Skip to main content
SpringerLink
Log in

Methods for Traffic Flow Assignment in Road Networks

  • Chapter
  • First Online:
Book cover Optimization Models and Methods for Equilibrium Traffic Assignment

Part of the book series: Springer Tracts on Transportation and Traffic ((STTT,volume 15))

  • 916 Accesses

Abstract

In this chapter is devoted to approaches for solving traffic flow assignment problems. The most popular gradient descent method for solving traffic assignment problems is discussed in the first section. New projection algorithms based on the obtained, explicitly fixed-point operators for the route-flow assignment problem and link-route assignment problem are presented in the third and fourth sections respectively. Obtained operators is proved to be contractive that leads to the linear convergence of provided algorithms. Moreover, under some fairly natural conditions the algorithms converge quadratically. The technique for representing a linear route-flow assignment problem in the form of a system of linear equations is presented in the fourth section. A simple example demonstrates the evident usability of the developed technique for its implementation and further extensions.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Frank M, Wolfe P (1956) An algorithm for quadratic programming. Naval Res Logist Quart 3:95–110

    Article  MathSciNet  Google Scholar 

  2. Gartner NH (1980) Optimal traffic assignment with elastic demands: a review Part II: algorithmic approaches. Transp Sci 14(2):192–208

    Article  Google Scholar 

  3. Van Vliet D, Dow PDC (1979) Capacity-restrained road assignment. Traffic Eng Control 20:296–305

    Google Scholar 

  4. Van Vliet D (1976) Road assignment – I: principles and parameters of model formulation. Transp Res 10:137–143

    Article  Google Scholar 

  5. Larsson T, Patriksson M (1992) Simplicial decomposition with disaggregated representation for the traffic assignment problem. Transp Sci 26:4–17

    Article  Google Scholar 

  6. Rose G, Daskin MS, Koppelman FS (1988) An examination of convergence error in equilibrium traffic assignment models. Transp Res 22B:261–274

    Article  Google Scholar 

  7. Golden BL (1975) A minimum-cost multicommodity network flow problem concerning imports and exports. Networks 5:331–356

    Article  MathSciNet  Google Scholar 

  8. LeBlanc LJ, Morlok EK, Pierskalla WP (1974) An accurate and efficient approach to equilibrium traffic assignment on congested networks. Transp Res Record 491:12–23

    Google Scholar 

  9. LeBlanc LJ, Morlok EK, Pierskalla WP (1975) An efficient approach to solving the road network equilibrium traffic assignment problem. Transp Res 9:309–318

    Article  Google Scholar 

  10. Nguyen S (1973) A mathematical programming approach to equilibrium methods of traffic assignment with fixed demands. Publication 138. Départment d’Informatique et de Reserche Opérationelle. Université de Montréal, Montréal

    Google Scholar 

  11. Steenbrink PA (1974) Optimization of transport networks. Wiley, London

    Google Scholar 

  12. Fratta L, Gerla M, Kleinrock L (1973) The flow-deviation method: an approach to store-and-forward computer communication network design. Networks 3:97–133

    Article  MathSciNet  Google Scholar 

  13. Klessig RW (1974) An algorithm for nonlinear multicommodity flow problems. Networks 4:343–355

    Article  MathSciNet  Google Scholar 

  14. Yaged B Jr (1971) Minimum cost routing for static network models. Networks 1:139–172

    Article  MathSciNet  Google Scholar 

  15. Patriksson M (2015) The traffic assignment problem: models and methods. Dover Publications Inc., Mineola, N.Y.

    Google Scholar 

  16. Florian M, Nguyen S (1976) An application and validation of equilibrium trip assignment methods. Transp Sci 10:374–390

    Article  Google Scholar 

  17. Dijkstra EW (1959) A note on two problems in connexion with graphs. Numerische Mathematik 1:269–271

    Article  MathSciNet  Google Scholar 

  18. Gallo G, Pallottino S (1982) A new algorithm to find the shortest paths between all pairs of nodes. Discrete Appl Math 4:23–35

    Article  MathSciNet  Google Scholar 

  19. Gallo G, Pallottino S (1986) Shortest path methods: a unifying approach. Math Progr Study 26:38–64

    Article  MathSciNet  Google Scholar 

  20. Halder AK (1970) The method of competing links. Transp Sci 4:36–51

    Article  Google Scholar 

  21. Loubal PS (1967) A network evaluation procedure. Highway Res Record 205:96–109

    Google Scholar 

  22. Rodionov VV (1968) The parametric problem of shortest distances. U.S.S.R. Comput Math Math Phys 8:336–343

    Article  Google Scholar 

  23. Wollmer R (1964) Removing arcs from a network. Oper Res 12:934–940

    Article  MathSciNet  Google Scholar 

  24. Canon MD, Cullum CD (1968) A tight upper bound on the rate of convergence of the Frank-Wolfe algorithm. SIAM J Control 6:509–516

    Article  MathSciNet  Google Scholar 

  25. Dem’janov VF, Rubinov AM (1965) On the problem of minimization of a smooth functional with convex constraints. Soviet Math Doklady 6:9–11

    Google Scholar 

  26. Dunn JC (1979) Rates of convergence for conditional gradient algorithms near singular and nonsingular extremals. SIAM J Control Optim 17:187–211

    Article  MathSciNet  Google Scholar 

  27. Dunn JC (1980) Convergence rates for conditional gradient sequences generated by implicit step length rules. SIAM J Control Optim 18:473–487

    Article  MathSciNet  Google Scholar 

  28. Levitin ES, Polyak BT (1966) Constrained minimization methods. USSR Compu Math Math Phys 6:1–50

    Article  Google Scholar 

  29. Zangwill WI (1969) Nonlinear programming: a unified approach. Prentice-Hall Inc, Englewood Clifs, N.J

    MATH  Google Scholar 

  30. Wolfe P (1970) Convergence theory in nonlinear programming. In: Abadie J (ed) Integer and Nonlinear Programming. North-Holland, Amsterdam (1970)

    Google Scholar 

  31. Zangwill WI (1969) Convergence conditions for nonlinear programming algorithms. Manag Sci 16:1–13

    Article  MathSciNet  Google Scholar 

  32. Lupi M (1986) Convergence of the Frank-Wolfe algorithm in transportation networks. Civil Eng Syst 3:7–15

    Article  Google Scholar 

  33. Janson BN, Zozaya-Gorostiza C (1987) The problem of cyclic flows in traffic assignment. Transp Res 21B:299–310

    Article  Google Scholar 

  34. Konnov IV (2017) An adaptive partial linearization method for optimization problems on product sets. J Optim Theory Appl 175(2):478–501

    Article  MathSciNet  Google Scholar 

  35. Krylatov AY (2016) Network flow assignment as a fixed point problem. J Appl Ind Math 10(2):243–256

    Article  MathSciNet  Google Scholar 

  36. Marcotte P (1986) Network design problem with congestion effects: a case of bilevel programming. Math Progr 34(2):142–162

    Article  MathSciNet  Google Scholar 

  37. Greenshields BD (1934) A study of traffic capacity. Proc (US) Highway Res Board 14:448–494

    Google Scholar 

  38. Long J, Gao Z, Zhang H, Szeto WY (2010) A turning restriction design problem in urban road networks. Eur J Oper Res 206(3):569–578

    Article  MathSciNet  Google Scholar 

  39. Yang H, Yagar S (1995) Traffic assignment and signal control in saturated road networks. Transp Res Part A 29(2):125–139

    Article  Google Scholar 

  40. Krylatov AY, Shirokolobova AP (2017) Projection approach versus gradient descent for networks flows assignment problem. Lect Notes Comput Sci 10556:345–350

    Article  Google Scholar 

  41. Krylatov AY (2018) Reduction of a minimization problem for a convex separable function with linear constraints to a fixed point problem. J Appl Ind Math 12(1):98–111

    Article  MathSciNet  Google Scholar 

  42. Sheffi Y (1985) Urban transportation networks: equilibrium analysis with mathematical programming methods. Prentice-Hall Inc, Englewood Cliffs, N.J

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Transport Problems, Russian Academy of Sciences, Saint Petersburg, Russia

    Alexander Krylatov

  2. Faculty of Applied Mathematics and Control Processes, Saint Petersburg State University, Saint Petersburg, Russia

    Alexander Krylatov & Victor Zakharov

  3. Faculty of Information Technology, University of Jyväskylä, Jyväskylä, Finland

    Tero Tuovinen

Authors
  1. Alexander Krylatov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Victor Zakharov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tero Tuovinen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alexander Krylatov .

Rights and permissions

Reprints and permissions

Copyright information

© 2020 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Krylatov, A., Zakharov, V., Tuovinen, T. (2020). Methods for Traffic Flow Assignment in Road Networks. In: Optimization Models and Methods for Equilibrium Traffic Assignment. Springer Tracts on Transportation and Traffic, vol 15. Springer, Cham. https://doi.org/10.1007/978-3-030-34102-2_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-34102-2_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-34101-5

  • Online ISBN: 978-3-030-34102-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation