A car following model with the backward looking effect and next-nearest-neighbor interaction in relative velocity

Based on the previous models of traffic flow, a new car following model which takes into account the preceding vehicle and the following vehicle with the consideration of the next-nearest-neighbor interaction in relative velocity is presented. The performance of the model is investigated analytically and numerically. The stability criterion is obtained by the linear stability analysis. By increasing the strengths of the effect of new consideration, the stable region increases and the traffic jam is suppressed effectively. The theoretical results are in good agreement with the simulation.