Side-Constrained Dynamic Traffic Equilibria

We study dynamic traffic assignment with side constraints. We first give a counter-example to a previous result from the literature regarding the existence of dynamic equilibria for volume-constrained traffic models in the classical linear 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 general side-constrained dynamic equilibria. We then propose a new framework for side-constrained dynamic equilibria based on the concept of admissible γ-deviations of flow particles in space and time. We show under which assumptions the resulting equilibria can still be characterized by means of quasi-variational and variational inequalities, respectively. Finally, we establish first existence results for side-constrained dynamic equilibria for the nonconvex setting of volume-constraints.

Funding: This work was supported by the Deutsche Forschungsgemeinschaft [Grants HA 8041/1-1 and HA 8041/4-1].

Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2023.0577.