Equilibrium model and algorithm of urban transit assignment based on augmented network

Article

Abstract

The passenger flow assignment problem for the urban transit network is relatively complicated due to the complexity of the network structure and many factors influencing the passengers’ route and line choices. In the past three decades, many models have been proposed to solve the passenger flow assignment problem. However, the common-line problem remains challenging in transit flow assignment. In this paper, the characteristics of the urban transit network is analysed and a new technique of augmented network is proposed to represent the urban transit system. The purpose is to eliminate the complex common-line problem when modeling transit passenger flow assignment. Through this augmentation technique, the urban transit system can be represented by an augmented network-it then behaves like a simple network and can be used as a generalized network for traffic assignment or network analysis. This paper presents a user equilibrium model for the urban transit assignment problem based on such a technique. A numerical example is also provided to illustrate the approach.

Keywords

transit network flow assignment user equilibrium algorithm 

References

  1. 1.
    Dafermos S C. Relaxation algorithm for the general asymmetric traffic equilibrium problem. Transportation Sci, 1982, 16: 231–240CrossRefMathSciNetGoogle Scholar
  2. 2.
    Smith M J. An algorithm for solving asymmetric equilibrium problem with a continuous cost-flow function. Transport Res, 1983, 18B: 432–448Google Scholar
  3. 3.
    Sheffi Y. Urban transportation networks: Equilibrium analysis with mathematical programming methods. New Jersey: Prentice-Hall, Englewood Cliffs, 1985Google Scholar
  4. 4.
    Huang H J. A study on Logit assignment which excludes all cyclic flows. Transportation Res, 1998, 32B: 401–412CrossRefGoogle Scholar
  5. 5.
    Yang H, Huang H J. The multi-class, multi-criteria traffic network equilibrium and system optimum problem. Transport Res, 2004, 38B: 1–15CrossRefGoogle Scholar
  6. 6.
    Dial R B. Transit pathfinder algorithms. Highway Research Record, 1967, 205: 67–85Google Scholar
  7. 7.
    Fearnside K, Draper D P. Public transport assignment—A new approach. Traffic Eng Control, 1971, 298–299Google Scholar
  8. 8.
    Le Clercq F. A public transport assignment model. Traffic Eng Control, 1972, 91–96Google Scholar
  9. 9.
    De Cea J, Fernández E. Transit assignment for congested public transport systems: An equilibrium model. Transport Sci, 1993, 27(2): 133–147MATHCrossRefGoogle Scholar
  10. 10.
    Wu J H, Florian M, Marcotte P. Transit equilibrium assignment: A model and solution algorithms. Transport Sci, 1994, 28(3): 193–203MATHCrossRefGoogle Scholar
  11. 11.
    Lam W H K, Gao Z Y, Chan K S, et al. A stochastic user equilibrium assignment model for congested transit networks. Transport Res, 1999, 33B: 351–368CrossRefGoogle Scholar
  12. 12.
    Cominetti R, Correa J. Common-lines and passenger assignment in congested transit networks. Transport Sci, 2001, 35(3): 250–267MATHCrossRefGoogle Scholar
  13. 13.
    Cepeda M, Cominetti R, Florian M. A frequency-based assignment model for congested transit networks with strict capacity constraints: Characterization and computation of equilibria. Transport Res, 2006, 40B: 437–459CrossRefGoogle Scholar
  14. 14.
    Chriqui C, Robillard P. Common bus lines. Transport Sci, 1975, 9: 115–121CrossRefGoogle Scholar
  15. 15.
    Spiess H, Florian M. Optimal strategies: A new assignment model for transit network. Transport Res, 1989, 23B: 83–102CrossRefGoogle Scholar
  16. 16.
    Nguyen S, Pallottino S. Hyperpaths and shortest hyperpaths, combinatiorial optimization. In: Lecture Note in Mathematics. Berlin: Springer-Verlag, 1989. 258–271Google Scholar
  17. 17.
    Kurauchi F, Bell M G H, Schmöcker J D. Capacity constrained transit assignment with common lines. J Math Model Algorithm, 2003, 2(4): 309–327MATHCrossRefGoogle Scholar
  18. 18.
    Si B F, Long J C, Gao Z Y. Optimization model and algorithm for mixed traffic of urban road network with flow interference. Sci China Ser E-Tech Sci, 2008, 51(12): 2223–2232CrossRefMathSciNetGoogle Scholar

Copyright information

© Science in China Press and Springer Berlin Heidelberg 2009

Authors and Affiliations

  • BingFeng Si
    • 1
  • Ming Zhong
    • 2
  • HuiJun Sun
    • 1
  • ZiYou Gao
    • 1
  1. 1.Institute of System Science, School of Traffic and TransportationBeijing Jiaotong UniversityBeijingChina
  2. 2.Department of Civil EngineeringUniversity of New BrunswickFrederictonCanada

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