An extended macroscopic model for traffic flow on a highway with slopes

摘要

In this paper, we present an extended car-following model with consideration of the gravitational force. A new macroscopic model taking into account the slope effects is developed using the relationship between the microscopic and macroscopic variables. The proposed model is applied to reflect the effect of the slope on uniform flow, traffic waves and small perturbation. The simulation results demonstrate that both the angle and the length of the slope have important impacts on traffic flow. The effect of the slope becomes more significant with the increase of the slope angle.