Multiple car-following model of traffic flow and numerical simulation

Abstract

On the basis of the full velocity difference (FVD) model, an improved multiple car-following (MCF) model is proposed by taking into account multiple information inputs from preceding vehicles. The linear stability condition of the model is obtained by using the linear stability theory. Through nonlinear analysis, a modified Korteweg-de Vries equation is constructed and solved. The traffic jam can thus be described by the kink–antikink soliton solution for the mKdV equation. The improvement of this new model over the previous ones lies in the fact that it not only theoretically retains many strong points of the previous ones, but also performs more realistically than others in the dynamical evolution of congestion. Furthermore, numerical simulation of traffic dynamics shows that the proposed model can avoid the disadvantage of negative velocity that occurs at small sensitivity coefficients λ in the FVD model by adjusting the information on the multiple leading vehicles. No collision occurs and no unrealistic deceleration appears in the improved model.