A characteristic particle method for traffic flow simulations on highway networks

Abstract

A characteristic particle method for the simulation of first order macroscopic traffic models on road networks is presented. The approach is based on the method particleclaw, which solves scalar one dimensional hyperbolic conservation laws exactly, except for a small error right around shocks. The method is generalized to nonlinear network flows, where particle approximations on the edges are suitably coupled together at the network nodes. It is demonstrated in numerical examples that the resulting particle method can approximate traffic jams accurately, while only devoting a few degrees of freedom to each edge of the network. © 2013 Springer-Verlag.