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Time-Expanded Graphs for Flow-Dependent Transit Times

Köhler, Ekkehard; Langkau, Katharina; Skutella, Martin

Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin

Motivated by applications in road traffic control, we study flows in networks featuring special characteristics. In contrast to classical static flow problems, time plays a decisive role. Firstly, there are transit times on the arcs of the network which specify the amount of time it takes for flow to travel through a particular arc; more precisely, flow values on arcs may change over time. Secondly, the transit time of an arc varies with the current amount of flow using this arc. Especially the latter feature is crucial for various real-life applications of flows over time; yet, it dramatically increases the degree of difficulty of the resulting optimization problems.