A Multiphase Car-Following Model of Traffic Flow and Numerical Tests

We present in this paper an empirical desired headway model for a single lane car-following theory based on the equation of motion of each vehicle. In this new model, traffic situation is suggested to be divided into car-following and free travel regions, and in car-following area the stimulus is a function of space difference between the current headway and the empirical desired headway with a constant sensitivity. We investigate this model with numerical method and it demonstrates some complex physical features observed in real traffic such as existence of three phases: free, synchronized, and jam flow; spontaneous formation of traffic jams; sudden flow drop in flow- density plane; local cluster effects in synchronized regime; traffic hysteresis in transition between the free and the synchronized flow. Furthermore, the proposed model also predicts that in the synchronized flow regime there exists a unique stable state to relative density, which is insusceptible to noise.