An extended car-following model considering the self-stabilizing driving behavior of headway

Considering the self-stabilizing driving behavior of headway, an extended car-following model called the self-stabilizing optimal velocity (SSOV) model is presented in this paper. To show the effect of the self-stabilizing driving behavior of headway, the SSOV model is investigated by the analytical and numerical methods. By using the linear analysis method, the stability condition of the SSOV model is obtained. And then by using the nonlinear analysis method, the Burgers, KdV and modified KdV equations are respectively derived to describe the propagating behavior of traffic density wave in the stable, unstable regions and near the critical point. The numerical simulations are presented to show the valid of the analytical results and the effect of the self-stabilizing driving behavior. The analytical and numerical results all show that the self stabilizing driving behavior plays an important role on the stability and flux of the traffic flow.