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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 290937, 10 pages
Research Article

Networked Timetable Stability Improvement Based on a Bilevel Optimization Programming Model

1School of Traffic and Transportation, Lanzhou Jiaotong University, P.O. Box 405, Anning West Road, Anning District, Lanzhou, Gansu 730070, China
2State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, No. 3 Shangyuancun, Haidian District, Beijing 100044, China

Received 28 November 2013; Revised 13 January 2014; Accepted 23 January 2014; Published 4 March 2014

Academic Editor: Wuhong Wang

Copyright © 2014 Xuelei Meng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Train timetable stability is the possibility to recover the status of the trains to serve as arranged according to the original timetable when the trains are disturbed. To improve the train timetable stability from the network perspective, the bilevel programming model is constructed, in which the upper level programming is to optimize the timetable stability on the network level and the lower is to improve the timetable stability on the dispatching railway segments. Timetable stability on the network level is defined with the variances of the utilization coefficients of the section capacity and station capacity. Weights of stations and sections are decided by the capacity index number and the degrees. The lower level programming focuses on the buffer time distribution plan of the trains operating on the sections and stations, taking the operating rules of the trains as constraints. A novel particle swarm algorithm is proposed and designed for the bilevel programming model. The computing case proves the feasibility of the model and the efficiency of the algorithm. The method outlined in this paper can be embedded in the networked train operation dispatching system.