Two-step optimization of train timetables rescheduling and response vehicles on a disrupted metro line

Abstract

Metro disruption management is currently one of the hot issues in metro research. Existing research has primarily focused on rescheduling normal train timetables or the design of bus bridging services, with limited consideration of the traffic dynamics. In this paper, we introduce a two-step optimization framework to derive a comprehensive evacuation plan encompassing the rescheduled train timetable and the response vehicle scheduling scheme. In the first step, an integer programming model is proposed to reschedule the normal train timetable. The objective function of this model is to minimize total passenger waiting time while considering various constraints such as the timetable rescheduling strategies (i.e., cancellation and short-turning), train headway, and train capacity. In the second step, the response vehicle scheduling model is established based on the Cell Transmission Model (CTM). This model aims to minimize the total travel time of the response vehicles and is capable of capturing traffic dynamics on the evacuation network. To bridge the gap between the mathematical models of the first and second steps, we establish a demand transformation process, which provides a formula for transforming the stranded passenger demand into the demand for response vehicles. Numerical cases of Beijing Metro Line 9 verify the efficiency and effectiveness of our proposed model, and results show that: (1) the direction with fewer train services experiences a greater impact from the disruption. The disruptions occurring within the central region of the metro line tend to affect a greater number of normal train services during peak hours, whereas disruptions occurring within the terminal areas of the metro line tend to affect a greater number of normal train services during off-peak hours; (2) compared with the static shortest route scheme, the dynamic shortest routes of response vehicles contribute a 7% reduction in total travel time.