Full velocity difference model for a car-following theory - art. no. 017101

In this paper, we present a full velocity difference model for a car-follow ing 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 t he model using both analytic and numerical methods, and find that the model can describe the phase transition of traffic flow and estimate the evoluti on of traffic congestion.