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Journal of Advanced Transportation
Volume 2017 (2017), Article ID 9216864, 16 pages
Research Article

Three Extensions of Tong and Richardson’s Algorithm for Finding the Optimal Path in Schedule-Based Railway Networks

1Department of Civil Engineering, The University of Hong Kong, Pokfulam, Hong Kong
2Department of Architecture and Civil Engineering, City University of Hong Kong, Kowloon, Hong Kong

Correspondence should be addressed to J. Xie

Received 2 July 2016; Accepted 26 October 2016; Published 12 January 2017

Academic Editor: Richard S. Tay

Copyright © 2017 J. Xie 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.


High-speed railways have been developing quickly in recent years and have become a main travel mode between cities in many countries, especially China. Studying passengers’ travel choices on high-speed railway networks can aid the design of efficient operations and schedule plans. The Tong and Richardson algorithm that is used in this model offers a promising method for finding the optimal path in a schedule-based transit network. However, three aspects of this algorithm limit its application to high-speed railway networks. First, these networks have more complicated common line problems than other transit networks. Without a proper treatment, the optimal paths cannot be found. Second, nonadditive fares are important factors in considering travel choices. Incorporating these factors increases the searching time; improvement in this area is desirable. Third, as high-speed railways have low-frequency running patterns, their passengers may prefer to wait at home or at the office instead of at the station. Thus, consideration of a waiting penalty is needed. This paper suggests three extensions to improve the treatments of these three aspects, and three examples are presented to illustrate the applications of these extensions. The improved algorithm can also be used for other transit systems.