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Journal of Siberian Federal University. Mathematics & Physics, 2020, Volume 13, Issue 2, Pages 218–230
DOI: https://doi.org/10.17516/1997-1397-2020-13-2-218-230
(Mi jsfu833)
 

This article is cited in 10 scientific papers (total in 10 papers)

Asymptotic analysis of retrial queueing system $M/M/1$ with impatient customers, collisions and unreliable server

Elena Yu. Danilyuka, Svetlana P. Moiseevaa, Janos Sztrikb

a National Research Tomsk State University, Tomsk, Russian Federation
b University of Debrecen, Debrecen, Hungary
References:
Abstract: The retrial queueing system of $M/M/1$ type with Poisson flow of arrivals, impatient customers, collisions and unreliable service device is considered in the paper. The novelty of our contribution is the inclusion of breakdowns and repairs of the service into our previous study to make the problem more realistic and hence more complicated. Retrial time of customers in the orbit, service time, impatience time of customers in the orbit, server lifetime (depending on whether it is idle or busy) and server recovery time are supposed to be exponentially distributed. An asymptotic analysis method is used to find the stationary distribution of the number of customers in the orbit. The heavy load of the system and long time patience of customers in the orbit are proposed as asymptotic conditions. Theorem about the Gaussian form of the asymptotic probability distribution of the number of customers in the orbit is formulated and proved. Numerical examples are given to show the accuracy and the area of feasibility of the proposed method.
Keywords: retrial queue, impatient customers, collisions, unreliable server, asymptotic analysis.
Funding agency Grant number
Russian Foundation for Basic Research 19-41-703002
The study was funded by Russian Foundation for Basic Research and Tomsk region (project no. 19-41-703002).
Received: 29.11.2019
Received in revised form: 04.12.2019
Accepted: 20.01.2020
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: English
Citation: Elena Yu. Danilyuk, Svetlana P. Moiseeva, Janos Sztrik, “Asymptotic analysis of retrial queueing system $M/M/1$ with impatient customers, collisions and unreliable server”, J. Sib. Fed. Univ. Math. Phys., 13:2 (2020), 218–230
Citation in format AMSBIB
\Bibitem{DanMoiSzt20}
\by Elena~Yu.~Danilyuk, Svetlana~P.~Moiseeva, Janos~Sztrik
\paper Asymptotic analysis of retrial queueing system $M/M/1$ with impatient customers, collisions and unreliable server
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2020
\vol 13
\issue 2
\pages 218--230
\mathnet{http://mi.mathnet.ru/jsfu833}
\crossref{https://doi.org/10.17516/1997-1397-2020-13-2-218-230}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000526181200009}
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  • https://www.mathnet.ru/eng/jsfu/v13/i2/p218
  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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