With rapid population growth and increasing demand for urban mobility, metropolitan areas such as Singapore, Tokyo, and Shanghai are increasingly dependent on public transport systems. Various strategies are proposed to improve the service quality and capacity of bus and subway systems. Express trains—i.e., trains that skip certain stations—are commonly used because they can travel at higher speeds, potentially reduce travel time, and serve more passengers. In this paper, we study cyclic express subway service (CESS), in which express trains provide routine transport service with cyclic (periodic) station-skip patterns that can be used in daily service. We propose an exact Mixed Integer Programming (MIP) model to optimize cyclic station-skip patterns for express trains operating in a single-track subway system. The objective is to reduce passengers’ total travel time—i.e., the sum of waiting time and riding time—while considering demand intensity and distribution and train headway, frequency, and capacity. We implement the model in a set of numerical experiments using real data from Singapore. To solve the optimization problem more efficiently, we also propose a heuristic to solve large-scale problems. We observe that the exact MIP model for CESS provides optimal cyclic express service patterns within a reasonable computational time, and the heuristic method can significantly reduce the computational time and provide a good solution. The case study demonstrates that passengers’ average travel time could be significantly reduced compared to local train service. We also discuss the potential transfer of passengers between express trains and evaluate its effects using numerical experiments.

随着人口的快速增长和城市交通需求的增加，新加坡、东京和上海等大都市地区越来越依赖公共交通系统。提出了各种策略来提高公交和地铁系统的服务质量和容量。特快列车——即跳过特定车站的列车——是常用的，因为它们可以以更高的速度行驶，可能会减少旅行时间，并为更多乘客提供服务。在本文中，我们研究了循环特快地铁服务 (CESS)，其中特快列车提供可用于日常服务的循环（周期性）跳站模式的常规运输服务。我们提出了一个精确的混合整数规划 (MIP) 模型，以优化在单轨地铁系统中运行的快车的循环跳站模式。目标是减少乘客的总旅行时间——即等待时间和乘车时间的总和——同时考虑需求强度和分布以及列车发车间隔、频率和容量。我们使用来自新加坡的真实数据在一组数值实验中实现了该模型。为了更有效地解决优化问题，我们还提出了一种启发式方法来解决大规模问题。我们观察到 CESS 的精确 MIP 模型在合理的计算时间内提供了最佳的循环快递服务模式，启发式方法可以显着减少计算时间并提供一个很好的解决方案。案例研究表明，与本地火车服务相比，乘客的平均旅行时间可以显着减少。