Research of a retrial queueing system with exclusion of customers and three-phase phased by follow-up
In this paper, we consider a retrial queueing system (RQ-system) which receives to the input a Poisson flow with a given intensity. If at the time of customer the server is busy, the displacement of customer standing on the server takes place. Customers that do not have time to be successfully se...
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Samara State Technical University
2020-01-01
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Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
Online Access: | http://mi.mathnet.ru/vsgtu1756 |
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doaj-cbf80a05b3914ffa92d303091bd691a02020-11-25T03:52:52ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812020-01-0124233134210.14498/vsgtu1756Research of a retrial queueing system with exclusion of customers and three-phase phased by follow-upNazarov, Anatolii AndreevichIzmailova, Yana Evgenevna In this paper, we consider a retrial queueing system (RQ-system) which receives to the input a Poisson flow with a given intensity. If at the time of customer the server is busy, the displacement of customer standing on the server takes place. Customers that do not have time to be successfully serviced go into orbit, in order to, after an accidental exponential delay, again turn to the server for maintenance. It is shown that the limiting characteristic function of the number of customers in the orbit and the states of the server converges to a three-dimensional Gaussian distribution. The mean vector and covariance matrix are obtained for this distribution. A stationary probability distribution of the server states is also found.http://mi.mathnet.ru/vsgtu1756 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Nazarov, Anatolii Andreevich Izmailova, Yana Evgenevna |
spellingShingle |
Nazarov, Anatolii Andreevich Izmailova, Yana Evgenevna Research of a retrial queueing system with exclusion of customers and three-phase phased by follow-up Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
author_facet |
Nazarov, Anatolii Andreevich Izmailova, Yana Evgenevna |
author_sort |
Nazarov, Anatolii Andreevich |
title |
Research of a retrial queueing system with exclusion of customers and three-phase phased by follow-up |
title_short |
Research of a retrial queueing system with exclusion of customers and three-phase phased by follow-up |
title_full |
Research of a retrial queueing system with exclusion of customers and three-phase phased by follow-up |
title_fullStr |
Research of a retrial queueing system with exclusion of customers and three-phase phased by follow-up |
title_full_unstemmed |
Research of a retrial queueing system with exclusion of customers and three-phase phased by follow-up |
title_sort |
research of a retrial queueing system with exclusion of customers and three-phase phased by follow-up |
publisher |
Samara State Technical University |
series |
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
issn |
1991-8615 2310-7081 |
publishDate |
2020-01-01 |
description |
In this paper, we consider a retrial queueing system (RQ-system) which receives to the input a Poisson flow with a given intensity. If at the time of customer the server is busy, the displacement of customer standing on the server takes place. Customers that do not have time to be successfully serviced go into orbit, in order to, after an accidental exponential delay, again turn to the server for maintenance. It is shown that the limiting characteristic function of the number of customers in the orbit and the states of the server converges to a three-dimensional Gaussian distribution. The mean vector and covariance matrix are obtained for this distribution. A stationary probability distribution of the server states is also found. |
url |
http://mi.mathnet.ru/vsgtu1756 |
work_keys_str_mv |
AT nazarovanatoliiandreevich researchofaretrialqueueingsystemwithexclusionofcustomersandthreephasephasedbyfollowup AT izmailovayanaevgenevna researchofaretrialqueueingsystemwithexclusionofcustomersandthreephasephasedbyfollowup |
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