This paper proposes a macroscopic model to describe the equilibrium distribution of passenger arrivals for the morning commute problem in a congested urban rail transit system. We employ a macroscopic train operation sub-model developed by Seo et al. (2017a,b) to express the interaction between dynamics of passengers and trains in a simplified manner while maintaining their essential physical relations. We derive the equilibrium conditions of the proposed model and discuss the existence of equilibrium. The characteristics of the equilibrium are then examined through numerical examples under different passenger demand settings. As an application of the proposed model, we finally analyze a simple time-dependent timetable optimization problem with equilibrium constraints and show that there exists a "capacity increasing paradox" in which a higher dispatch frequency can increase the equilibrium cost. Further insights into the design of the timetable and its influence on passengers' equilibrium travel costs are also obtained.

中文翻译：

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拥挤的城市轨道交通系统中的早晨通勤：旅客到达平衡分布的宏观模型

本文提出了一个宏观模型来描述拥挤的城市轨道交通系统中早晨通勤问题的旅客到达的均衡分布。我们采用由Seo等人开发的宏观列车运行子模型。（2017a，b）以简化的方式表达乘客和火车动力之间的相互作用，同时保持其基本的物理关系。我们推导了所提出模型的平衡条件，并讨论了平衡的存在。然后通过数值示例在不同的乘客需求设置下检查平衡的特征。作为所提出模型的应用，我们最后分析了一个带有平衡约束的简单的与时间有关的时间表优化问题，并表明存在“容量增加的悖论”。其中较高的调度频率会增加均衡成本。还可以获得对时间表设计及其对乘客平衡旅行成本的影响的进一步见解。