A novel macro model of traffic flow with the consideration of anticipation optimal velocity

• A new macro model of traffic flow is proposed by incorporating anticipation effect.
• The stability of traffic flow with anticipation effect term has been explored.
• The numerical simulation is carried out to confirm the validity of anticipation effect.
• The results show that the anticipation effect can improve the stability of traffic flow.

In this paper, a novel macro model which can investigate wide moving jams is derived from car-following model by applying the relationship between the micro and macro variables with the consideration of anticipation optimal velocity on single lane. The theoretic analysis and numerical simulation show that the new macro model of traffic flow can correctly reproduce common evolution of shock, rarefaction wave and local cluster effect under small perturbation, which shows that the congested traffic patterns about wide moving jam propagation are in accordance with empirical results. Furthermore, the results uncover that the anticipation effect can smooth the front of the shock wave and the rarefaction wave, which means that anticipation effect hasten the diffusion process of congregate in the shock wave and dissolution in rarefaction wave. The key improvement of this new macro model over the previous ones lies in the fact that the anticipation traffic behaviors can improve the stability of traffic flow with the consideration of the proper anticipation effect.