Sojourn Times in a Queueing System with Breakdowns and General Retrial Times

This paper centers on a discrete-time retrial queue where the server experiences breakdowns and repairs when arriving customers may opt to follow a discipline of a last-come, first-served (LCFS)-type or to join the orbit. We focused on the extensive analysis of the system, and we obtained the statio...

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Autores principales:	Ivan Atencia, José Luis Galán-García
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	discrete-time queueing system general retrial times breakdown repairs sojourn times Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/0e7ee5d7c20744199babb29756f3c79e
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spelling	oai:doaj.org-article:0e7ee5d7c20744199babb29756f3c79e2021-11-25T18:16:49ZSojourn Times in a Queueing System with Breakdowns and General Retrial Times10.3390/math92228822227-7390https://doaj.org/article/0e7ee5d7c20744199babb29756f3c79e2021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2882https://doaj.org/toc/2227-7390This paper centers on a discrete-time retrial queue where the server experiences breakdowns and repairs when arriving customers may opt to follow a discipline of a last-come, first-served (LCFS)-type or to join the orbit. We focused on the extensive analysis of the system, and we obtained the stationary distributions of the number of customers in the orbit and in the system by applying the generation function (GF). We provide the stochastic decomposition law and the application bounds for the proximity between the steady-state distributions for the queueing system under consideration and its corresponding standard system. We developed recursive formulae aimed at the calculation of the steady-state of the orbit and the system. We proved that our discrete-time system approximates <i>M</i>/<i>G</i>/1 with breakdowns and repairs. We analyzed the busy period of an auxiliary system, the objective of which was to study the customer’s delay. The stationary distribution of a customer’s sojourn in the orbit and in the system was the object of a thorough and complete study. Finally, we provide numerical examples that outline the effect of the parameters on several performance characteristics and a conclusions section resuming the main research contributions of the paper.Ivan AtenciaJosé Luis Galán-GarcíaMDPI AGarticlediscrete-time queueing systemgeneral retrial timesbreakdownrepairssojourn timesMathematicsQA1-939ENMathematics, Vol 9, Iss 2882, p 2882 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	discrete-time queueing system general retrial times breakdown repairs sojourn times Mathematics QA1-939
spellingShingle	discrete-time queueing system general retrial times breakdown repairs sojourn times Mathematics QA1-939 Ivan Atencia José Luis Galán-García Sojourn Times in a Queueing System with Breakdowns and General Retrial Times
description	This paper centers on a discrete-time retrial queue where the server experiences breakdowns and repairs when arriving customers may opt to follow a discipline of a last-come, first-served (LCFS)-type or to join the orbit. We focused on the extensive analysis of the system, and we obtained the stationary distributions of the number of customers in the orbit and in the system by applying the generation function (GF). We provide the stochastic decomposition law and the application bounds for the proximity between the steady-state distributions for the queueing system under consideration and its corresponding standard system. We developed recursive formulae aimed at the calculation of the steady-state of the orbit and the system. We proved that our discrete-time system approximates <i>M</i>/<i>G</i>/1 with breakdowns and repairs. We analyzed the busy period of an auxiliary system, the objective of which was to study the customer’s delay. The stationary distribution of a customer’s sojourn in the orbit and in the system was the object of a thorough and complete study. Finally, we provide numerical examples that outline the effect of the parameters on several performance characteristics and a conclusions section resuming the main research contributions of the paper.
format	article
author	Ivan Atencia José Luis Galán-García
author_facet	Ivan Atencia José Luis Galán-García
author_sort	Ivan Atencia
title	Sojourn Times in a Queueing System with Breakdowns and General Retrial Times
title_short	Sojourn Times in a Queueing System with Breakdowns and General Retrial Times
title_full	Sojourn Times in a Queueing System with Breakdowns and General Retrial Times
title_fullStr	Sojourn Times in a Queueing System with Breakdowns and General Retrial Times
title_full_unstemmed	Sojourn Times in a Queueing System with Breakdowns and General Retrial Times
title_sort	sojourn times in a queueing system with breakdowns and general retrial times
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/0e7ee5d7c20744199babb29756f3c79e
work_keys_str_mv	AT ivanatencia sojourntimesinaqueueingsystemwithbreakdownsandgeneralretrialtimes AT joseluisgalangarcia sojourntimesinaqueueingsystemwithbreakdownsandgeneralretrialtimes
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Sojourn Times in a Queueing System with Breakdowns and General Retrial Times

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