A new car-following model considering velocity anticipation

The full velocity difference model proposed by Jiang et al. [2001 Phys. Rev. E 6 4 017101] has been improved by introducing velocity anticipation. Velocity anticipation means the follower estimates the future velocity of the leader. The stability condition of the new model is obtained by using the linear stability theory. Theoretical results show that the stability region increases when we increase the anticipation time interval. The mKdV equation is derived to describe the kink-antikink soliton wave and obtain the coexisting stability line. The delay time of car motion and kinematic wave speed at jam density are obtained in this model. Numerical simulations exhibit that when we increase the anticipation time interval enough, the new model could avoid accidents under urgent braking cases. Also, the traffic jam could be suppressed by considering the anticipation velocity. All results demonstrate that this model is an improvement on the full velocity difference model.