Flows over Time

Time plays an important role in transport:

All these time-oriented processes benefit from good structure and control. Planning them requires an appropriate model.

There is a variety of very different mathematical approaches to model dynamic behaviour. In combinatorial optimization it can be modelled as flows in networks. The underlying structure, for example streets and junctions in traffic systems, is described as a network. Moving objects like cars are interpreted as flow in this network.

Research in flow theory from the last forty years has been focussed on static flows. Such flows do not reflect time. Flows over time or dynamic flows as a generalization of static flows provide an appropriate way to include time aspects. For both static and dynamic flows, underlying networks consists of nodes and arcs with arc capacities. In static flows, to every arc a flow value is assigned limited by the given arc capacity. Flows over time, however, are described by a flow rate which enters an arc at a specified time. Arc capacities limit the amount of flow entering an arc at the same time and transit times describe how long it takes to travel over an arc.

Our work is strongly related to applications in road networks. We investigate various theoretic questions in the context of dynamic flows.







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