A lattice model of mixed traffic flow based on critical safety potential field and driver vigilance feedback: Numerical simulation of critical safety potential field fluctuations characterizing the effects of vehicle mass and volume differences

With the rapid development of intelligent connected vehicles, managing mixed traffic flow composed of conventional passenger cars, lightweight passenger cars, and commercial vehicles has become a significant challenge in the field of transportation. This paper proposes a lattice model of traffic flow based on a critical safety potential field and driver vigilance feedback to address the stability and safety issues caused by differences in vehicle mass, volume, and length in mixed traffic environments. First, the model introduces lightweight passenger vehicles to establish a new scenario for mixed traffic flow. Second, it improves the traditional safety potential field model by incorporating vehicle speed, mass, and length characteristics into the macro-traffic flow model. Finally, it introduces driver vigilance feedback for different vehicle types to create a novel lattice model for mixed traffic environments. Linear and nonlinear stability analyses indicate that while the increase in commercial vehicle volume and mass slightly enhances traffic flow stability through driver vigilance feedback, increasing driver vigilance feedback for commercial vehicles can effectively improve traffic stability, whereas increasing vigilance feedback for lightweight passenger cars tends to exacerbate traffic congestion. Numerical analyses further verify the theoretical accuracy of the model, integrating micro-traffic flow with macro-traffic flow and simulating the evolution of density waves and critical safety potential field forces under mixed traffic conditions with varying vehicle mass and volume differences. The model proposed in this paper, by introducing driver vigilance feedback and a critical safety potential field, offers a new theoretical framework for understanding and predicting the dynamic behavior of mixed traffic flow, providing an innovative solution to address traffic stability issues in mixed traffic environments.