Stability and nonlinear analyses for mixed traffic comprising human-driven vehicles and connected human-driven vehicles with different control strategies

With the gradual improvement of vehicle automation, mixed traffic with various levels of autonomous vehicles will be the main characteristics of future road traffic. In this paper, a novel mixed traffic system comprising human-driven vehicles (HDVs) and connected human-driven vehicles (CHDVs) is constructed. The control strategies of HDVs and CHDVs are considered differently. The control strategy of HDVs is based on safety, but the control strategy of CHDVs is based on the acceleration of the preceding vehicle. The linear stability criterion of the new model is established through linear stability analysis. The results indicate that the control strategies of HDVs and CHDVs can effectively reduce the unstable area in the headway-sensitivity space. In addition, the propagation behavior of the mixed traffic in the unstable region is explored with nonlinear analysis, and the unstable traffic wave can be depicted by the kink-antikink solution of the mKdV equation. Finally, the theoretical analysis results are validated through numerical experiments, and the impacts of the control strategies of HDVs and CHDVs, along with the penetration rate of CHDVs on the mixed traffic system are illustrated. The results indicate that the control strategies of HDVs and CHDVs, as well as the penetration rate of CHDVs, can enhance the stability and driving comfort of the mixed traffic system significantly, offering some suggestions for the control scheme design in mixed traffic environment.