The Effect of the Relative Velocity on Traffic Flow**The project supported by National Naturel Science Foundation of China under Grants Nos 19872042 and 19932020

Abstract

The optimal velocity model of traffic is extended to take the relative velocity into account. The traffic behavior is investigated numerically and analytically with this model. It is shown that the car interaction with the relative velocity can effect the stability of the traffic flow and raise critical density. The jamming transition between the freely moving and jamming phases is investigated with the linear stability analysis and nonlinear perturbation methods. The traffic jam is described by the kink solution of the modified Korteweg–de Vries equation. The theoretical result is in good agreement with the simulation.