Study on traffic flows with connected vehicles and human-driven vehicles

This paper proposes a heterogeneous traffic model based on the intelligent driver model (IDM), which is composed of connected autonomous vehicles (CAVs) and human-driven vehicles (HDVs). Since these CAVs are equipped with V2V (Vehicle-to-vehicle communications), we consider the velocity and acceleration of multi-vehicle ahead under the communication area to describe the following behavior of CAVs. A Markov chain to organize the distribution of vehicles on the road is constructed to explore the compactness of the number of CAVs and their degradation under different permeability in traffic. The string stability condition of heterogeneous traffic is derived, which can be used to describe the velocity and acceleration of multiple vehicles in front of the general following model, and to draw the stability curve under different permeability. We then investigate the conditions under which Hopf bifurcations are generated in a traffic system consisting of HDVs and CAVs. It is found that the Hopf bifurcation corresponds to the phase transition of traffic from a locally stable to an unstable state. We perform the numerical simulation for different vehicle entry lanes under open boundary conditions and compare them with HDV traffic. The results indicate that the penetration rate of connected autonomous vehicles has an important impact on improving the stability of traffic flow and road capacity. Moreover, we use the data collected by the urban expressway to verify the extended IDM. Simulation studies show that the extended IDM is close to the actual data, while the original IDM may generate traffic congestion.