can be described by a sequence of static flows featuring special properties, so-called `thin flows with resetting'. This insight can also be used algorithmically to compute Nash flows over time. We present an extension of these results to networks with multiple sources and sinks which are much more relevant in practical applications. In particular, we come up with a subtle generalization of thin flows with resetting, which yields a compact description as well as an algorithmic approach for computing multi-terminal Nash flows over time.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Network flows
  • Theory of computation → Network games
  • Network congestion
  • Nash equilibrium
  • dynamic routing game
  • deterministic queuing model


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