An integrated model of energy-efficient timetabling of the urban rail transit system with multiple interconnected lines

Urban rail transit (URT) has been considered an effective means of addressing urban congestion problems in metropolises. The operations of a URT system involve high energy consumption and its trade-off with passenger travel times. Existing energy-efficient timetabling studies have predominately focused on single URT lines and thus are incapable of accurately modeling the energy consumption in a URT network with transfer opportunities and synchronization between the URT lines. To extend the energy-efficient timetabling from one single line to multiple interlinked lines, we propose a bi-level model incorporating the operator’s decision on a regular timetable and passengers’ path choice in a URT network. The objective of energy consumption and timetable constraints of the upper level are linearized and formulated as mixed-integer linear programming. The lower level captures the user equilibrium based path choice behavior responding to the timetable. We develop a heuristic algorithm for the bi-level model that produces near-optimal timetable solutions in a relaxation process. The proposed model and solution algorithm are validated in the URT network of Xi’an (China). It is found that the energy consumption is considerably reduced, compared with using the current timetable, at the expense of an acceptable increase in the average travel time.