Modelling the fundamental diagram of traffic flow mixed with connected vehicles based on the risk potential field

The fundamental diagram (FD) of traffic flow can effectively characterize the macroscopic characteristics of traffic flow and provide a theoretical foundation for traffic planning and control. The rapid development of connected vehicles (CVs) has led to changes in traffic flow characteristics. However, research on the FD of traffic flow involving CVs and non-connected vehicles (NCVs) is still in its early stages. Most FDs do not well characterize the motion behaviour of different vehicles, nor do they study the interaction between mixed vehicles. Therefore, in this study, the FD of mixed traffic flows (i.e. with CVs and NCVs) was constructed within a unified framework. First, the car-following behaviours of CVs and NCVs were modelled based on risk potential field theory. Subsequently, the FD of mixed traffic flows was derived based on the relationship between car-following behaviour and the macroscopic traffic flow under steady-state conditions. To validate the model, rigorous verifications were conducted via numerical experiments using the Monte Carlo method. The results indicate significant agreement between the scatter plots obtained from the experiments and the theoretical curves for different penetration rates. The proposed FD has a unified framework and a more rigorous mathematical structure.