Synchronized flow and wide moving jams from balanced vehicular traffic

Abstract

Recently we proposed an extension to the traffic model of Aw, Rascle, and Greenberg. The extended traffic model can be written as a hyperbolic system of balance laws and numerically reproduces the reverse-lambda shape of the fundamental diagram of traffic flow. In the current work we analyze the steady-state solutions of the model and their stability properties. In addition to the equilibrium flow curve the trivial steady-state solutions form two additional branches in the flow-density diagram. We show that the characteristic structure excludes parts of these branches, resulting in the reverse-lambda shape of the flow-density relation. The upper branch is metastable against the formation of synchronized flow for intermediate densities and unstable for high densities, whereas the lower branch is unstable for intermediate densities and metastable for high densities. Moreover, the model can reproduce the typical speed of the downstream front of wide moving jams. It further reproduces a constant outflow from wide moving jams, which is far below the maximum free flow. Applying the model to simulate traffic flow at a bottleneck we observe a general pattern with wide moving jams traveling through the bottleneck.