A Velocity-Separation Difference Model for Car-Following Theory and Simulation Tests

This paper attempts to introduce a velocity -separation difference model that modifies the previous models in the literature. The improvement of this new model over the previous ones lies in that it performs more realistically than others in the dynamical evolution of congestion. Furthermore, the proposed model is investigated with analytic and numerical method, with the finding that this model can demonstrate some complex physical features observed in real traffic such as the existence of three phases: free flow, coexisting flow and jam flow; sudden flow drop; traffic hysteresis in transition between the free and the coexisting flow.