The Effect of Estimated Headway on Gradient Highway by Means of Linear and Nonlinear Stability

An extended car-following model is presented in this paper, which considers both gradient and estimated headway. The study analyzes the impact of these factors on traffic flow stability using linear stability theory and the nonlinear reductive perturbation method. Numerical simulation reveals that the kink– antikink solution of the modified Korteweg–de Vries equation can describe the propagating behavior of traffic density waves near critical points. Furthermore, considering estimated headway information enhances traffic flow stability on both slope roads and flat roads, indicating its crucial role in alleviating congestion.