A new compressible fluid model for traffic flow with density-dependent reaction time of drivers

Abstract

In this paper, we have proposed a new compressible fluid model for the one-dimensional traffic flow taking into account a variation of the reaction time of drivers, which is based on the actual measurements. The model is a generalization of the 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, which is observed in real traffic flow. Moreover, the condition of the nonlinear saturation of density against small perturbation is theoretically derived from the reduction perturbation method.