Advertisement

GeoInformatica

, Volume 11, Issue 2, pp 269–285 | Cite as

A Schedule-based Pathfinding Algorithm for Transit Networks Using Pattern First Search

  • Ruihong Huang
Article

Abstract

The lack of effective and efficient schedule-based pathfinding algorithms for transit networks has limited the application of GIS in transit trip planning services. This paper introduces a schedule-based path finding algorithm for transit networks. Based on a pattern-centered spatiotemporal transit network model, the algorithm searches the network by following route patterns. A pattern is a spatial layout of a route in transit terminology. A route usually has many patterns to serve various locations at different times. This path search algorithm is significantly different from traditional shortest path algorithms that are based on adjacent node search. By establishing a set of lemmas and theorems the paper proves that paths generated by the PFS algorithm are schedule-coordinated fastest paths for trips with given constraints. After analyzing computation and database query complexities of the algorithm the paper indicates that the PFS is efficient in computation and database query. Finally, effectiveness and efficiency of the algorithm are demonstrated by implementations in GIS-based online transit trip planners in Wisconsin, US.

Keywords

GIS transportation transit network pathfinding algorithm trip planning complexity 

Notes

Acknowledgement

The author gratefully acknowledges the insightful comments and suggestions made by the anonymous referees as well as the editing contributions by Chris Donnermeyer.

References

  1. 1.
    R.E. Bellman. “On a routing problem,” Quarterly of Applied Mathematics, Vol. 16:87–90, 1958.Google Scholar
  2. 2.
    J. De Cea and J.E. Fernandez. “Transit assignment to minimal routes: an efficient new algorithm,” Traffic Engineering and Control, Vol. 30:491–494, 1989.Google Scholar
  3. 3.
    R.B. Dial. “A probabilistic multipath traffic assignment model which obviates path enumeration,” Transportation Research, Vol. 5:83–111, 1971.CrossRefGoogle Scholar
  4. 4.
    E.W. Dijkstra. “A note on two problems in connection with graphs,” Numerische Mathematik, Vol. 1:269–271, 1959.CrossRefGoogle Scholar
  5. 5.
    H.A. Eiselt and C.-L. Sandblom. Integer Programming and Network Models. Springer: Berlin Heidelberg New York, 2000.Google Scholar
  6. 6.
    S. Even. Graph Algorithms. Maryland: Computer Science, 1979.Google Scholar
  7. 7.
    J.R. Evans and E. Minieka. Optimization Algorithms for Networks and Graphs. 2nd edition. New York: Dekker, 1992.Google Scholar
  8. 8.
    M. Florian. “Finding shortest time-dependent paths in schedule-based transit networks: a label setting algorithm,” in Niguel H.M. Wilson and Agostino Nuzzolo (Eds.), Schedule-based Dynamic Transit Modeling: Theory and Applications, 43–53, Dordrecht: Kluwer, 2004.Google Scholar
  9. 9.
    R.W. Floyd. “Algorithm 97: shortest path,” Communications of the ACM, Vol. 5:345, 1962.CrossRefGoogle Scholar
  10. 10.
    M. Friedrich, I. Hofsäß and S. Wekeck. “Timetable-based transit assignment using branch and bound,” Proceedings of the 80th Annual Meeting of Transportation Research Board (CD-ROM), Washington, DC, 2001.Google Scholar
  11. 11.
    B.G. Heydecker and J.D. Addison. “Analysis of traffic models for dynamic equilibrium traffic assignment,” in Michael G.H. Bell (Ed.), Transportation Networks: Recent Methodological Advances, 35–49, Pergamon: New York, 1998.Google Scholar
  12. 12.
    R. Huang and Z.-R. Peng. “An object-oriented GIS data model for transit trip planning system,” in TRB, National Research Council (Eds.), Transportation Research Record, no. 1804, 205–211, TRB, National Research Council: Washington DC, 2002.Google Scholar
  13. 13.
    R. Huang and Z. Peng. “A spatiotemporal data model for dynamic transit networks,” International Journal of Geographic Information Science, (forthcoming).Google Scholar
  14. 14.
    W.H.K. Lam, Z.Y. Gao, K.S. Chan and H. Yang, “A stochastic user equilibrium assignment model for congested transit networks,” Transportation Research B, Vol. 33:351–368, 1999.CrossRefGoogle Scholar
  15. 15.
    F. Le Clercq. “A Public transport assignment method,” Traffic Engineering and Control, Vol. 13:91–96, 1972.Google Scholar
  16. 16.
    NTCIP 1404, TCIP SCH Objects, 2002.Google Scholar
  17. 17.
    F. Russo. “Schedule-based dynamic assignment models for public transport networks,” in Niguel H.M. Wilson and Agostino Nuzzolo (Eds.), Schedule-based Dynamic Transit Modeling: Theory and Applications, 79–93, Dordrecht: Kluwer , 2004.Google Scholar
  18. 18.
    H. Spiess and M. Florian. “Optimal strategies: A new assignment model for transit networks,” Transportation Research B, Vol. 23B(2):83–102, 1989.CrossRefGoogle Scholar
  19. 19.
    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(2):145–161, 1984.CrossRefGoogle Scholar
  20. 20.
    C.O. Tong and S.C. Wang. “Minimum path algorithms for a schedule-based transit network with a general fare structure,” in Niguel H.M. Wilson and Agostino Nuzzolo (Eds.), Schedule-based Dynamic Transit Modeling: Theory and Applications, 241–261, Dordrecht: Kluwer , 2004.Google Scholar
  21. 21.
    S.C. Wong and C.O. Tong. “Estimation of time-dependent origin-destination matrices for transit networks,” Transportation Research B, 32(1):35–48, 1998.CrossRefGoogle Scholar
  22. 22.
    J.H. Wu, M. Florian and P. Marcotte. “Transit equilibrium assignment: a model and solution algorithms,” Transportation Science, Vol. 28(3):193–203, 1994.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of Geography, Planning and RecreationNorthern Arizona UniversityFlagstaffUSA

Personalised recommendations