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Diskretnyi Analiz i Issledovanie Operatsii, 2016, Volume 23, Issue 2, Pages 63–87
DOI: https://doi.org/10.17377/daio.2016.23.503 (Mi da845) 		 
This article is cited in 17 scientific papers (total in 17 papers)

Network flow assignment as a fixed point problem

A. Yu. Krylatovab

a Saint Petersburg State University, 7/9 Universitetskaya Nab., 199034 St. Petersburg, Russia
b Solomenko Institute of Transport Problems of the RAS, 13 12th Line VO, 199178 St. Petersburg, Russia
Full-text PDF (336 kB) Citations (17)
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DOI: https://doi.org/10.17377/daio.2016.23.503
Abstract: This paper deals with the user equilibrium problem (flow assignment with equal journey time by alternative routes) and system optimum (flow assignment with minimal average journey time) in a network consisting of parallel routes with a single origin-destination pair. The travel time is simulated by arbitrary smooth nondecreasing functions. We prove that the equilibrium and optimal assignment problems for such a network can be reduced to the fixed point problem expressed explicitly. A simple iterative method of finding equilibrium and optimal flow assignment is developed. The method is proved to converge geometrically; under some fairly natural conditions the method is proved to converge quadratically. Bibliogr. 30.
Keywords: user-equilibrium, system optimum, fixed point, network routes.
Received: 31.07.2015
Revised: 24.11.2015
English version:
Journal of Applied and Industrial Mathematics, 2016, Volume 10, Issue 2, Pages 243–256
DOI: https://doi.org/10.1134/S1990478916020095
Bibliographic databases:
Document Type: Article
UDC: 519.8
Language: Russian
Citation: A. Yu. Krylatov, “Network flow assignment as a fixed point problem”, Diskretn. Anal. Issled. Oper., 23:2 (2016), 63–87; J. Appl. Industr. Math., 10:2 (2016), 243–256
Citation in format AMSBIB
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\by A.~Yu.~Krylatov
\paper Network flow assignment as a~fixed point problem
\jour Diskretn. Anal. Issled. Oper.
\yr 2016
\vol 23
\issue 2
\pages 63--87
\mathnet{http://mi.mathnet.ru/da845}
\crossref{https://doi.org/10.17377/daio.2016.23.503}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3557594}
\elib{https://elibrary.ru/item.asp?id=26129767}
\transl
\jour J. Appl. Industr. Math.
\yr 2016
\vol 10
\issue 2
\pages 243--256
\crossref{https://doi.org/10.1134/S1990478916020095}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84971282398}
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    • This publication is cited in the following 17 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Дискретный анализ и исследование операций
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