This paper presents a study on traffic flow models in one-dimensional (1D) and two-dimensional (2D) lattices. The models incorporate generalized look-ahead rules that consider nonlocal slow-down effects. The proposed cellular automata (CA) models use stochastic rules to determine the movement of cars based on the traffic configuration ahead of each car. Specifically, a look-ahead rule is used that considers both the car density ahead and a generalized interaction function based on the distance between cars. The CA models are simulated using an efficient kinetic Monte Carlo (KMC) algorithm. The numerical results in 1D demonstrate that the flows from the KMC simulations align with the macroscopic averaged fluxes for the look-ahead rule, across various parameter settings. In the 2D results, a sharp phase transition is observed from freely flowing traffic to global jamming, depending on the initial density of cars.

中文翻译：

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一维和二维交通流的动力学蒙特卡洛模拟：具有广义前瞻规则的非局部模型


本文介绍了一维 （1D） 和二维 （2D） 晶格中的交通流模型的研究。这些模型包含考虑非局部减速效应的广义前瞻规则。提出的元胞自动机 （CA） 模型使用随机规则，根据每辆车前面的交通配置来确定汽车的运动。具体来说，使用了前瞻规则，该规则同时考虑了前方的汽车密度和基于汽车之间距离的广义交互函数。CA 模型使用高效的动力学蒙特卡洛 （KMC） 算法进行模拟。一维数值结果表明，在各种参数设置中，来自 KMC 仿真的流量与前瞻规则的宏观平均磁通量一致。在 2D 结果中，观察到从自由流动的交通到全球拥堵的急剧相变，具体取决于汽车的初始密度。