A new macro model of traffic flow by incorporating both timid and aggressive driving behaviors

In this paper, a novel macro model is derived from car-following model by applying the relationship between the micro and macro variables by incorporating the timid and aggressive effects of optimal velocity on a single lane. Numerical simulation shows that the timid and aggressive macro model of traffic flow can correctly reproduce common evolution of shock, rarefaction waves and local cluster effects under small perturbation. Also, the results uncover that the aggressive effect can smoothen the front of the shock wave and the timid effect results in local press peak, which means that the timid effect hastens the process of congregation in the shock wave. The more timid traffic behaviors are, the smaller is the stable range. Furthermore, the research shows that the advantage of the aggressive effect over the timid one lies in the fact that the aggressive traffic behaviors can improve the stability of traffic flow with the consideration of incorporating timid and aggressive driving behaviors at the same time.