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Teoriya Veroyatnostei i ee Primeneniya, 2022, Volume 67, Issue 4, Pages 792–801
DOI: https://doi.org/10.4213/tvp5527 (Mi tvp5527) 		 
Short Communications

Accuracy of estimation of the vector of queue lengths for open Jackson networks

E. O. Lenena

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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DOI: https://doi.org/10.4213/tvp5527
Abstract: The accuracy of approximation of the vector of queue lengths for an open Jackson network with regenerative input flow and unreliable servers is estimated. A theorem on the accuracy of approximation of the vector of queue lengths in open Jackson networks is put forward, i.e., an estimate for the probability of deviations of the norm of the difference between the process of queue lengths and the constructed reflected Brownian motion is obtained. As a corollary, an estimate of the Wasserstein distance is given.
Keywords: Jackson network, unreliable servers, reflected Brownian motion, heavy traffic conditions.
Received: 13.08.2021
Revised: 15.04.2022
Accepted: 10.06.2022
English version:
Theory of Probability and its Applications, 2022, Volume 67, Issue 4, Pages 633–639
DOI: https://doi.org/10.1137/S0040585X97T991180
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: E. O. Lenena, “Accuracy of estimation of the vector of queue lengths for open Jackson networks”, Teor. Veroyatnost. i Primenen., 67:4 (2022), 792–801; Theory Probab. Appl., 67:4 (2022), 633–639
Citation in format AMSBIB
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\by E.~O.~Lenena
\paper Accuracy of estimation of the vector of queue lengths for open Jackson networks
\jour Teor. Veroyatnost. i Primenen.
\yr 2022
\vol 67
\issue 4
\pages 792--801
\mathnet{http://mi.mathnet.ru/tvp5527}
\crossref{https://doi.org/10.4213/tvp5527}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4548667}
\transl
\jour Theory Probab. Appl.
\yr 2022
\vol 67
\issue 4
\pages 633--639
\crossref{https://doi.org/10.1137/S0040585X97T991180}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85153220073}
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