A Macroscopic Model of Heterogeneous Traffic Flow Based on the Safety Potential Field Theory

The macroscopic traffic flow model is the cornerstone of traffic flow theory and can be applied to investigate manytraffic planning and management issues. However, the macroscopic model of the heterogeneous traffic flow has not been profoundly studied. This paper developed a novel macroscopic model of the heterogeneous traffic flow under a partly connected and automated environment based on the safety potential field (SPF) theory. The SPF model was applied to describe the microscopic driving behaviour of traditional human-driven vehicles (HVs) and connected and automated vehicles (CAVs). A fundamental diagram (FD) model was derived according to the correlation with the microscopic car-following model under a steady-state condition. To verify the correlation between the FD and the microscopic simulation results, a Monte-Carlo-simulation was also performed. Finally, the macroscopic model of the heterogeneous traffic flow was validated through a simulation on a road section with a bottleneck under different CAVs market penetration rates ranging from 0.0 to 1.0. The results indicate that introducing the CAVs into the pure traffic flow of HVs may slightly have a negligible impact on road capacity when the CAVs penetration rate at a lower level, but the impact increases significantly as the CAVs penetration rate increased.