Mathematical Methods of Operations Research

, Volume 64, Issue 2, pp 327–334

A note on vector network equilibrium principles

Original Article

DOI: 10.1007/s00186-006-0089-x

Cite this article as:
Li, S.J., Yang, X.Q. & Chen, G.Y. Math Meth Oper Res (2006) 64: 327. doi:10.1007/s00186-006-0089-x


An example is given to show that the necessary conditions of Theorem 4.5 [in Chen et al. Math Methods Oper Res 49:239–253, 1999] and Theorem 2.1 (i) [in Goh and Yang Eur J Oper Res 116:615–628, 1999] for (weak) vector equilibrium flows may not hold. New ξ-equilibrium and parametric equilibrium flows are introduced. As a result, necessary and sufficient conditions between a weak vector equilibrium flow and an ξ-equilibrium flow and between a vector equilibrium flow and a parametric equilibrium flow are established.


Vector traffic network equilibrium model (Weak) vector equilibrium Weak ξ-equilibrium Weak parametric equilibrium 

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.College of Mathematics and ScienceChongqing UniversityChongqingChina
  2. 2.Department of Applied MathematicsThe Hong Kong Polytechnic UniversityHong KongChina
  3. 3.Institute of Systems ScienceChinese Academy of ScienceBeijingChina

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