Skip to main content
SpringerLink
Log in

Principles of Wardrop for Traffic Assignment in a Road Network

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

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

Abstract

In this chapter is devoted to user equilibrium and system optimum of Wardrop. Discussion on the mathematical formulation of traffic assignment problems with regard to their meaning is available in the Sect. 2.1. The specification of necessary basic statements completes this discussion further. The dual traffic assignment problem with travel times between all origins and destinations as dual variables is considered in the Sect. 2.2. The practical significance of such dual formulation is shown to become evident due to the wide spread of online traffic services. The route-flow assignment problem and link-flow assignment problem are reduced to fixed-point problems with explicit operators in the Sect. 2.3 and Sect. 2.4 respectively. Proofs of corresponding theorems are fully given.

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. Wardrop JG (1952) Some theoretical aspects of road traffic research. Proc Inst Civil Eng 2:325–378

    Google Scholar 

  2. Pang J-S, Fukushima M (2005) Quasi-variational inequalities, generalized Nash equilibria, and multileader-follower games. Comput Manag Sci 2(1):21–56

    Article  MathSciNet  Google Scholar 

  3. Xie J, Yu N, Yang X (2013) Quadratic approximation and convergence of some bush-based algorithms for the traffic assignment problem. Transp Res Part B 56:15–30

    Article  Google Scholar 

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

    Google Scholar 

  5. Beckmann MJ, McGuire CB, Winsten CB (1956) Studies in the economics of transportation. Yale University Press, New Haven, CT

    Google Scholar 

  6. Dafermos SC, Sparrow FT (1969) The traffic assignment problem for a general network. J Res Nat Bureau Stand 73B:91–118

    Article  MathSciNet  Google Scholar 

  7. Dafermos SC (1968) Traffic assignment and resource allocation in transportation networks. PhD thesis. Johns Hopkins University, Baltimore, MD

    Google Scholar 

  8. Patriksson M (2015) The traffic assignment problem: models and methods. Dover Publications Inc., New York

    Google Scholar 

  9. Shen W, Zhang HM (2009) On the morning commute problem in a corridor network with multiple bottlenecks: its system-optimal traffic flow patterns and the realizing tolling scheme. Transp Res Part B 43:267–284

    Article  Google Scholar 

  10. Ahuja RK, Magnanti TL, Orlin JB (1993) Network flows: theory, algorithms, and applications. Prentice-Hall, Englewood Cliffs, NJ

    MATH  Google Scholar 

  11. Bertsekas DP (1999) Nonlinear programming, 2nd edn. Athena Scientific, Belmont, MA

    MATH  Google Scholar 

  12. Krylatov AY, Shirokolobova AP, Zakharov VV (2016) OD-matrix estimation based on a dual formulation of traffic assignment problem. Informatica (Slovenia) 40(4):393–398

    MathSciNet  Google Scholar 

  13. Fisk C (1984) A nonlinear equation framework for solving network equilibrium problems. Environ Plan 16A:67–80

    Article  Google Scholar 

  14. Fisk C, Nguyen S (1980) A unified approach for the solution of network equilibrium problems. Publication 169. Centre de rechercher sur les transports, Universite de Montreal, Montreal (1980)

    Google Scholar 

  15. Chen R-J, Meyer RR (1988) Parallel optimization for traffic assignment. Math Program 42:327–345

    Article  MathSciNet  Google Scholar 

  16. Patriksson M (1993) A unified description of iterative algorithms for traffic equilibria. Eur J Oper Res 71:154–176

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  18. Swamy MNS, Thulasiraman K (1981) Graphs, networks, and algorithms. Wiley, New York

    Google Scholar 

  19. 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 

  20. Gantmacher F (1959) Theory of matrices. AMS Chelsea Publishing, New York

    MATH  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). Principles of Wardrop for Traffic Assignment in a Road Network. 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_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-34102-2_2

  • 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