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Algorithms for Traffic Assignment to Transportation Networks

  • Ennio Cascetta
Part of the Applied Optimization book series (APOP, volume 49)

Abstract

In Chapter 5 several (within-day static) assignment models were formulated under for various assumptions on users’ behavior and network congestion. Computing link flows and other relevant variables resulting from assignment is computationally for real size networks with thousands of nodes and tens of thousands of links and intensive requires efficient algorithms. This chapter describes the theoretical foundations and the structure of some of the simplest algorithms for solving (within-day) static assignment models (algorithms for within-day dynamic assignment presented in Chapter 6 are still at a reasearch stage). The main emphasis is on presenting simple and effective solution approaches for assignment to large-scale networks, rather than providing an exhaustive analysis of the many existing algorithms.

Keywords

Link Cost Traffic Assignment Short Path Tree Link Flow Stochastic User Equilibrium 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Reference Notes

  1. [234]
    Sheffi Y. (1985). Urban transportation networks. Prentice Hall, Englewood Cliff, NJ.Google Scholar
  2. [220]
    Patriksson M. (1994). The Traffic Assignment Problem: Model and Methods. VSP, Utrecht, The Netherlands.Google Scholar
  3. [127]
    Gallo G. and S. Pallottino (1988). Shortest path algorithms. In Fortran Codes for network Optimization, edited by B. Simeone, P. Toth, G. Gallo, F. Maffioli, and S. Pallottino. Annals of Operations Research 13: 3–79.Google Scholar
  4. [128]
    Gallo G., Longo G., Nguyen S. and Pallottino S. (1993). Directed hypergraphs and applications. Discrete Applied Mathematics 2: 177–201.Google Scholar
  5. [3]
    Ahuja R.K. T.L. Magnanti, and J.B. Orlin (1993). Networks flows: Theory, Algorithms, and Application. Prentice —Hall, Englewood Cliffs, NJ USA.Google Scholar
  6. [107]
    Dial R.B. (1971). A Probabilistic Multipath Traffic Assignment Model with Obviates Path Enumeration Transportation Research.Google Scholar
  7. [243]
    Van Vliet D. (1981) Selected Node-Pair Analysis in Dial’s Assignment Algorithms Transportation Research 15B: 65–68.Google Scholar
  8. [232]
    Russo F., and A. Vitetta (1998). A C-Logit assignment without explicit path enumeration Quaderno del dipartimento di Informatica, Matematica, Elettronica e Trasporti, University of Reggio Calabria.Google Scholar
  9. [46]
    Burrell J.E. (1968). Multiple route assignment and its application to capacity restraint. In Proceedings o the 4t International Symposium on the Theory of Road Traffic Flow, W. Leutzbach and P. Baron eds. Karlsruhe, Germany.Google Scholar
  10. [101]
    Daganzo C.F., and Y. Sheffi (1982). Unconstrained Extremal formulation of Some Transportation Equilibrium Problems. Transportation Science 16: 332–360.Google Scholar
  11. [176]
    Maher M.J., and P.C. Hughes (1997). A Probit-Based Stochastic User Equilibrium Assignment Model. Transportation Research 31B: 341–355.Google Scholar
  12. [226]
    Powell W.B. and Y. Sheffi (1982). The Convergence of Equilibrium Algorithms with Predetermined Step Sizes. Transportation Science 16: 45–55.Google Scholar
  13. [176]
    Maher M.J., and P.C. Hughes (1997). A Probit-Based Stochastic User Equilibrium Assignment Model. Transportation Research 31B: 341–355.Google Scholar
  14. [96]
    Daganzo C. (1983). Stochastic Network equilibrium problem with multiple vehicle types and asiymmetric, indefinite link cost jacobians Transportation Science 17: 282–300.Google Scholar
  15. [34]
    Blum J.R. (1954). Multidimensional Stochastic Approximation Methods. Ann. Math. Stat. 25: 737–744.MATHCrossRefGoogle Scholar
  16. [49]
    Cantarella G.E. (1997). A General Fixed-Point Approach to Multi-Mode Multi-User Equilibrium Assignment with Elastic Demand Transportation Science 31: 107–128.Google Scholar
  17. [115]
    Fisk C. (1980) Some Developments In Equilibrium Traffic Assignment Methodology Transportation Research B: 243–255.Google Scholar
  18. [15]
    Bell M., D. Inaudi, W. Lam, and G. Ploss (1993). Stochastic User Equilibrium Assignment and Iterative Balancing Proceedings of the 12`h International Symposium on Traffic and Transportation Theory, Berkekey: 427–440.Google Scholar
  19. [86]
    Chen M., and A. Sule Alfa (1991) Algorithms for solving Fisk’s Stochastic Traffic Assignment Model Transportation Research 25B: 405–412.Google Scholar
  20. [103]
    Damberg O., J.T Lundgren, and M. Patriksson (1996) An algorithm for the stochastic user equilibrium problem Transportation Research 30B: 115–131.Google Scholar
  21. [162]
    Le Blanc L. J. (1975). An algorithm for the discrete network design problem. Transportation Science 9: 183–199.Google Scholar
  22. [198]
    Nguyen S. (1976). A Unified Approach to Equilibrium Methods for Traffic Assignments In Traffic Equilibrium Methods, M. Florian editor, vol.118 of Lecture Notes in Economics and Mathematical Systems: 148–182.Google Scholar
  23. [119]
    Florian M., and H. Spiess (1982). The convergence of diagonalization algorithms for asymmetric network equilibrium problems Transportation Research 16B: 477–483.Google Scholar
  24. [126]
    Fukushima M. (1984). A modified Frank-Wolfe algorithm for solving the traffic assignment problem Transportation Research 18B: 169–178.Google Scholar
  25. [171]
    Lupi M. (1986) Convergence of the Franke-Wolf algorithm in transportation networks Civ. Enging. Syst. 3.Google Scholar
  26. [244]
    Van Vliet D. (1987) The Frank-Wolfe Algorithm for Equilibrium Traffic Assignment Viewed as a Variational Inequality Transportation Research 21: 87–89.Google Scholar
  27. [135]
    Hearn D.W., S. Lawphongpanich, and S. Nguyen (1984). Convex Programming Formulation of the Asymmetric Traffic Assignment Problem. Transportation Research 18B: 357–365.Google Scholar
  28. [199]
    Nguyen S. and S. Pallottino (1988). Equilibrium Traffic Assignment for Large Scale Transit Networks. European Journal of Operational Research 37: 176–186.Google Scholar
  29. [173]
    M. Florian, and Spiess H. (1989). Optimal strategies: a new assignment model for transit networks. Transportation Research 23B: 82–102.Google Scholar
  30. [265]
    Wu J.H., M. Florian, and P. Marcotte (1994). Transit Equilibrium Assignment: a Model and Solution Algorithms. Transportation Science 28: 193–203.Google Scholar
  31. [49]
    Cantarella G.E. (1997). A General Fixed-Point Approach to Multi-Mode Multi-User Equilibrium Assignment with Elastic Demand Transportation Science 31: 107–128.Google Scholar
  32. [50]
    Cantarella G.E., and A. Vitetta (2000). Stochastic assignment to high frequency transit networks: models, and algorithms, and applications with different perceived cost distributions. In Proceedings of the 7`h Meeting of the EURO Working Group on Transportation. Helsinki, and Finland, and August 1999, forthcoming.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Ennio Cascetta
    • 1
  1. 1.Dipartimento di Ingegneria dei Trasporti “Luigi Tocchetti”Università degli Studi di Napoli “Federico II”NapoliItaly

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