Optimization of Station-Skip in a Cyclic Express Subway Service

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.