Analysis and simulation of vehicle following behavior with consideration of multiple time delays

With the application of intelligent transportation system, drivers can receive more traffic status information in the process of driving, but they may have multiple time delays when they are presented with different information. As a result, to further research the influence of multiple time delays on vehicle following behavior, this study comes up with a modified car following model, which takes into account multiple time delays in sensing both distance and velocity information, based on the backward looking and velocity difference model. The linear stability theory is used to explore the influence of multiple time delays on the stability of the extended model. Different nonlinear equations are derived using nonlinear theory, which include Burgers, Korteweg–de Vries, and Modified Korteweg–de Vries equations and are used to depict triangular wave, soliton wave and kink–antikink wave corresponding to stable, metastable and unstable regions respectively. In the end, numerical simulation is used to further study the improved model to depict the dynamic evolution of traffic stream. The results display that the improvement of time delay in sensing distance can induce traffic congestion, conversely, the time delay in sensing velocity offsets the negative effect of time delay in sensing distance. The theoretical results and numerical simulation results are consistent with each other.