A performance assessment method for urban rail transit last train network based on percolation theory

With global urbanization, mega-cities like Beijing, New York, and Tokyo have emerged. Urban rail transit (URT) in these cities is essential for public transportation and serves as the backbone of the urban transportation system. However, inadequate last train connections and poor timetable planning create problems in operation and management, preventing passengers from having a seamless journey within the URT system. This problem undoubtedly increases travel time and costs for passengers. To tackle this problem, we need to assess the performance of the previous train timetable for train operations. This article focuses on the Beijing and Shanghai Rail Transit Systems, creating a dynamic URT last train network (LTN) model. By studying the network's organizational mechanism using percolation theory, we evaluate the performance of the LTN in both systems and identify crucial last trains using a network performance evaluation framework. The results reveal that the critical percolation time of the network is an important operational parameter that reflects the reasonableness of network connection. The identification of the crucial last train highlights that, in the presence of alternative routes within the network, even if the line in question bears a significant passenger load, its impact on the LTN remains relatively minimal. With the proposed method in this study, it is possible to effectively evaluate the performance of the LTN in URT systems, providing theoretical support for URT operators in formulating practical operational plans.