Abstract
There are many different models of traffic flow proposed up to now. In this paper, we will concentrate on cellular automaton (CA) models and study their validity in detail. The rule-184 model is considered as a prototype of all CA models. The model is extended to more realistic ones by adding new rules. Among them, we will mainly consider the Fukui-Ishibashi model, the Nagel-Schreckenberg model, the slow-to-start model and the Burgers model. We will also study the relationship among different models by using the methods of ultradiscretization and Euler-Lagrange transforma-tion. Moreover, a new hybrid Lagrange model, which is recently proposed by using the above methods, is reviewed and we consider complex phase transition from free to jamming state by using the model.
