Dynamic Flows with Adaptive Route Choice
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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 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.
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