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Mosc. Math. J., 2001, Volume 1, Number 3, Pages 407–419 (Mi mmj28)  

Steady solutions for FIFO networks

K. M. Khaninabcd, D. V. Khmelevedc, A. N. Rybkof, A. A. Vladimirovf

a Basic Research Institute in the Mathematical Sciences
b L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
c Heriot Watt University
d Isaac Newton Institute for Mathematical Sciences
e M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
f Institute for Information Transmission Problems, Russian Academy of Sciences

Abstract: We consider the fluid model of a reentrant line with FIFO discipline and look for solutions with constant flows (steady solutions). In the case of constant viscosities we prove the uniqueness of such a solution. If viscosities are different, we present an example with multiple steady solutions. We also prove that for some classes of reentrant lines uniqueness holds even if the viscosities are different.

Key words and phrases: Kelly networks, fluid models, uniqueness of steady solution, fixed points.

DOI: https://doi.org/10.17323/1609-4514-2001-1-3-407-419

Full text: http://www.ams.org/.../abst1-3-2001.html
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MSC: 90B10, 94C99, 37Lxx
Received: July 31, 2001; in revised form September 11, 2001
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Citation: K. M. Khanin, D. V. Khmelev, A. N. Rybko, A. A. Vladimirov, “Steady solutions for FIFO networks”, Mosc. Math. J., 1:3 (2001), 407–419

Citation in format AMSBIB
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\by K.~M.~Khanin, D.~V.~Khmelev, A.~N.~Rybko, A.~A.~Vladimirov
\paper Steady solutions for FIFO networks
\jour Mosc. Math.~J.
\yr 2001
\vol 1
\issue 3
\pages 407--419
\mathnet{http://mi.mathnet.ru/mmj28}
\crossref{https://doi.org/10.17323/1609-4514-2001-1-3-407-419}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1877601}
\zmath{https://zbmath.org/?q=an:1030.90008}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000208587500007}


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