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Traffic Network Equilibrium Problems with Capacity Constraints of Arcs and Linear Scalarization Methods

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  • X. Q. Tian
  • Y. D. Xu

Abstract

Traffic network equilibrium problems with capacity constraints of arcs are studied. A (weak) vector equilibrium principle with vector‐valued cost functions, which are different from the ones in the work of Lin (2010), and three kinds of parametric equilibrium flows are introduced. Some necessary and sufficient conditions for a (weak) vector equilibrium flow to be a parametric equilibrium flow are derived. Relationships between a parametric equilibrium flow and a solution of a scalar variational inequality problem are also discussed. Some examples are given to illustrate our results.

Suggested Citation

  • X. Q. Tian & Y. D. Xu, 2012. "Traffic Network Equilibrium Problems with Capacity Constraints of Arcs and Linear Scalarization Methods," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:612142
    DOI: 10.1155/2012/612142
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    References listed on IDEAS

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