Nonlinear study for a mixed traffic system with delayed compensation and control scheme resist to communication interruption of CAVs

Mixed traffic with human-driven vehicles (HDVs) and connected autonomous vehicles (CAVs) is a transitional stage and future trend before fully autonomous driving. In response to the difference of the information exchange mechanism and dynamic behavior of HDVs and CAVs in mixed traffic, this paper constructed a new mixed traffic model which adopts a delayed compensation and control strategy under communication interruption of CAVs. Firstly, linear stability analysis is conducted for the proposed model, and a linear stability condition is derived and the neutral stability curves are displayed in the headway-sensitivity phase space to depict the varying trend of stability of the proposed model. In addition, the propagation behavior of mixed traffic in unstable region is explored through nonlinear analysis. The unstable traffic wave can be described by the kink-antikink solution of the mKdV equation. Finally, numerical experiments are conducted to verify the theoretical analysis results and vividly illustrate the influence of CAVs penetration, communication interruption, the delayed compensation and control strategy on the mixed traffic system. The results show that the delayed compensation and control strategy can significantly improve the unstable level of the mixed traffic system resulted from communication interruption.