A note on vector network equilibrium principles

S. J. Li; Xiaoqi Yang; G. Y. Chen

doi:10.1007/s00186-006-0089-x

A note on vector network equilibrium principles

S. J. Li
, Xiaoqi Yang
, G. Y. Chen

Research output: Journal article publication › Journal article › Academic research › peer-review

10 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	327-334
Number of pages	8
Journal	Mathematical Methods of Operations Research
Volume	64
Issue number	2
DOIs	https://doi.org/10.1007/s00186-006-0089-x
Publication status	Published - 1 Oct 2006

Keywords

(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

More information

10.1007/s00186-006-0089-x

Cite this

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title = "A note on vector network equilibrium principles",

abstract = "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.",

keywords = "(Weak) vector equilibrium, Vector traffic network equilibrium model, Weak ξ-equilibrium, Weak parametric equilibrium",

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AU - Li, S. J.

AU - Yang, Xiaoqi

AU - Chen, G. Y.

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N2 - 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.

AB - 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.

KW - (Weak) vector equilibrium

KW - Vector traffic network equilibrium model

KW - Weak ξ-equilibrium

KW - Weak parametric equilibrium

UR - https://www.scopus.com/pages/publications/33749001196

U2 - 10.1007/s00186-006-0089-x

DO - 10.1007/s00186-006-0089-x

M3 - Journal article

SN - 1432-2994

VL - 64

SP - 327

EP - 334

JO - Mathematical Methods of Operations Research

JF - Mathematical Methods of Operations Research

IS - 2

ER -

A note on vector network equilibrium principles

Abstract

Keywords

ASJC Scopus subject areas

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