A modified full velocity difference model with the consideration of velocity deviation

Abstract

In this paper, a modified full velocity difference model (FVDM) based on car-following theory is proposed with the consideration of velocity deviation which represents the inexact judgement of velocity. The stability condition is obtained by the use of linear stability analysis. It is shown that the stability of traffic flow varies with the deviation extent of velocity. The Burgers, Korteweg-de Vries (KdV) and modified K-dV (MKdV) equations are derived to describe the triangular shock waves, soliton waves and kink–antikink waves in the stable, metastable and unstable region, respectively. The numerical simulations show a good agreement with the analytical results, such as density wave, hysteresis loop, acceleration, deceleration and so on. The results show that traffic congestion can be suppressed by taking the positive effect of velocity deviation into account. By taking the positive effect of high estimate of velocity into account, the unrealistic high deceleration and negative velocity which occur in FVDM will be eliminated in the proposed model.