Influence of coarse toll on the dynamic properties of traffic flow in a single-entry traffic corridor

Abstract

In this paper, we investigate the effects of coarse toll on the user equilibrium (UE) state in a single-entry traffic corridor with early and late arrivals from analytical and numerical perspective. Unlike previous studies on traffic tolls, the flow congestion model is used to take into account the dynamic propagation of traffic flow. The LWR (Lighthill–Whitham–Richards) model and the Greenshields’ velocity–density function are used to describe the dynamic properties of traffic flow. The quasi-analytic solutions of the three possible cases in UE due to different charges are derived. Both analytical and numerical results indicate that rarefaction waves and shock waves appear in the corridor under the coarse toll. The three-dimensional evolution diagrams of traffic flow and space–time diagrams illustrate that the introduction of course toll lets flow patterns more complicated. This extends the knowledge given by the classical bottleneck model.