Modeling and stability analysis of an extended car-following model behavior of the currents vehicle based on delay of response and signal interruption probability

Abstract

This paper studies the modeling and stability analysis of an extended car-following model based on delay of response and signal interruption probability. First, by linear analysis, we give the stability condition of the model. The result shows that the stability region of the traffic flow will expand with the decrease in the probability p of signal transmission interruption. When the delay of response effect of the driver weakens, the traffic flow will become more and more stable. Second, the mKdV equation is derived based on the nonlinear reduction perturbation method. This result shows that with the decrease of parameter p, the amplitude of the traffic flow density wave decreases, the traffic flow becomes more and more stable, and the traffic congestion is gradually improved. Finally, numerical simulation verifies the correctness of the solution results.