The M/G/∞ queue busy period distribution exponentiality
Autor(a) principal: | |
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Data de Publicação: | 2011 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10071/5660 |
Resumo: | Infinite servers queuing systems are often used to solve a large number of practical problems, namely in Engineering, Biology, Management, Finance and Sociology. The study of the M/G/∞ systems busy period is very important. Yet it is a very difficult task. This paper presents a service time distributions collection for which the length of the busy period is almost exponential. It is also shown that in heavy-traffic conditions, for a certain class of service time distributions, the length of the busy period of the M/G/∞ systems is approximately exponentially distributed. Thus, in all these cases, the study of this busy period is much simpler.It is also exemplified, with the power function and the Pareto service distributions, that it is possible to have in some particular situations an approximately exponential behaviour for the M/G/∞ queue busy period length. |
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The M/G/∞ queue busy period distribution exponentialityM/G/∞ queueBusy periodExponential distributionPower function distributionPareto distributionInfinite servers queuing systems are often used to solve a large number of practical problems, namely in Engineering, Biology, Management, Finance and Sociology. The study of the M/G/∞ systems busy period is very important. Yet it is a very difficult task. This paper presents a service time distributions collection for which the length of the busy period is almost exponential. It is also shown that in heavy-traffic conditions, for a certain class of service time distributions, the length of the busy period of the M/G/∞ systems is approximately exponentially distributed. Thus, in all these cases, the study of this busy period is much simpler.It is also exemplified, with the power function and the Pareto service distributions, that it is possible to have in some particular situations an approximately exponential behaviour for the M/G/∞ queue busy period length.Slovak University of Technology2013-09-30T13:42:04Z2011-01-01T00:00:00Z2011info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10071/5660eng1337-636510.1155/4185Ferreira, Manuel Alberto M.Andrade, Marinainfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-25T17:24:46ZPortal AgregadorONG |
dc.title.none.fl_str_mv |
The M/G/∞ queue busy period distribution exponentiality |
title |
The M/G/∞ queue busy period distribution exponentiality |
spellingShingle |
The M/G/∞ queue busy period distribution exponentiality Ferreira, Manuel Alberto M. M/G/∞ queue Busy period Exponential distribution Power function distribution Pareto distribution |
title_short |
The M/G/∞ queue busy period distribution exponentiality |
title_full |
The M/G/∞ queue busy period distribution exponentiality |
title_fullStr |
The M/G/∞ queue busy period distribution exponentiality |
title_full_unstemmed |
The M/G/∞ queue busy period distribution exponentiality |
title_sort |
The M/G/∞ queue busy period distribution exponentiality |
author |
Ferreira, Manuel Alberto M. |
author_facet |
Ferreira, Manuel Alberto M. Andrade, Marina |
author_role |
author |
author2 |
Andrade, Marina |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Ferreira, Manuel Alberto M. Andrade, Marina |
dc.subject.por.fl_str_mv |
M/G/∞ queue Busy period Exponential distribution Power function distribution Pareto distribution |
topic |
M/G/∞ queue Busy period Exponential distribution Power function distribution Pareto distribution |
description |
Infinite servers queuing systems are often used to solve a large number of practical problems, namely in Engineering, Biology, Management, Finance and Sociology. The study of the M/G/∞ systems busy period is very important. Yet it is a very difficult task. This paper presents a service time distributions collection for which the length of the busy period is almost exponential. It is also shown that in heavy-traffic conditions, for a certain class of service time distributions, the length of the busy period of the M/G/∞ systems is approximately exponentially distributed. Thus, in all these cases, the study of this busy period is much simpler.It is also exemplified, with the power function and the Pareto service distributions, that it is possible to have in some particular situations an approximately exponential behaviour for the M/G/∞ queue busy period length. |
publishDate |
2011 |
dc.date.none.fl_str_mv |
2011-01-01T00:00:00Z 2011 2013-09-30T13:42:04Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10071/5660 |
url |
http://hdl.handle.net/10071/5660 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
1337-6365 10.1155/4185 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Slovak University of Technology |
publisher.none.fl_str_mv |
Slovak University of Technology |
dc.source.none.fl_str_mv |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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1777303946838147072 |