A velocity-difference-separation model for car-following theory

We introduce a velocity-difference-separation model that modifies the previousmodels in the literature. The improvement of this new model over the previous oneslies in that it not only theoretically retains many strong points of the previousones, but also performs more realistically than others in the dynamical evolution ofcongestion. Furthermore, the proposed model is investigated with analytic andnumerical methods, with the finding that it can demonstrate some complex physicalfeatures observed in real traffic such as the existence of three phases: free flow,synchronized flow, and wide moving jam; sudden flow drop in flow-density plane; andtraffic hysteresis in transition between the free and the synchronized flow.