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.
- (Weak) vector equilibrium
- Vector traffic network equilibrium model
- Weak ξ-equilibrium
- Weak parametric equilibrium
ASJC Scopus subject areas
- Applied Mathematics
- Management Science and Operations Research