一类新的具有前瞻规则的非局部交通流模型
On a class of new nonlocal traffic flow models with look-ahead rules
摘要：
本文提出了一类新的一维（1D）交通模型的前瞻规则，考虑到两个影响：非局部减速效应和右偏非凹不对称的基本图。所提出的一维元胞自动机（CA）模型与Arabius型前瞻性的相互作用，实现随机规则的汽车运动的配置，前面的交通每辆车。特别地，我们采用两种不同的前瞻规则：一种是基于所考虑的汽车到它前面的汽车的距离;另一种取决于前面的汽车密度。这两种规则都具有多重移动的新思想，它在恢复宏观动力学中的非凹通量方面起着关键作用。通过一个半离散的介观随机过程，我们得到了CA模型的粗粒度宏观动力学。我们还设计了一个数值方案来模拟所提出的CA模型与一个有效的基于列表的动力学蒙特卡罗（KMC）算法。我们的结果表明，在各种参数设置下，不同的前瞻规则下，KMC模拟的通量与粗粒度的宏观平均通量一致。
英文摘要：
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.
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