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arXiv · 2211.03194

Side-Constrained Dynamic Traffic Equilibria

Lukas Graf·Tobias Harks
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Abstract

We study dynamic traffic assignment with side-constraints. We first give a counter-example to a key result from the literature regarding the existence of dynamic equilibria for volume-constrained traffic models in the classical edge-delay model. Our counter-example shows that the feasible flow space need not be convex and it further reveals that classical infinite dimensional variational inequalities are not suited for the definition of side-constrained dynamic equilibria. We propose a new framework for side-constrained dynamic equilibria based on the concept of feasible $\gamma$-deviations of flow particles in space and time. Under natural assumptions, we characterize the resulting equilibria by means of quasi-variational and variational inequalities, respectively. Finally, we establish first existence results for side-constrained dynamic equilibria for the non-convex setting of volume-constraints.

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Lukas Graf, Tobias Harks. 2022-11-06. Side-Constrained Dynamic Traffic Equilibria. https://doi.org/10.1287/opre.2023.0577

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