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首页> 外文期刊>Physica, A. Statistical mechanics and its applications >Statistical mechanical approach to cellular automaton models of highway traffic flow
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Statistical mechanical approach to cellular automaton models of highway traffic flow

机译：公路交通流元胞自动机模型的统计力学方法

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Cellular automaton models for traffic flow problems in one dimension are considered. Starting with a microscopic relation for the updating rule describing the occupancy on each site of the road, a macroscopic time-evolution relation is obtained for the average speed of cars by carrying out statistical averages. Mean field equations are obtained as the asymptotic limit 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 can be regarded as a nonlinear mapping between the average speeds at two consecutive time steps. The mean field results are, thus, obtained by studying the attractors of the mapping. The approach is applied to the model recently proposed by Fukui and Ishibashi (FI) for one dimensional traffic flow. The calculation leads to the evaluation of spatial correlation functions involving a string of sites on the road. Our calculations show that for FI models in which the maximum speed of each car is M, a decoupling scheme retaining correlations upto M + 1 sites can be applied to the calculation of spatial correlations involving more than M + 1 sites. Details are given for the cases of M = 1 and M = 2 without and with random delay. Results are reported for the case of M = 3 without random delay. Exact results are obtained using our approach for models without random delay. For models with random delay, results are in good agreement with simulation results. (C) 1998 Elsevier Science B.V. All rights reserved. [References: 16]
机译：考虑了用于一维交通流问题的元胞自动机模型。从描述道路每个位置上的占用率的更新规则的微观关系开始，通过执行统计平均值来获得汽车平均速度的宏观时间演化关系。获得了平均场方程作为演化关系的渐近极限。这给出了长时间内平均轿厢速度与轿厢密度的关系。演化关系可以看作是两个连续时间步长的平均速度之间的非线性映射。因此，通过研究映射的吸引子可以获得平均场结果。该方法适用于Fukui和Ishibashi（FI）最近针对一维交通流提出的模型。该计算导致对涉及道路上一系列站点的空间相关函数的评估。我们的计算结果表明，对于每辆车的最大速度为M的FI模型，可以将保留高达M +1个站点的相关性的解耦方案应用于涉及M +1个以上站点的空间相关性的计算。对于没有随机延迟和随机延迟的M = 1和M = 2的情况，给出了详细信息。报告的结果是M = 3的情况，没有随机延迟。使用我们的方法获得的准确结果可用于无随机延迟的模型。对于具有随机延迟的模型，结果与仿真结果非常吻合。 （C）1998 Elsevier Science B.V.保留所有权利。 [参考：16]

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