Transient Behavior of a Queueing Model with Hyper-Exponentially Distributed Processing Times and Finite Buffer Capacity

In the paper, a finite-capacity queueing model is considered in which jobs arrive according to a Poisson process and are being served according to hyper-exponential service times. A system of equations for the time-sensitive queue-size distribution is established by applying the paradigm of embedded...

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Autores principales: Kempa, Wojciech M., Paprocka, Iwona
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9788344/
https://www.ncbi.nlm.nih.gov/pubmed/36560276
http://dx.doi.org/10.3390/s22249909
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author Kempa, Wojciech M.
Paprocka, Iwona
author_facet Kempa, Wojciech M.
Paprocka, Iwona
author_sort Kempa, Wojciech M.
collection PubMed
description In the paper, a finite-capacity queueing model is considered in which jobs arrive according to a Poisson process and are being served according to hyper-exponential service times. A system of equations for the time-sensitive queue-size distribution is established by applying the paradigm of embedded Markov chain and total probability law. The solution of the corresponding system written for Laplace transforms is obtained via an algebraic approach in a compact form. Numerical illustration results are attached as well.
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spelling pubmed-97883442022-12-24 Transient Behavior of a Queueing Model with Hyper-Exponentially Distributed Processing Times and Finite Buffer Capacity Kempa, Wojciech M. Paprocka, Iwona Sensors (Basel) Article In the paper, a finite-capacity queueing model is considered in which jobs arrive according to a Poisson process and are being served according to hyper-exponential service times. A system of equations for the time-sensitive queue-size distribution is established by applying the paradigm of embedded Markov chain and total probability law. The solution of the corresponding system written for Laplace transforms is obtained via an algebraic approach in a compact form. Numerical illustration results are attached as well. MDPI 2022-12-16 /pmc/articles/PMC9788344/ /pubmed/36560276 http://dx.doi.org/10.3390/s22249909 Text en © 2022 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Kempa, Wojciech M.
Paprocka, Iwona
Transient Behavior of a Queueing Model with Hyper-Exponentially Distributed Processing Times and Finite Buffer Capacity
title Transient Behavior of a Queueing Model with Hyper-Exponentially Distributed Processing Times and Finite Buffer Capacity
title_full Transient Behavior of a Queueing Model with Hyper-Exponentially Distributed Processing Times and Finite Buffer Capacity
title_fullStr Transient Behavior of a Queueing Model with Hyper-Exponentially Distributed Processing Times and Finite Buffer Capacity
title_full_unstemmed Transient Behavior of a Queueing Model with Hyper-Exponentially Distributed Processing Times and Finite Buffer Capacity
title_short Transient Behavior of a Queueing Model with Hyper-Exponentially Distributed Processing Times and Finite Buffer Capacity
title_sort transient behavior of a queueing model with hyper-exponentially distributed processing times and finite buffer capacity
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9788344/
https://www.ncbi.nlm.nih.gov/pubmed/36560276
http://dx.doi.org/10.3390/s22249909
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