Queues with the dropping function and general service time

We present an analysis of queueing systems with the dropping function, infinite buffer and general distribution of the service time. Firstly, a stability condition, more general than the well-known ρ < 1, is proven. Secondly, the formulas for the queue size distribution, loss ratio and mean durat...

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Detalles Bibliográficos
Autores principales: Chydzinski, Andrzej, Adamczyk, Blazej
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2019
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6636820/
https://www.ncbi.nlm.nih.gov/pubmed/31314765
http://dx.doi.org/10.1371/journal.pone.0219444
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author Chydzinski, Andrzej
Adamczyk, Blazej
author_facet Chydzinski, Andrzej
Adamczyk, Blazej
author_sort Chydzinski, Andrzej
collection PubMed
description We present an analysis of queueing systems with the dropping function, infinite buffer and general distribution of the service time. Firstly, a stability condition, more general than the well-known ρ < 1, is proven. Secondly, the formulas for the queue size distribution, loss ratio and mean duration of the busy period, are derived. Thirdly, numerical examples are given, including optimizations of the shape of the dropping function with regard to the combined cost of the queue size and loss ratio.
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spelling pubmed-66368202019-07-25 Queues with the dropping function and general service time Chydzinski, Andrzej Adamczyk, Blazej PLoS One Research Article We present an analysis of queueing systems with the dropping function, infinite buffer and general distribution of the service time. Firstly, a stability condition, more general than the well-known ρ < 1, is proven. Secondly, the formulas for the queue size distribution, loss ratio and mean duration of the busy period, are derived. Thirdly, numerical examples are given, including optimizations of the shape of the dropping function with regard to the combined cost of the queue size and loss ratio. Public Library of Science 2019-07-17 /pmc/articles/PMC6636820/ /pubmed/31314765 http://dx.doi.org/10.1371/journal.pone.0219444 Text en © 2019 Chydzinski, Adamczyk http://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
spellingShingle Research Article
Chydzinski, Andrzej
Adamczyk, Blazej
Queues with the dropping function and general service time
title Queues with the dropping function and general service time
title_full Queues with the dropping function and general service time
title_fullStr Queues with the dropping function and general service time
title_full_unstemmed Queues with the dropping function and general service time
title_short Queues with the dropping function and general service time
title_sort queues with the dropping function and general service time
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6636820/
https://www.ncbi.nlm.nih.gov/pubmed/31314765
http://dx.doi.org/10.1371/journal.pone.0219444
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