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Modeling traffic in road networks is a widely studied but challengingproblem, especially under the assumption that drivers act selfishly. A commonapproach is the deterministic queuing model, for which the structure of dynamicequilibria has been studied extensively in the last couple of years. The basicidea is to model traffic by a continuous flow that travels over time through anetwork, in which the arcs are endowed with transit times and capacities.Whenever the flow rate exceeds the capacity the flow particles build up aqueue. So far it was not possible to represent spillback or kinematic waves inthis model. By introducing a storage capacity arcs can become full, and thus,might block preceding arcs, i.e., spillback occurs. Furthermore, we modelkinematic waves by upstream moving flows over time representing the gapsbetween vehicles. We carry over the main results of the original model to ourgeneralization, i.e., we characterize Nash flows over time by sequences ofparticular static flows, so-called spillback thin flows. Furthermore, we give aconstructive proof for the existence of dynamic equilibria, which suggests analgorithm for their computation. This solves an open problem stated by [13].

Nash Flows over Time with Spillback and Kinematic Waves