A Compressible Fluid Model for Traffic Flow and Nonlinear Saturation of Perturbation Growth

In this paper, we have proposed a new compressible fluid model for the one-dimensional traffic flow taking into account the reaction time of drivers, which is based on the actual measurements. This model is a generalization of Payne model by introducing a density-dependent function of reaction time. The linear stability analysis of this new model shows the instability of homogeneous flow around a critical density of vehicles. Moreover, the condition of the nonlinear saturation of density against small perturbation is derived from the analysis by using reduction perturbation method.