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Zbl 1131.90010
Li, S.J.; Yang, X.Q.; Chen, G.Y.
A note on vector network equilibrium principles. (English)
[J] Math. Methods Oper. Res. 64, No. 2, 327-334 (2006). ISSN 1432-2994; ISSN 1432-5217/e

Summary: An example is given to show that the necessary conditions of Theorem 4.5 [in {\it G. Y. Chen} et al. Math. Methods Oper. Res. 49, No.~2, 239--253 (1999; Zbl 0939.90014)] and Theorem 2.1 (i) [in {\it X. Q. C. J. Goh} and {\it X. Q. Yang}, Eur. J. Oper. Res. 116, 615--628 (1999; Zbl 1009.90093)] for (weak) vector equilibrium flows may not hold. New $\xi$-equilibrium and parametric equilibrium flows are introduced. As a result, necessary and sufficient conditions between a weak vector equilibrium flow and an $\xi$-equilibrium flow and between a vector equilibrium flow and a parametric equilibrium flow are established.

MSC 2000:: *90B10 Flows in networks
90B20 Highway traffic
91A40 Game-theoretic models

Keywords: Vector traffic network equilibrium model; (Weak) vector equilibrium; Weak $\xi$-equilibrium; Weak parametric equilibrium

Citations: Zbl 0939.90014; Zbl 1009.90093

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