Integrated scheduling of metro trains and shuttle buses with passenger flow control strategy on an oversaturated metro line

In some large cities, metro lines typically experience large passenger flow and overwhelming passenger density during peak hours, leading to a mismatch between metro system resources and travel demand. Fortunately, the continuous improvement in urban multimodal transportation networks provides more possibilities for alleviating the operation pressure of a single transportation system. To tackle this issue, this study proposes a novel metro passenger flow control strategy that integrates shuttle buses to ensure normal passenger travel. Specifically, this study aims to discover an effective way to integrate the scheduling problems of metro systems and shuttle bus systems into an optimization model, where the optimization problem in metro systems considers train timetabling, rolling stock circulation, and passenger flow control strategy, while that in shuttle bus systems consider bus timetabling, vehicle utilization, short-turn and flexible limited-stop strategies. These two types of systems are coupled via passengers affected by the flow control measure of metro systems, thereby achieving a joint optimization. Using linearization techniques, we formulate a mixed integer linear programming (MILP) model to alleviate passenger dissatisfaction while simultaneously decreasing system operating costs. Based on the historical time-varying data of Beijing Metro Batong Line, a series of numerical experiments are carried out. The results demonstrate that the joint optimization schedule can effectively alleviate congestion in the metro system during morning peak hours, ensuring operation safety and improving service levels.