Full velocity difference model for a car-following theory

In this paper, we present a full velocity difference model for a car-following theory based on the previous models in the literature. To our knowledge, the model is an improvement over the previous ones theoretically, because it considers more aspects in car-following process than others. This point is verified by numerical simulation. Then we investigate the property of the model using both analytic and numerical methods, and find that the model can describe the phase transition of traffic flow and estimate the evolution of traffic congestion.