Energy-saving time allocation strategy with uncertain dwell times in urban rail transit: Two-stage stochastic model and nested dynamic programming framework

During practical operations, the urban rail transit system suffers from various uncertainties, particularly uncertain dwell times, which significantly impact the execution of the timetable and affect its performance, regarding train energy consumption and timetable stability. Using multi-scenario dwell times to capture its uncertainty, in this study, a two-stage chance-constrained stochastic model involving a section-time allocation stage and an optimal driving strategy stage is developed to minimize the expected energy consumption and improve stability. An exact nested dynamic programming (NDP) framework was designed to solve the model. The effectiveness and performance of the proposed methodology were investigated using a series of numerical experiments based on a small-scale instance from the Beijing Yizhuang Line. The optimized section-time allocation strategy reduced the expected energy consumption by 6.6% and improved the the minimum stability ratio by 8.5% by selecting the appropriate weight ratio. Four other sensitivity analyses were conducted to provide realistic managerial insights. Finally, a large-scale study of the Beijing 4-Daxing Subway Line was conducted to validate the scalability and efficiency of the NDP framework.