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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 7609572, 13 pages
http://dx.doi.org/10.1155/2016/7609572
Research Article

Least Expected Time Paths in Stochastic Schedule-Based Transit Networks

Faculty of Computer Science & Engineering, Ho Chi Minh City University of Technology, VNU-HCM, 268 Ly Thuong Kiet Street, Ho Chi Minh City 740500, Vietnam

Received 14 December 2015; Revised 9 February 2016; Accepted 18 February 2016

Academic Editor: Wuhong Wang

Copyright © 2016 Dang Khoa Vo 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. S. T. Waller and A. K. Ziliaskopoulos, “On the online shortest path problem with limited arc cost dependencies,” Networks, vol. 40, no. 4, pp. 216–227, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. B. Y. Chen, W. H. K. Lam, A. Sumalee, and Z.-L. Li, “Reliable shortest path finding in stochastic networks with spatial correlated link travel times,” International Journal of Geographical Information Science, vol. 26, no. 2, pp. 365–386, 2012. View at Publisher · View at Google Scholar · View at Scopus
  3. W. Dong, H. L. Vu, Y. Nazarathy, B. Q. Vo, M. Li, and S. P. Hoogendoorn, “Shortest paths in Stochastic time-dependent networks with link travel time correlation,” Transportation Research Record, no. 2338, pp. 58–64, 2013. View at Publisher · View at Google Scholar · View at Scopus
  4. G. H. Polychronopoulos and J. N. Tsitsiklis, “Stochastic shortest path problems with recourse,” Networks, vol. 27, no. 2, pp. 133–143, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  5. S. Gao and I. Chabini, “Optimal routing policy problems in stochastic time-dependent networks,” Transportation Research Part B, vol. 40, no. 2, pp. 93–122, 2006. View at Publisher · View at Google Scholar · View at Scopus
  6. H. Huang and S. Gao, “Optimal paths in dynamic networks with dependent random link travel times,” Transportation Research Part B: Methodological, vol. 46, no. 5, pp. 579–598, 2012. View at Publisher · View at Google Scholar · View at Scopus
  7. C. Tong, A schedule-based transit network model [Ph.D. thesis], Monash University, Victoria, Australia, 1986.
  8. S. C. Wong and C. O. Tong, “Estimation of time-dependent origin-destination matrices for transit networks,” Transportation Research Part B: Methodological, vol. 32, no. 1, pp. 35–48, 1998. View at Publisher · View at Google Scholar · View at Scopus
  9. A. Nuzzolo and F. Russo, “Departure time and path choice models for intercity transit assignment,” in Proceedings of the 7th IATBR Conference, Valle Nevado, Chile, June 1994.
  10. F. Schulz, D. Wagner, and K. Weihe, “Dijkstra’s algorithm on-line: an empirical case study from public railroad transport,” Journal of Experimental Algorithmics, vol. 5, article12, 2000. View at Publisher · View at Google Scholar
  11. C. O. Tong and S. C. Wong, “A stochastic transit assignment model using a dynamic schedule-based network,” Transportation Research Part B, vol. 33, no. 2, pp. 107–121, 1999. View at Google Scholar · View at Scopus
  12. A. Nuzzolo, F. Russo, and U. Crisalli, “A doubly dynamic schedule-based assignment model for transit networks,” Transportation Science, vol. 35, no. 3, pp. 268–285, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  13. M. Muller-Hannemann and M. Schnee, “Finding all attractive train connections by multi-criteria pareto search,” in Algorithmic Methods for Railway Optimization, vol. 4359 of Lecture Notes in Computer Science, pp. 246–263, Springer, Berlin, Germany, 2007. View at Publisher · View at Google Scholar
  14. L. Hame and H. Hakula, “Dynamic journeying in scheduled networks,” IEEE Transactions on Intelligent Transportation Systems, vol. 14, no. 1, pp. 360–369, 2013. View at Publisher · View at Google Scholar · View at Scopus
  15. R. Dial, “Transit pathfinder algorithm,” Highway Research Record, vol. 205, pp. 67–85, 1967. View at Google Scholar
  16. 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 Zentralblatt MATH · View at MathSciNet · View at Scopus
  17. H. Spiess and M. Florian, “Optimal strategies: a new assignment model for transit networks,” Transportation Research Part B, vol. 23, no. 2, pp. 83–102, 1989. View at Publisher · View at Google Scholar · View at Scopus
  18. Q. Li, P. Chen, and Y. Nie, “Finding optimal hyperpaths in large transit networks with realistic headway distributions,” European Journal of Operational Research, vol. 240, no. 1, pp. 98–108, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. R. W. Hall, “The fastest path through a network with random time-dependent travel times,” Transportation Science, vol. 20, no. 3, pp. 182–188, 1986. View at Publisher · View at Google Scholar · View at Scopus
  20. E. W. Dijkstra, “A note on two problems in connexion with graphs,” Numerische Mathematik, vol. 1, no. 1, pp. 269–271, 1959. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. A. Nuzzolo and U. Crisalli, “The schedule-based approach in dynamic transit modeling: a general overview,” in Schedule-Based Dynamic Transit Modeling: Theory and Applications, N. H. M. Wilson and A. Nuzzolo, Eds., chapter 1, pp. 1–24, Springer, 2004. View at Google Scholar
  22. J. Aǹez, T. de la Barra, and B. Pérez, “Dual graph representation of transport networks,” Transportation Research Part B, vol. 30, no. 3, pp. 209–216, 1996. View at Publisher · View at Google Scholar · View at Scopus
  23. C. O. Tong and A. J. Richardson, “Estimation of time-dependent origin-destination matrices for transit networks,” Transportation Research Part B, vol. 18, pp. 145–161, 1984. View at Google Scholar
  24. E. Pyrga, F. Schulz, D. Wagner, and C. Zaroliagis, “Towards realistic modeling of time-table information through the time-dependent approach,” Electronic Notes in Theoretical Computer Science, vol. 92, pp. 85–103, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  25. M. Datar and A. Ranade, “Commuting with delay prone buses,” in Proceedings of the 11th Annual ACM SIAM Symposium on Discrete Algorithms, pp. 22–29, Society for Industrial and Applied Mathematics, San Francisco, Calif, USA, January 2000.
  26. J. Boyan and M. Mitzenmacher, “Improved results for route planning in stochastic transportation networks,” in Proceedings of the Symposium on Discrete Algorithms, Washington, DC, USA, January 2001.
  27. W. Y. Szeto, M. Solayappan, and Y. Jiang, “Reliability-based transit assignment for congested stochastic transit networks,” Computer-Aided Civil and Infrastructure Engineering, vol. 26, no. 4, pp. 311–326, 2011. View at Publisher · View at Google Scholar · View at Scopus
  28. W. Y. Szeto, Y. Jiang, K. I. Wong, and M. Solayappan, “Reliability-based stochastic transit assignment with capacity constraints: formulation and solution method,” Transportation Research—Part C: Emerging Technologies, vol. 35, pp. 286–304, 2013. View at Publisher · View at Google Scholar · View at Scopus
  29. Q. Fu, R. Liu, and S. Hess, “A review on transit assignment modelling approaches to congested networks: a new perspective,” Procedia—Social and Behavioral Sciences, vol. 54, pp. 1145–1155, 2012. View at Publisher · View at Google Scholar
  30. 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, N. H. M. Wilson and A. Nuzzolo, Eds., Kluwer Academic, New York, NY, USA, 2007. View at Google Scholar
  31. M. Friedrich, “Multi-day dynamic transit assignment,” in Schedule-Based Modeling of Transportation Networks, N. H. M. Wilson and A. Nuzzolo, Eds., Kluwer Academic Publisher, 2007. View at Google Scholar
  32. C. O. Tong and S. C. Wong, “A 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., pp. 241–262, Kluwer Academic Publishers, 2004. View at Google Scholar
  33. Y. Hamdouch and S. Lawphongpanich, “Schedule-based transit assignment model with travel strategies and capacity constraints,” Transportation Research Part B: Methodological, vol. 42, no. 7-8, pp. 663–684, 2008. View at Publisher · View at Google Scholar · View at Scopus
  34. A. Sumalee, Z. Tan, and W. H. K. Lam, “Dynamic stochastic transit assignment with explicit seat allocation model,” Transportation Research Part B: Methodological, vol. 43, no. 8-9, pp. 895–912, 2009. View at Publisher · View at Google Scholar · View at Scopus
  35. A. Nuzzolo, U. Crisalli, and L. Rosati, “A schedule-based assignment model with explicit capacity constraints for congested transit networks,” Transportation Research Part C, vol. 20, no. 1, pp. 16–33, 2012. View at Publisher · View at Google Scholar · View at Scopus
  36. G. S. Brodal and R. Jacob, “Time-dependent networks as models to achieve fast exact time-table queries,” Electronic Notes in Theoretical Computer Science, vol. 92, pp. 3–15, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  37. Y. Disser, M. Müller-Hannemann, and M. Schnee, “Multi-criteria shortest paths in time-dependent train networks,” in Experimental Algorithms, C. C. McGeoch, Ed., vol. 5038 of Lecture Notes in Computer Science, pp. 347–361, Springer, 2008. View at Publisher · View at Google Scholar
  38. F. Guerriero and R. Musmanno, “Label correcting methods to solve multicriteria shortest path problems,” Journal of Optimization Theory and Applications, vol. 111, no. 3, pp. 589–613, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  39. P. Hansen, “Bicriterion path problems,” in Multiple Criteria Decision Making Theory and Application, vol. 177 of Lecture Notes in Economics and Mathematical Systems, pp. 109–127, Springer, Berlin, Germany, 1979. View at Publisher · View at Google Scholar