This paper presents a new class of one-dimensional (1D) traffic models with look-ahead rules that take into account of two effects: nonlocal slow-down effect and right-skewed non-concave asymmetry in the fundamental diagram. The proposed 1D cellular automata (CA) models with the Arrhenius type look-ahead interactions implement stochastic rules for cars’ movement following the configuration of the traffic ahead of each car. In particular, we take two different look-ahead rules: one is based on the distance from the car under consideration to the car in front of it; the other one depends on the car density ahead. Both rules feature a novel idea of multiple moves, which plays a key role in recovering the non-concave flux in the macroscopic dynamics. Through a semi-discrete mesoscopic stochastic process, we derive the coarse-grained macroscopic dynamics of the CA model. We also design a numerical scheme to simulate the proposed CA models with an efficient list-based kinetic Monte Carlo (KMC) algorithm. Our results show that the fluxes of the KMC simulations agree with the coarse-grained macroscopic averaged fluxes for the different look-ahead rules under various parameter settings.

本文提出了具有预见规则的一类新的一维（1D）交通模型，该模型考虑了两种影响：基本图中的非局部减速影响和右偏非凹不对称。拟议的具有Arrhenius类型前瞻性交互功能的一维元胞自动机（CA）模型根据每辆汽车前方的交通配置，为汽车的移动实施随机规则。特别是，我们采用两种不同的前瞻规则：一种基于从所考虑的汽车到其前方汽车的距离；另一个取决于前面的汽车密度。这两个规则都具有新颖的多步运动思想，这在恢复宏观动力学中的非凹面通量方面起着关键作用。通过半离散的介观随机过程，我们推导了CA模型的粗粒度宏观动力学。我们还设计了一种数值方案，以一种基于列表的有效动力学蒙特卡洛（KMC）算法来仿真提出的CA模型。我们的结果表明，在各种参数设置下，对于不同的预见规则，KMC模拟的通量与粗粒度宏观平均通量一致。