Resource System with Losses in a Random Environment

The article deals with queueing systems with random resource requirements modeled as bivariate Markov jump processes. One of the process components describes the service system with limited resources. Another component represents a random environment that submits multi-class requests for resources t...

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Autores principales:	Valeriy Naumov, Konstantin Samouylov
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	product form loss system resource requirement random environment Marked Markovian Arrival Process Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/5db38f2e5aff4fa7be106aa8cabbb19e
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spelling	oai:doaj.org-article:5db38f2e5aff4fa7be106aa8cabbb19e2021-11-11T18:15:06ZResource System with Losses in a Random Environment10.3390/math92126852227-7390https://doaj.org/article/5db38f2e5aff4fa7be106aa8cabbb19e2021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2685https://doaj.org/toc/2227-7390The article deals with queueing systems with random resource requirements modeled as bivariate Markov jump processes. One of the process components describes the service system with limited resources. Another component represents a random environment that submits multi-class requests for resources to the service system. If the resource request is lost, then the state of the service system does not change. The change in the state of the environment interacting with the service system depends on whether the resource request has been lost. Thus, unlike in known models, the service system provides feedback to the environment in response to resource requests. By analyzing the properties of the system of integral equations for the stationary distribution of the corresponding random process, we obtain the conditions for the stationary distribution to have a product form. These conditions are expressed in the form of three systems of nonlinear equations. Several special cases are explained in detail.Valeriy NaumovKonstantin SamouylovMDPI AGarticleproduct formloss systemresource requirementrandom environmentMarked Markovian Arrival ProcessMathematicsQA1-939ENMathematics, Vol 9, Iss 2685, p 2685 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	product form loss system resource requirement random environment Marked Markovian Arrival Process Mathematics QA1-939
spellingShingle	product form loss system resource requirement random environment Marked Markovian Arrival Process Mathematics QA1-939 Valeriy Naumov Konstantin Samouylov Resource System with Losses in a Random Environment
description	The article deals with queueing systems with random resource requirements modeled as bivariate Markov jump processes. One of the process components describes the service system with limited resources. Another component represents a random environment that submits multi-class requests for resources to the service system. If the resource request is lost, then the state of the service system does not change. The change in the state of the environment interacting with the service system depends on whether the resource request has been lost. Thus, unlike in known models, the service system provides feedback to the environment in response to resource requests. By analyzing the properties of the system of integral equations for the stationary distribution of the corresponding random process, we obtain the conditions for the stationary distribution to have a product form. These conditions are expressed in the form of three systems of nonlinear equations. Several special cases are explained in detail.
format	article
author	Valeriy Naumov Konstantin Samouylov
author_facet	Valeriy Naumov Konstantin Samouylov
author_sort	Valeriy Naumov
title	Resource System with Losses in a Random Environment
title_short	Resource System with Losses in a Random Environment
title_full	Resource System with Losses in a Random Environment
title_fullStr	Resource System with Losses in a Random Environment
title_full_unstemmed	Resource System with Losses in a Random Environment
title_sort	resource system with losses in a random environment
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/5db38f2e5aff4fa7be106aa8cabbb19e
work_keys_str_mv	AT valeriynaumov resourcesystemwithlossesinarandomenvironment AT konstantinsamouylov resourcesystemwithlossesinarandomenvironment
_version_	1718431887663300608

Resource System with Losses in a Random Environment

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