We study dynamic network flows and introduce a notion of instantaneous dynamic equilibrium (IDE) requiring that for any positive inflow into an edge, this edge must lie on a currently shortest path towards the respective sink. We measure current shortest path length by current waiting times in queues plus physical travel times. As our main results, we show (1) existence of IDE flows for multi-source single sink networks, (2) finite termination of IDE flows for multi-source single sink networks assuming bounded and finitely lasting inflow rates, and, (3) the existence of a complex multi-commodity instance in which any IDE flow is caught in cycles and flow remains forever in the network.

Short Bio: Tobias Harks is professor of optimization in the Institute of Mathematics at the University of Augsburg. Before joining Augsburg, he was a Postdoc at the Technical University Berlin, and afterwards Assistant and Associate Professor at Maastricht University. His research interests include the design of algorithms, algorithmic game theory, and discrete and continuous optimization.

Einladung von Prof. Megow