Phase diagram in multi-phase heterogeneous traffic flow model integrating the perceptual range difference under human-driven and connected vehicles environment

With the gradual development of autonomous driving and connected communication technology, urban road networks will be shared by a combination of Human-driven vehicles (HDVs) and Connected vehicles (CVs) for a long era. Besides, as the actual vehicle operator, the driver regulates the vehicle state with an accelerator, gear lever, or brake, whereas the stepwise acceleration process is overlooked in the literature. Motivated by this, comprehensive kinetic difference between the two types of vehicles, we propose a novel heterogeneous multi-phase traffic flow accounting for the HDVs and CVs to close this hole. In the section on linear stability analysis, the reductive perturbation approach was applied to figure out the stability norm of the new model. The findings show that, on the one hand, inhibiting traffic bottlenecks is positively impacted by the penetration rate of CVs and the number of preceding vehicles taken into account; on the other hand, by varying the headway between following vehicles, the multiple-phase transition occurs; consequently, the number of turning points in the optimal velocity function is the sole factor that affects the number of stages in multi-phase transitions. Subsequently, the modified Korteweg-de Vries (mKdV) equation corresponding to the new model is deduced to investigate the nonlinear phenomenon of traffic flow at the vicinity of the critical point, and the kink-antikink soliton wave solution by solving the above characteristic equation can describe the "stop-and-go" phenomenon in real traffic flow. Finally, the conclusion of the numerical experiments is consistent with the above theoretical analysis. This research can provide insight into the dynamic evolution of road traffic flow during the transition from HDVs to semi-CVs and eventually to CVs.