On the stability of queues with the dropping function

In this paper, the stability of the queueing system with the dropping function is studied. In such system, every incoming job may be dropped randomly, with the probability being a function of the queue length. The main objective of the work is to find an easy to use condition, sufficient for the ins...

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Autor principal:	Andrzej Chydzinski
Formato:	article
Lenguaje:	EN
Publicado:	Public Library of Science (PLoS) 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/b10d782c9f8a496dae2dfbbf7db60067
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spelling	oai:doaj.org-article:b10d782c9f8a496dae2dfbbf7db600672021-11-11T07:14:44ZOn the stability of queues with the dropping function1932-6203https://doaj.org/article/b10d782c9f8a496dae2dfbbf7db600672021-01-01T00:00:00Zhttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC8565781/?tool=EBIhttps://doaj.org/toc/1932-6203In this paper, the stability of the queueing system with the dropping function is studied. In such system, every incoming job may be dropped randomly, with the probability being a function of the queue length. The main objective of the work is to find an easy to use condition, sufficient for the instability of the system, under assumption of Poisson arrivals and general service time distribution. Such condition is found and proven using a boundary for the dropping function and analysis of the embedded Markov chain. Applicability of the proven condition is demonstrated on several examples of dropping functions. Additionally, its correctness is confirmed using a discrete-event simulator.Andrzej ChydzinskiPublic Library of Science (PLoS)articleMedicineRScienceQENPLoS ONE, Vol 16, Iss 11 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Andrzej Chydzinski On the stability of queues with the dropping function
description	In this paper, the stability of the queueing system with the dropping function is studied. In such system, every incoming job may be dropped randomly, with the probability being a function of the queue length. The main objective of the work is to find an easy to use condition, sufficient for the instability of the system, under assumption of Poisson arrivals and general service time distribution. Such condition is found and proven using a boundary for the dropping function and analysis of the embedded Markov chain. Applicability of the proven condition is demonstrated on several examples of dropping functions. Additionally, its correctness is confirmed using a discrete-event simulator.
format	article
author	Andrzej Chydzinski
author_facet	Andrzej Chydzinski
author_sort	Andrzej Chydzinski
title	On the stability of queues with the dropping function
title_short	On the stability of queues with the dropping function
title_full	On the stability of queues with the dropping function
title_fullStr	On the stability of queues with the dropping function
title_full_unstemmed	On the stability of queues with the dropping function
title_sort	on the stability of queues with the dropping function
publisher	Public Library of Science (PLoS)
publishDate	2021
url	https://doaj.org/article/b10d782c9f8a496dae2dfbbf7db60067
work_keys_str_mv	AT andrzejchydzinski onthestabilityofqueueswiththedroppingfunction
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On the stability of queues with the dropping function

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