Side-Constrained Dynamic Traffic Equilibria

Dynamic flows are a well-studied model for car traffic in road networks. The assumption that every driver chooses her route in such a way as to selfishly minimize her own travel costs leads to the solution concept of dynamic equilibria, that is, dynamic flows wherein every flow particle travels along a cost minimal route (under the travel costs induced by this flow). In practice, however, there are often additional constraints on certain parts of the networks that restrict the options of the individual drivers like traffic limits due to security concerns in tunnels or to keep emission levels in some areas below certain thresholds. In “Side-Constrained Dynamic Traffic Equilibria,” Graf and Harks develop a general framework for incorporating such additional side constraints into dynamic flow models. They provide characterization results for the resulting equilibria via (quasi-)variational inequalities and show the first existence result for the nonconvex setting of volume constraints.