Equity-based Timetable Synchronization Optimization In Urban Subway Network

With the acceleration of urbanization process, urban subway transit has become an important mode for public transportation, which not only has the characteristic of large capacity, fast, safe and high efficiency, but also energy-conserving, land-saving, and plays a significant role in relieving the pressure of ground transportation. At present, urban subway network has changed from single line into network operating gradually, and transfer stations assume intensive passenger flow and train flow, which makes transfer efficiency have great influence on the transport efficiency of the whole urban subway network. As a consequence, the research on transfer coordination optimization has become an important subject to urban subway transit.This paper studies the urban subway network and proposes the concept of train connection equity and passenger waiting time equity at transfer stations. Starting with the operating and connecting of trains at transfer stations, we establish equity-based train connecting time and equity-based passenger waiting time timetable synchronization optimization models respectively, which are described in detail as follow:(1) Equity-based train connecting time timetable synchronization optimizationThis model aims at optimizing the worst train connecting time of all transfer directions among the whole urban subway network. By adjusting the leaving time of the first train at terminal station, running time, dwelling time and headways of each operating line, the equity of train connecting time will be improved. Binary variables substitute (BVS) method is proposed, and the model is solved by genetic algorithm combined with BVS method. The model and algorithm are proved effective by adopting them to a preliminary test network.(2) Equity-based passenger waiting time timetable synchronization optimizationWith the consideration of the influence of passenger flow, a bi-level model based on the train connecting time timetable synchronization optimization model is proposed. In the model, the objective of the upper model is to minimize the total difference between passenger weighted waiting time of each transfer direction and the average weighted waiting time, which can optimizes the timetable using the transfer flow obtained by the lower user equilibrium assignment model. According to the specialty of urban subway network, a modified Floyd shortest path searching algorithm is developed and a quick solving algorithm is proposed. By analyzing the preliminary test network, the model and algorithm are proved feasible.(3) Case study of Beijing urban subway network timetable synchronization optimizationThe proposed equity-based train connecting time and equity-based passenger waiting time timetable synchronization optimization models are adopted in Beijing urban subway network respectively. It shows that the proposed models are able to improve the transfer efficiency and balance the train connecting time and passenger waiting time, which can provide theory basis for efficient operation and management of urban subway network.