Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10. Prikladnaya Matematika. Informatika. Protsessy Upravleniya
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Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10. Prikladnaya Matematika. Informatika. Protsessy Upravleniya, 2019, Volume 15, Issue 2, Pages 199–211
DOI: https://doi.org/10.21638/11701/spbu10.2019.204
(Mi vspui401)
 

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
References:
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
Bibliographic databases:
Document Type: Article
UDC: 519.85
MSC: 90C90
Language: Russian
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
Citation in format AMSBIB
\Bibitem{MalSol19}
\by V.~N.~Malozemov, N.~A.~Solovyeva
\paper A generalized Gibbs' lemma and a Wardrop equilibrium
\jour Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr.
\yr 2019
\vol 15
\issue 2
\pages 199--211
\mathnet{http://mi.mathnet.ru/vspui401}
\crossref{https://doi.org/10.21638/11701/spbu10.2019.204}
\elib{https://elibrary.ru/item.asp?id=38552365}
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    Вестник Санкт-Петербургского университета. Серия 10. Прикладная математика. Информатика. Процессы управления
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    Abstract page:168
    Full-text PDF :27
    References:31
    First page:6
     
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