An extended car-following model accounting for two preceding vehicles with mixed maximum velocity

In reality, the types of vehicles running on the road and the driving experience of different drivers are probably different. Thus, the maximum velocity of each vehicle is usually different. Moreover, common driving experience indicates that drivers not only pay attention to the motion status of individual preceding vehicle in their view. With that in mind, an extended car-following model accounting for two preceding vehicles with mixed maximum velocity is constructed in this study. For analyzing the traffic flow’s evolution more accurately, theoretical and numerical analyses are conducted. In theoretical analysis, the model’s stability condition is inferred by using the control theory, and the mKdV equation is also derived to depict the propagation of traffic density wave by means of nonlinear analysis. Numerical experiments are performed to verify the correctness of theoretical analysis and to make a detailed analysis concerning the influences of factors considered on traffic flow. Theoretical and experimental results indicate that increasing the higher maximum velocity and the appearing probability of a car having higher maximum velocity is not conducive to traffic flow stability, and compared to only considering individual preceding vehicle’s motion status, it is obvious that the traffic flow with mixed maximum velocity is more stable when two preceding vehicles’ motion status is considered.