Bi-Objective Network Equilibrium, Traffic Assignment and Road Pricing

  • Judith Y.  T. Wang
  • Matthias EhrgottEmail author
Conference paper
Part of the Operations Research Proceedings book series (ORP)


Multi-objective equilibrium models of traffic assignment state that users of road networks travel on routes that are efficient with respect to several objectives, such as travel time and toll. This concept provides a general framework for modelling traffic flow in tolled road networks. We present the concept of time surplus maximisation as a way of handling user preferences. Given a toll, users have a maximum time they are willing to spend for a trip. Time surplus is this maximum time minus actual travel time. A rational user can be assumed to maximise time surplus, leading to the definition of time surplus maximisation bi-objective user equilibrium. We propose to use such models on the lower level of bi-level models for pricing in road networks under multiple upper level objectives such as minimising total travel time and emissions. In such a model a multi-objective optimisation problem at the upper level is combined with a multi-objective equilibrium problem at the lower level.


Travel Time Route Choice User Equilibrium Traffic Assignment Total Travel Time 
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This research was partially supported by the Marsden Fund project “Multiobjective network equilibria—From definitions to algorithms”, grant number 9075 362506.


  1. 1.
    Bureau of Public Roads: Traffic assignment manual. U.S. Department of Commerce, Urban Planning Division, Washington D.C. (1964)Google Scholar
  2. 2.
    Commission, European: Planning and research of policies for land use and transport for increasing urban sustainablity PROPOLIS: Final report to European commission. European Commission, Brussels, Belgium (2004)Google Scholar
  3. 3.
    European Conference of Ministers of Transport: Sustainable transport policies. Available at (2000)
  4. 4.
    Lo, H.K., Chen, A.: Traffic equilibrium problem with route-specific costs: Formulation and algorithms. Transp. Res. Part B Methodol. 34(6), 493–513 (2000)CrossRefGoogle Scholar
  5. 5.
    Nagurney, A.: Congested urban transportation networks and emission paradoxes. Transp. Res. Part D 5, 145–151 (2000)CrossRefGoogle Scholar
  6. 6.
    Niemeier, D.A., Sugawara, S.: How much can vehicle emissions be reduced? Exploratory analysis of an upper boundary using an emissions-optimized trip assignment. Transp. Res. Rec. 1815, 29–37 (2002)CrossRefGoogle Scholar
  7. 7.
    Wang, J.Y.T., Ehrgott, M.: Modelling stochastic route choice with bi-objective traffic assignment. In: International Choice Modelling Conference 2011 held in Leeds on 4–6 July 2011Google Scholar
  8. 8.
    Wang, J.Y.T., Raith, A., Ehrgott, M.: Tolling analysis with bi-objective traffic assignment. In: Ehrgott, M., Naujoks, B., Stewart, T., Wallenius, J. (eds.) Multiple Criteria Decision Making for Sustainable Energy and Transportation Systems, pp. 117–129. Springer, Berlin (2010)Google Scholar
  9. 9.
    Wardrop, J.G.: Some theoretical aspects of road traffic research. In: Proceedings of the Institution of Civil Engineers, Part II, vol. 1, pp. 325–362 (1952)Google Scholar
  10. 10.
    Yin, Y., Lawphongpanich, S.: Internalizing emission externality on road networks. Transp. Res. Part D 11, 292–301 (2006)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of Engineering ScienceThe University of AucklandAucklandNew Zealand

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