Dynamic Flows with Adaptive Route Choice

We study dynamic network flows and investigate instantaneous dynamic equilibria (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 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 where IDE flows exist, but all of them are caught in cycles and persist forever.