Principles of Wardrop for Traffic Assignment in a Road Network

  • Alexander KrylatovEmail author
  • Victor Zakharov
  • Tero Tuovinen
Part of the Springer Tracts on Transportation and Traffic book series (STTT, volume 15)


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.


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Copyright information

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

Authors and Affiliations

  1. 1.Institute of Transport ProblemsRussian Academy of SciencesSaint PetersburgRussia
  2. 2.Faculty of Applied Mathematics and Control ProcessesSaint Petersburg State UniversitySaint PetersburgRussia
  3. 3.Faculty of Information TechnologyUniversity of JyväskyläJyväskyläFinland

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