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Applied mathematics
A generalized Gibbs' lemma and a Wardrop equilibrium
V. N. Malozemov, N. A. Solovyeva St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
Abstract:
In the article, a generalized Gibbs' lemma is stated and proved. A conclusion of this lemma corresponds to a definition of Wardrop equilibrium in transport networks. This allows us to naturally introduce a well known convex programming problem with linear constraints whose solution is a Wardrop equilibrium vector. The complicated definition of the Wardrop equilibrium is analyzed in detail (typical examples are given). The reason of the Braess paradox' appearance is specified. A large example, that illustrates how the Wardrop equilibrium vector changes when a road with zero driving time is added into the transport network, is also given.
Keywords:
generalized Gibbs' lemma, Wardrop equilibrium, Braess paradox, convex programming.
Received: August 21, 2018 Accepted: March 15, 2019
Citation:
V. N. Malozemov, N. A. Solovyeva, “A generalized Gibbs' lemma and a Wardrop equilibrium”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 15:2 (2019), 199–211
Linking options:
https://www.mathnet.ru/eng/vspui401 https://www.mathnet.ru/eng/vspui/v15/i2/p199
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Abstract page: | 168 | Full-text PDF : | 25 | References: | 31 | First page: | 6 |
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