Network Equilibrium Models for Urban Transport

  • David Boyce
Reference work entry


Methods for the analysis and prediction of travel conforming to macroscopic assumptions about choices of the urban population cut a broad swath through the field of regional science: economic behavior, spatial analysis, optimization methods, parameter estimation techniques, computational algorithms, network equilibria, and plan evaluation and analysis. This chapter seeks to expose one approach to the construction of models of urban travel choices and implicitly location choices. Beginning with the simple route choice problem faced by vehicle operators in a congested urban road network, exogenous constants are relaxed and replaced with additional assumptions and fewer constants, leading toward a more general forecasting method. The approach, and examples based upon it, reflects the author’s research experience of 40 years with the formulation, implementation, and solution of such models.


Public Transport Mode Choice Route Choice User Equilibrium Traffic Assignment 
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.



Professor Huw Williams, Cardiff University, offered many useful comments on earlier drafts of this chapter. Dr. Hillel Bar-Gera, Ben-Gurion University of the Negev, has offered many stimulating insights and contributions to my thinking on combined network equilibrium models during the past 15 years. Dr. Yu (Marco) Nie, Northwestern University, has been a stimulating colleague during my renewed association with my undergraduate alma mater.

Their contributions are greatly appreciated. Remaining errors are my responsibility.


  1. Abrahamsson T, Lundqvist L (1999) Formulation and estimation of combined network equilibrium models with applications to Stockholm. Transport Sci 33(1):80–100CrossRefGoogle Scholar
  2. Bar-Gera H (2002) Origin-based algorithm for the traffic assignment problem. Transport Sci 36(4):398–417CrossRefGoogle Scholar
  3. Bar-Gera H (2010) Traffic assignment by paired alternative segments. Transport Res B 44(8–9):1022–1046CrossRefGoogle Scholar
  4. Bar-Gera H, Boyce D (2003) Origin-based algorithms for combined travel forecasting models. Transport Res B 37(5):405–422CrossRefGoogle Scholar
  5. Bar-Gera H, Boyce D (2007) Some amazing properties of road traffic network equilibria. In: Friesz TL (ed) Network science, nonlinear science and infrastructure systems. Springer, Berlin, pp 305–335Google Scholar
  6. Bar-Gera H, Boyce D, Nie Y (2012) User-equilibrium route flows and the condition of proportionality. Transport Res B 46(3):440–462CrossRefGoogle Scholar
  7. Beckmann M, McGuire CB, Winsten CB (1956) Studies in the economics of transportation. Yale University Press, New HavenGoogle Scholar
  8. Bell MGH, Iida Y (1997) Transportation network analysis. Wiley, ChichesterGoogle Scholar
  9. Bernardin VL Jr, Koppelman F, Boyce D (2009) Enhanced destination choice models incorporating agglomeration related to trip chaining while controlling for spatial competition. Transport Res Rec 2131:143–151CrossRefGoogle Scholar
  10. Boyce D, Bar-Gera H (2003) Validation of urban travel forecasting models combining origin–destination, mode and route choices. J Regional Science 43(3):517–540CrossRefGoogle Scholar
  11. Boyce D, Bar-Gera H (2004) Multiclass combined models for urban travel forecasting. Netw Spat Econ 4(1):115–124CrossRefGoogle Scholar
  12. De Cea J, Fernandez JE, Soto A, Dekock V (2005) Solving network equilibrium on multimodal urban transportation networks with multiple user classes. Transport Rev 25(3):293–317CrossRefGoogle Scholar
  13. Dial RB (2006) A path-based user-equilibrium traffic assignment algorithm that obviates path storage and enumeration. Transport Res B 40(10):917–936CrossRefGoogle Scholar
  14. Erlander S, Stewart NF (1990) The gravity model in transportation analysis. VSP, UtrechtGoogle Scholar
  15. Evans SP (1973) A relationship between the gravity model for trip distribution and the transportation problem in linear programming. Transport Res 7(1):39–61CrossRefGoogle Scholar
  16. Evans SP (1976) Derivation and analysis of some models for combining trip distribution and assignment. Transport Res 10(1):37–57CrossRefGoogle Scholar
  17. Florian M (2008) Models and software for urban and regional transportation planning: contributions of the center for research on transportation. INFOR 46(1):29–49Google Scholar
  18. Florian M, Hearn D (1995) Network equilibrium models and algorithms. In: Ball MO, Magnanti TL, Monma CL, Nemhauser GL (eds) Network routing, handbooks in operations research and management science 8. Elsevier Science, Amsterdam, pp 485–550Google Scholar
  19. Florian M, Wu JH, He S (2002) A multi-class multi-mode variable demand network equilibrium model with hierarchical logit structures. In: Gendreau M, Marcotte P (eds) Transportation and network analysis: current trends. Kluwer, Dordrecht, pp 119–133CrossRefGoogle Scholar
  20. Kuhn HW, Tucker AW (1951) Nonlinear programming. In: Neyman J (ed) Proceedings of the second Berkeley symposium on mathematical statistics and probability. University of California Press, Berkeley, pp 481–492Google Scholar
  21. Lam WHK, Huang H-J (1992) A combined trip distribution and assignment model for multiple user classes. Transport Res B 26(4):275–287CrossRefGoogle Scholar
  22. Lee D-H, Meng Q, Deng W (2010) Origin-based partial linearization method of the stochastic user equilibrium traffic assignment problem. J Transp Eng-ASCE 136:52–60CrossRefGoogle Scholar
  23. Marcotte P, Patriksson M (2007) Traffic equilibrium. In: Barnhart C, Laporte G (eds) Transportation, handbooks in operations research and management science 14. Elsevier Science, Amsterdam, pp 623–713Google Scholar
  24. Nagurney A (1999) Network economics, 2nd edn. Kluwer, BostonCrossRefGoogle Scholar
  25. Oppenheim N (1995) Urban travel demand modeling. Wiley, New YorkGoogle Scholar
  26. Ortúzar JD, Willumsen LG (2011) Modelling transport, 4th edn. Wiley, New YorkCrossRefGoogle Scholar
  27. Patriksson M (1994) The traffic assignment problem: models and methods. VSP, UtrechtGoogle Scholar
  28. Sheffi Y (1985) Urban transportation networks. Prentice-Hall, Englewood CliffsGoogle Scholar
  29. Williams HCWL (1977) On the formation of travel demand models and economic evaluation measures of user benefit. Environ Plann 9(3):285–344CrossRefGoogle Scholar
  30. Wilson AG (1970) Entropy in urban and regional modeling. Pion, LondonGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringNorthwestern UniversityEvanstonUSA

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