A remark on a standard and linear vector network equilibrium problem with capacity constraints |
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Authors: | SJ Li KL Teo XQ Yang |
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Institution: | 1. College of Mathematics and Science, Chongqing University, Chongqing 400044, China;2. Department of Mathematics and Statistics, Curtin University of Technology GPO Box U1987, Perth, WA 6845, Australia;3. Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong |
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Abstract: | In this paper, (weak) vector equilibrium principle with capacity constraints is introduced. A necessary condition that a vector minimum cost flow is a vector equilibrium flow with capacity constraints is obtained. When the number of paths connecting with each pair of source and sink is less than or equal to 2, a sufficient condition for a vector minimum cost flow to be a vector equilibrium flow is also obtained. A generalized (weak) vector equilibrium principle is also introduced. Without any additional assumption, a necessary and sufficient condition for a (weak) vector minimum cost flow to be a generalized (weak) vector equilibrium flow is obtained. |
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Keywords: | Traffic network equilibrium model Vector equilibrium principle Vector minimum cost flow |
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