A macro-model for traffic flow with consideration of driver's reaction time and distance

Reaction delays from drivers are indispensable factors in modeling vehicle movements. In this paper, we present an extended car-following model considering the drivers reaction time and distance. A new macroscopic model based on the driver's reaction time and distance is developed using the relationship between the microscopic and macroscopic variables. Analytical results show that the increase in reaction time and distance can potentially lead to more stable traffic flow. Furthermore, numerical results show that the proposed model can reproduce the evolution of shock, rarefaction wave, and small perturbation.