高速公路交通流元胞自动机模型的一种统计平均解耦处理

对于高速公路交通流的一维元胞自动机模型，提出一种从微观格点状态更新规则出发，经过逐步的统计系综平均和截断退耦近似处理，推导宏观演化规律，从而获得描述车流稳态平均速度与车辆密度之间关系的基本图曲线的平均场方程方法.宏观演化规律表现为相继两个时刻车流平均速度的一个非线性映射.平均场论可以作为这一非线性映射的吸引子得到.将此法应用于Fukui-Ishibashi建议的高速运动车模型，计算表明：在单辆车最大速度为M的情形，可以采用截断退耦到仅保留M+1格点耦合的近似法计算空间关联函数.对于不考虑随机减速的决定论模

STATISTICAL MECHANICAL APPROACH TO CELLULAR AUTOMATON MODELS OF HIGHWAY TRAFFIC FLOW

The cellular automaton models for one-dimensional traffic flow problems are considered.Starting with a microscopic relation for the updating rule describing the occupancy on each site of the road,a macroscopic evolution relation for the average speed of cars can be obtained by carrying out statistical averages.Mean field equations are obtained by considering the asymptotic form of the evolution relation.This gives the average car speed in the long time limit as a function of the car density.The evolution relation is a nonlinear mapping between the average speeds at two consecutive time steps.The mean field results can be obtained by studying the attractors of the mapping.The approach is applied to the study of the model recently proposed by Fukui and Ishibashi.Our calculations show that for models in which the maximum speed of each car is M,a decoupling scheme retaining correlations up to M+1 sites can be applied to the calculation of spatial correlations involving more than M+1 sites. Exact results are obtained using our approach for models without random delay.For models with random delay,results are in good agreement with the simulation results.