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Flows over time with load-dependent transit times

Köhler, Ekkehard; Skutella, Martin

Inst. Mathematik

Flow variation over time is an important feature in network flow problems arising in various applications such as road or air traffic control, production systems, communication networks (e.g., the Internet), and financial flows. Another crucial phenomenon in many of those applications is that the time taken to traverse an edge varies with the current amount of flow on this edge. Since it is already a highly nontrivial problem to map these two aspects into an appropriate and tractable mathematical network flow model, there are hardly any algorithmic techniques known which are capable of providing reasonable solutions even for networks of rather modest size.