Spillback changes the long-term behavior of dynamic equilibria in fluid queuing networks

Abstract

We study the long-term behavior of dynamic traffic equilibria and find that it heavily depends on whether spillback is captured in the traffic model or not. We give an example where no steady state is reached. Although the example consists of a single-commodity instance with constant inflow rate, the Nash flow over time consists of infinitely many phases. This is in contrast to what has been proven for Nash flows over time without spillback [Cominetti et al., 2021; Olver et al., 2021]. Additionally, we show that similar phase oscillations as in the Nash flow over time with spillback can be observed in the co-evolutionary transport simulation MATSim. This reaffirms the robustness of the findings as the simulation does (in contrast to Nash flows over time) not lead to exact user equilibra and, moreover, models discrete time steps and vehicles.