Science China Technological Sciences

, Volume 61, Issue 11, pp 1642–1653 | Cite as

Traffic network equilibrium problems with demands uncertainty and capacity constraints of arcs by scalarization approaches

  • JinDe CaoEmail author
  • RuoXia LiEmail author
  • Wei Huang
  • JianHua Guo
  • Yun Wei


This paper focuses on the vector traffic network equilibrium problem with demands uncertainty and capacity constraints of arcs, in which, the demands are not exactly known and assumed as a discrete set that contains finite scenarios. For different scenario, the demand may be changed, which seems much more reasonable in practical programming. By using the linear scalarization method, we introduce several definitions of parametric equilibrium flows and reveal their mutual relations. Meanwhile, the relationships between the scalar variational inequality as well as the (weak) vector equilibrium flows are explored, meanwhile, some necessary and sufficient conditions that ensure the (weak) vector equilibrium flows are also considered. Additionally, by means of nonlinear scalarization functionals, two kinds of equilibrium principles are derived. All of the derived conclusions contain the demands uncertainty and capacity constraints of arcs, thus the results proposed in this paper improved some existing works. Finally, some numerical examples are employed to show the merits of the improved conclusions.


traffic network demands uncertainty capacity equilibrium flow scalarization 


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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics, Research Center for Complex Systems and Network SciencesSoutheast UniversityNanjingChina
  2. 2.Intelligent Transportation System Research CenterSoutheast UniversityNanjingChina
  3. 3.National Engineering Laboratory for Green & Safe Construction Technology in Urban Rail TransitBeijingChina

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