A finite time combinatorial algorithm for instantaneous dynamic equilibrium flows

Abstract Instantaneous dynamic equilibrium (IDE) is a standard game-theoretic concept in traffic assignment which individual flow particles myopically select en route currently shortest paths towards their destination. We analyze IDE within the Vickrey bottleneck model, where current travel times along path consist of physical plus sum waiting all queues path. Although have been studied for decades, several fundamental questions regarding computation and complexity are not well understood. In particular, existence results computational methods based on fixed-point theorems numerical discretization schemes no exact finite time algorithm known to date. As our main result we show that natural extension needs only finitely many phases converge leading first combinatorial computing an IDE. complement this by hardness showing with properties NP-hard.