Nonlinear Analysis of an Anisotropic Continuum Model for Traffic Flow

Based on the continuum model with the consideration of the driver's forecast effect (DFE) proposed by Tang et al., a new macro version is obtained using the relationship between micro variables and the macro ones to study the density wave problem and the stop-and-go phenomena. The stability condition of the model is derived by using linear analysis. The triangular shock wave, one type of density wave, which is determined by Burgers equation in the stable region, is discussed in great detail with reductive perturbation method. The local cluster appears when the authors perform the numerical simulations for the model. It also proves the DFE has the positive effect of reducing the local cluster.