A force model for single-line traffic

Based on the assumption that a vehicle always tries to keep a certain speed and a proper distance from the one in front of it, a force model, being a kind of microscopic models which is similar to van der Waal's molecule model, is established. We develop three approaches to study the equilibrium state and the phase transition of traffic: the two-vehicle model in which the traffic is simplified into a leading vehicle and its follower, the numerical simulation in which we study the initially uniformly distributed vehicles, and the corresponding macroscopic model. It is shown that the trajectories of phase transitions in the last two approaches are consistent with each other and all end at the same equilibrium states we anticipate from the results of the first one. We point out, however, that some phenomena can only be explained by the microscopic model.