Dynamic Flows with Adaptive Route Choice
Abstract
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 and constructive computation of IDE flows for single-source single-sink networks assuming constant network inflow rates, 2. finite termination of IDE flows for multi-source single-sink networks assuming bounded and finitely lasting inflow rates, 3. the existence of IDE flows for multi-source multi-sink instances assuming general measurable network inflow rates, 4. the existence of a complex single-source multi-sink instance in which any IDE flow is caught in cycles and flow remains forever in the network.
Keywords
Cite
@article{arxiv.1811.07381,
title = {Dynamic Flows with Adaptive Route Choice},
author = {Lukas Graf and Tobias Harks and Leon Sering},
journal= {arXiv preprint arXiv:1811.07381},
year = {2022}
}
Comments
40 pages, shorter version published in the "Proceedings of the 20th Conference on Integer Programming and Combinatorial Optimization, 2019"