元胞自动机交通流模型的相变特性研究

On the characteristics of phase transition in CA traffic models

系统地研究VDR模型和T2模型在不同车流密度时车辆位置的相关性.通过VDR模型、BJH模型和T2模型的序参量计算,确定在这三个模型中车流从自由流动到阻塞的相变特性,结果发现引入慢启动规则后,在不同的延迟概率和最大速度情况下,将引起交通相变特性的改变.

In this paper, the correlation functions in the CA （cellular automaton） traffic models incorporating the ‘slow-to-start＇ rule, such as VDR model, BJH model and T^2 model, are systematically studied at different traffic densities. The results show that there are anti-correlations and correlations between cars at low density. When anti-correlation disappears with the increases of density, it means the transition from free flow to jamming. In order to study the characteristics of phase transition, we study the order parameters of these models with the delay probability and slow-to-start probability. We found that the CA traffic model with ‘ slow-to-start＇ rule will change the characteristics of phase transition. Independently of the delay probability and in the case of less than maximal velocity, the transition from free flow to jamming in the CA model with slow-to-start probability not exceeding 0.5 is the second phase transition, which has an analogy to one in the deterministic NaSch model. Otherwise, the first phase transition will appear. Under conditions of stochastic delay, the crossover phenomena will occur. When the limiting velocity has larger values, it will show the first phase transition in spite of the delay probability.