Study on Transient Queue-Size Distribution in the Finite-Buffer Model with Batch Arrivals and Multiple Vacation Policy

The transient behavior of the finite-buffer queueing model with batch arrivals and generally distributed repeated vacations is analyzed. Such a system has potential applications in modeling the functioning of production systems, computer and telecommunication networks with energy saving mechanism ba...

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Autores principales:	Wojciech M. Kempa, Rafał Marjasz
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	finite buffer multiple vacation policy potential method queue size transient state Science Q Astrophysics QB460-466 Physics QC1-999
Acceso en línea:	https://doaj.org/article/96d41b5dc9e146e4af7414336acd577b
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id	oai:doaj.org-article:96d41b5dc9e146e4af7414336acd577b
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spelling	oai:doaj.org-article:96d41b5dc9e146e4af7414336acd577b2021-11-25T17:29:26ZStudy on Transient Queue-Size Distribution in the Finite-Buffer Model with Batch Arrivals and Multiple Vacation Policy10.3390/e231114101099-4300https://doaj.org/article/96d41b5dc9e146e4af7414336acd577b2021-10-01T00:00:00Zhttps://www.mdpi.com/1099-4300/23/11/1410https://doaj.org/toc/1099-4300The transient behavior of the finite-buffer queueing model with batch arrivals and generally distributed repeated vacations is analyzed. Such a system has potential applications in modeling the functioning of production systems, computer and telecommunication networks with energy saving mechanism based on cyclic monitoring the queue state (Internet of Things, wireless sensors networks, etc.). Identifying renewal moments in the evolution of the system and applying continuous total probability law, a system of Volterra-type integral equations for the time-dependent queue-size distribution, conditioned by the initial buffer state, is derived. A compact-form solution for the corresponding system written for Laplace transforms is obtained using an algebraic approach based on Korolyuk’s potential method. An illustrative numerical example presenting the impact of the service rate, arrival rate, initial buffer state and single vacation duration on the queue-size distribution is attached as well.Wojciech M. KempaRafał MarjaszMDPI AGarticlefinite buffermultiple vacation policypotential methodqueue sizetransient stateScienceQAstrophysicsQB460-466PhysicsQC1-999ENEntropy, Vol 23, Iss 1410, p 1410 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	finite buffer multiple vacation policy potential method queue size transient state Science Q Astrophysics QB460-466 Physics QC1-999
spellingShingle	finite buffer multiple vacation policy potential method queue size transient state Science Q Astrophysics QB460-466 Physics QC1-999 Wojciech M. Kempa Rafał Marjasz Study on Transient Queue-Size Distribution in the Finite-Buffer Model with Batch Arrivals and Multiple Vacation Policy
description	The transient behavior of the finite-buffer queueing model with batch arrivals and generally distributed repeated vacations is analyzed. Such a system has potential applications in modeling the functioning of production systems, computer and telecommunication networks with energy saving mechanism based on cyclic monitoring the queue state (Internet of Things, wireless sensors networks, etc.). Identifying renewal moments in the evolution of the system and applying continuous total probability law, a system of Volterra-type integral equations for the time-dependent queue-size distribution, conditioned by the initial buffer state, is derived. A compact-form solution for the corresponding system written for Laplace transforms is obtained using an algebraic approach based on Korolyuk’s potential method. An illustrative numerical example presenting the impact of the service rate, arrival rate, initial buffer state and single vacation duration on the queue-size distribution is attached as well.
format	article
author	Wojciech M. Kempa Rafał Marjasz
author_facet	Wojciech M. Kempa Rafał Marjasz
author_sort	Wojciech M. Kempa
title	Study on Transient Queue-Size Distribution in the Finite-Buffer Model with Batch Arrivals and Multiple Vacation Policy
title_short	Study on Transient Queue-Size Distribution in the Finite-Buffer Model with Batch Arrivals and Multiple Vacation Policy
title_full	Study on Transient Queue-Size Distribution in the Finite-Buffer Model with Batch Arrivals and Multiple Vacation Policy
title_fullStr	Study on Transient Queue-Size Distribution in the Finite-Buffer Model with Batch Arrivals and Multiple Vacation Policy
title_full_unstemmed	Study on Transient Queue-Size Distribution in the Finite-Buffer Model with Batch Arrivals and Multiple Vacation Policy
title_sort	study on transient queue-size distribution in the finite-buffer model with batch arrivals and multiple vacation policy
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/96d41b5dc9e146e4af7414336acd577b
work_keys_str_mv	AT wojciechmkempa studyontransientqueuesizedistributioninthefinitebuffermodelwithbatcharrivalsandmultiplevacationpolicy AT rafałmarjasz studyontransientqueuesizedistributioninthefinitebuffermodelwithbatcharrivalsandmultiplevacationpolicy
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Study on Transient Queue-Size Distribution in the Finite-Buffer Model with Batch Arrivals and Multiple Vacation Policy

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