An extended car-following model accounting for the honk effect and numerical tests

In this paper, an extended car-following model is proposed to simulate traffic flow by considering the honk effect. The stability condition of this model is obtained by using the linear stability analysis. The phase diagram shows that the honk effect plays an important role in improving the stabilization of traffic system. The mKdV equation near the critical point is derived to describe the evolution properties of traffic density waves by applying the reductive perturbation method. Furthermore, the numerical simulation is carried out to validate the analytical results and indicates that the traffic jam can be suppressed efficiently via taking into account the honk effect.