具有时变边界的完全非对称简单排斥过程：交叉口车辆与行人的相互作用
Totally asymmetric simple exclusion process with a time-dependent boundary: interaction between vehicles and pedestrians at intersections
摘要：
车辆和行人之间的相互作用在许多领域，如人行横道和交叉口。本文研究了一个完全不对称的简单排斥过程，该过程在边界处有一个由相互作用引起的瓶颈。由于行人速度的时间依赖性，即使最后一个站点的平均跳跃概率相同，模型的流量也会发生变化。我们用两种近似：（2+1）-集团近似和孤立的稀疏波近似分析了这一现象。近似结果捕捉到了模型的有趣特征。此外，我们还讨论了车辆在交叉口右转的情况下，通过添加一个交通灯的边界条件。研究结果表明，行人紧急抢行是消除右转车道交通拥堵的有效措施。
英文摘要：
Interaction between vehicles and pedestrians is seen in many areas such as crosswalks and intersections. In this paper, we study a totally asymmetric simple exclusion process with a bottleneck at a boundary caused by an interaction. Due to the time-dependent effect originating from the speed of pedestrians, the flow of the model varies even if the average hopping probability at the last site is the same. We analyze the phenomenon by using two types of approximations: (2+1)-cluster approximation and isolated rarefaction wave approximation. The approximate results capture intriguing features of the model. Moreover, we discuss the situation where vehicles turn right at the intersection by adding a traffic light at the boundary condition. The result suggests that pedestrian scrambles are valid to eliminate traffic congestion in the right turn lane.
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