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ASYMPTOTIC WAITING TIME ANALYSIS OF A FINITE-SOURCE M/M/1 RETRIAL QUEUEING SYSTEM

Published online by Cambridge University Press:  18 July 2018

E. Sudyko ,
A.A. Nazarov  and
J. Sztrik
E. Sudyko
Affiliation:
National Research Tomsk State University, 36 Lenina ave., 634050 Tomsk, Russia E-mail: esudyko@yandex.ru
A.A. Nazarov
Affiliation:
Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, 117198 Moscow, Russia E-mail: nazarov.tsu@gmail.com
J. Sztrik
Affiliation:
University of Debrecen, Debrecen, Hungary E-mail: sztrik.janos@inf.unideb.hu
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Abstract

The aim of the paper is to derive the distribution of the number of retrial of the tagged request and as a consequence to present the waiting time analysis of a finite-source M/M/1 retrial queueing system by using the method of asymptotic analysis under the condition of the unlimited growing number of sources. As a result of the investigation, it is shown that the asymptotic distribution of the number of retrials of the tagged customer in the orbit is geometric with given parameter, and the waiting time of the tagged customer has a generalized exponential distribution. For the considered retrial queuing system numerical and simulation software packages are also developed. With the help of several sample examples the accuracy and range of applicability of the asymptotic results in prelimit situation are illustrated showing the effectiveness of the proposed approximation.

Keywords

accuracy and area of applicability of approximationsasymptotic analysisclosed queueing systemfinite-source queueing systemlimiting distributionnumber of retrialsretrial queuewaiting time
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 33 , Issue 3 , July 2019 , pp. 387 - 403
Copyright
Copyright © Cambridge University Press 2018 

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