Metro Scheduling to Minimize Travel Time and Operating Cost Considering Spatial and Temporal Constraints on Passenger Boarding

Abstract

Passengers on metro platforms can board a train only when the train has surplus capacity and the dwell time is sufficient, while the latter condition is omitted in previous studies. Taking into account the impacts of train capacity and dwell time on passengers boarding, this study develops a model on optimizing metro timetable to reduce passenger travel time and metro operating cost, through regulating trains' inter-station run-time, dwell time and headway. The NSGA-II algorithm is employed to obtain the near-optimal Pareto Frontier of the proposed model. To address insufficient dwell time scheduled in the timetable, three operating strategies are proposed and compared: a. sticking to nominal timetable; b. extending dwell time only; c. extending dwell time and recovering delay as soon as possible by compressing train inter-station run-time. Case studies on real-life metro line prove that some passengers cannot board the train during peak hours due to insufficient dwell time. In this context, strategy a brings low-quality service because passengers are stranded at platform even though the train has surplus capacity. In contrast, more passengers can board the train with strategies b and c because dwell time is extended for passengers' boarding when train has surplus capacity. Compared to strategy b, strategy c reduces the average in-vehicle time of passengers by 2.5% through compressing inter-station run-time to recover the delay. The timetable optimized based on strategy c saves total travel time of passengers by 3.1% without increasing operating cost when compared to the practical timetable.

Last Train Delay Management in a Metro System: A Multi-Objective Rescheduling Optimization Model

“…There is a large amount of literature on the train timetable scheduling problem, which considers different objectives, including passenger waiting time [2], [3], [4], travel time [5], [6], energy consumption [7], [8], [9], operating costs [10], [11], robustness [12], and network accessibility [13], [14], [15]. From the perspective of the last-train scheduling problem, it is different from the non-last train in terms of research purposes and methods.…”

“…To ensure the safety of train operation, headway limitation is set for the last and the penultimate trains on all lines, as in (11) and (12). In addition, the rescheduled departure time of the last train at the origin station is determined by headway, as in (13).…”

“…The initial population in which the adjustment factors meet the upper and lower restrictions is determined at random, and the generated chromosomes must satisfy formulas (11) and (12) in the model to ensure that they are feasible for reproduction. Once the chromosomes do not satisfy the boundary conditions, they need to be adjusted using formulas (17) and (18).…”

“…Finally, the offspring population is generated by a series of selection, crossover, and mutation operations, which must satisfy formula (5) or (6) and formulas (11) and (12).…”