A general framework for nonlocal traffic flow models on networks

Abstract

We present a general computational framework for macroscopic nonlocal traffic flow models on networks with multiple commodities. The model combines scalar conservation laws on edges with nonlocal velocity functions and couples them via buffer-based junction dynamics. Routing is defined in general as a prescription for distributing drivers across outgoing road segments. As an example, we implement dynamic k-shortest-path routing, where travel times along roads and waiting times at intersections are used to compute shortest paths to the commodities' destinations at each time step, and drivers are distributed accordingly. In another example, we optimize routing over a considered time horizon to minimize the total travel time. This framework naturally creates a feedback loop between traffic evolution and route choice. Numerical examples, ranging from small test cases to large grid-like networks, demonstrate the robustness of the approach and allow for a comparison of different routing strategies.