The KdV–Burgers equation in a new continuum model with consideration of driverʼs forecast effect and numerical tests

Abstract

Abstract A new continuum traffic flow model is proposed based on an improved car-following model, which takes the driverʼs forecast effect into consideration. The backward travel problem is overcome by our model and the neutral stability condition of the new model is obtained through the linear stability analysis. Nonlinear analysis shows clearly that the density fluctuation in traffic flow leads to a variety of density waves and the Korteweg–de Vries–Burgers (KdV–Burgers) equation is derived to describe the traffic flow near the neutral stability line. The corresponding solution for traffic density wave is also derived. Finally, the numerical results show that our model can not only reproduce the evolution of small perturbation, but also improve the stability of traffic flow.