New periodically variable speed limits rule for highways with mathematical model and simulation

Variable speed limits (VSL) are used to balance traffic safety and transportation efficiency on the highway. However, driver satisfaction usually affects both aspects because human behaviour is an important factor in the traffic system. Therefore, this study aims to propose a VSL rule that combines traffic flow, risk level and driver satisfaction. First, the authors present a physical model of the lane-changing process, and the psychology of drivers when judging whether to change lanes is measured by mathematical expectation and membership functions. Considering the above three factors as target functions, a new VSL rule for two-lane highways and a periodic VSL rule for three-lane highways are formulated. Simulation results indicate that the rule for two-lane highways has good performance in the three aspects, but when it is extended to the three-lane situation, the driver satisfaction does not improve significantly. However, the periodic speed limit rule can help increase driver satisfaction. Therefore, the VSL rules that are proposed reveal a potentially highly effective way to improve the vehicle speed on the highway and advance rule making.