Phase transitions in operation of heterogeneous vehicles mixed with human-driven and connected autonomous vehicles under speed restriction circumstances

In the traffic road physical environment, there are many physical factors that affect vehicles speed, such as slopes, bends, and spiral roads. For vehicle safety on non-flat road, the speed restriction requirements are applied for road management. Especially in the mixed traffic involving connected autonomous vehicles (CAVs) and human-driven vehicles (HDVs), it is even more necessary to enhance vehicle safety through speed restriction on rugged roads. Consequently, to cope with the influence of complex road physical facilities, the speed restriction effect (SRE) is adopted to build a novel lattice model for heterogeneous vehicles covering CAVs and HDVs. Subsequently, we infer the stable requirement affected by the SRE and the penetration of CAVs. Also, the mKdV equation is significantly affected by the SRE and the penetration of CAVs based on nonlinear analysis. Additionally, the impacts of the SRE and the penetration of CAVs on mixed traffic behaviors have been investigated from two aspects involving density wave and limit loop via simulations. Simulation results discover that heterogeneous vehicles behaviors exhibit a positive stability trend owing to the SRE and the penetration of CAVs, which signifies that the SRE is an important factor being considered in heterogeneous vehicles including CAVs and HDVs.