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Journal of Advanced Transportation
Volume 2017 (2017), Article ID 9216864, 16 pages
https://doi.org/10.1155/2017/9216864
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.

Linked References

  1. C. O. Tong and A. J. Richardson, “A computer model for finding the time-dependent minimum path in a transit system with fixed schedules,” Journal of Advanced Transportation, vol. 18, no. 2, pp. 145–161, 1984. View at Google Scholar
  2. C. Chriqui and P. Robillard, “Common bus lines,” Transportation Science, vol. 9, no. 2, pp. 115–121, 1975. View at Publisher · View at Google Scholar · View at Scopus
  3. S. Nguyen and S. Pallottino, “Equilibrium traffic assignment for large scale transit networks,” European Journal of Operational Research, vol. 37, no. 2, pp. 176–186, 1988. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. H. Spiess and M. Florian, “Optimal strategies: a new assignment model for transit networks,” Transportation Research Part B: Methodological, vol. 23, no. 2, pp. 83–102, 1989. View at Publisher · View at Google Scholar · View at Scopus
  5. E. W. Dijkstra, “A note on two problems in connexion with graphs,” Numerische Mathematik, vol. 1, pp. 269–271, 1959. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. C. O. Tong and S. C. Wong, “Minimum path algorithms for a schedule-based transit network with a general fare structure,” in Schedule-Based Dynamic Transit Modeling: Theory and Applications, N. H. M. Wilson and A. Nuzzolo, Eds., vol. 28 of Operations Research/Computer Science Interfaces Series, pp. 241–261, Springer, New York, NY, USA, 2004. View at Publisher · View at Google Scholar
  7. A. Khani, M. Hickman, and H. Noh, “Trip-based path algorithms using the transit network hierarchy,” Networks and Spatial Economics, vol. 15, no. 3, pp. 635–653, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. W. Xu, S. He, R. Song, and S. S. Chaudhry, “Finding the K shortest paths in a schedule-based transit network,” Computers and Operations Research, vol. 39, no. 8, pp. 1812–1826, 2012. View at Publisher · View at Google Scholar · View at Scopus
  9. M. Friedrich, I. Hofsäß, and S. Wekeck, “Timetable-based transit assignment using branch and bound techniques,” Transportation Research Record: Journal of the Transportation Research Board, no. 1752, pp. 100–107, 2001. View at Google Scholar
  10. R. Huang and Z.-R. Peng, “Schedule-based path-finding algorithms for transit trip-planning systems,” Transportation Research Record, no. 1783, pp. 142–148, 2002. View at Google Scholar · View at Scopus
  11. M. Friedrich and S. Wekech, “A schedule-based transit assignment model addressing the passengers' choice among competing connections,” Computer Science Interfaces Series, vol. 28, pp. 159–173, 2004. View at Publisher · View at Google Scholar · View at Scopus
  12. R. Huang, “A schedule-based pathfinding algorithm for transit networks using pattern first search,” GeoInformatica, vol. 11, no. 2, pp. 269–285, 2007. View at Publisher · View at Google Scholar · View at Scopus
  13. S. Y. Zhu, Y. F. Yan, H. Wang, and S. B. Li, “An optimal transit path algorithm based on the terminal walking time judgment and multi-mode transit schedules,” in Proceedings of the International Conference on Intelligent Computation Technology and Automation (ICICTA '10), pp. 623–627, Changsha, China, May 2010. View at Publisher · View at Google Scholar · View at Scopus
  14. D. Canca, A. Zarzo, P. L. González-R, E. Barrena, and E. Algaba, “A methodology for schedule-based paths recommendation in multimodal public transportation networks,” Journal of Advanced Transportation, vol. 47, no. 3, pp. 319–335, 2013. View at Publisher · View at Google Scholar · View at Scopus
  15. M. Florian, “Finding shortest time-dependent paths in schedule-based transit networks: a label setting algorithm,” in Schedule-Based Dynamic Transit Modeling: Theory and Applications, N. H. M. Wilson and A. Nuzzolo, Eds., vol. 28 of Operations Research/Computer Science Interfaces Series, pp. 43–52, Springer, New York, NY, USA, 2004. View at Publisher · View at Google Scholar
  16. O. A. Nielsen and R. D. Frederiksen, “Large-scale schedule-based transit assignment-further optimization of the solution algorithms,” in Schedule-Based Modeling of Transportation Networks, pp. 1–26, Springer, Berlin, Germany, 2009. View at Google Scholar
  17. O. A. Nielsen, O. Landex, and R. D. Frederiksen, “Passenger delay models for rail networks,” in Schedule-Based Modeling of Transportation Networks, pp. 1–23, Springer, Berlin, Germany, 2009. View at Google Scholar
  18. Y.-L. Chen and H.-H. Yang, “Finding the first K shortest paths in a time-window network,” Computers and Operations Research, vol. 31, no. 4, pp. 499–513, 2004. View at Google Scholar
  19. C.-W. Yang and C.-C. Chang, “Applying price and time differentiation to modeling cabin choice in high-speed rail,” Transportation Research Part E: Logistics and Transportation Review, vol. 47, no. 1, pp. 73–84, 2011. View at Publisher · View at Google Scholar · View at Scopus
  20. L. Deng, Z. Zhang, K. Liu, W. Zhou, and J. Ma, “Fare optimality analysis of urban rail transit under various objective functions,” Discrete Dynamics in Nature and Society, vol. 2014, Article ID 910736, 8 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus