Solving logistics problems using M|G|∞ queue systems busy period

Detalhes bibliográficos
Autor(a) principal: Ferreira, Manuel Alberto M.
Data de Publicação: 2010
Outros Autores: Filipe, José António
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10071/5684
Resumo: In the M|G|∞ queuing systems customers arrive according to a Poisson process at rate λ . Each of them receives immediately after its arrival a service whose length is a positive random variable with distribution function G(.) and mean value α . An important parameter of the system is the traffic intensity ρ = λα . The service of a customer is independent of the services of the other customers and of the arrival process. The busy period of a queuing system begins when a customer arrives there, finding it empty, and ends when a customer leaves the system letting it empty. During the busy period there is always at least one customer in the system. Therefore in a queuing system there is a sequence of idle and busy periods. For these systems with infinite servers the busy period length distribution is difficult to derive, except for a few exceptions. But formulae that allow the calculation of some of the busy period length parameters for the M|G|∞ queuing system are presented. These results can be applied in logistics (see, for instance, Ferreira [4,5] and Ferreira, Andrade and Filipe [9]). For instance, they can be applied to the failures which occur in the operation of an aircraft, shipping or trucking fleet. The customers are the failures. And their service time is the time that goes from the instant at which they occur till the one at which they are completely repaired. Here a busy period is a period in which there is at least one failure waiting for reparation or being repaired. The formulae referred allow the determination of measures of the system performance.
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spelling Solving logistics problems using M|G|∞ queue systems busy periodM|G|∞Busy periodFailuresIn the M|G|∞ queuing systems customers arrive according to a Poisson process at rate λ . Each of them receives immediately after its arrival a service whose length is a positive random variable with distribution function G(.) and mean value α . An important parameter of the system is the traffic intensity ρ = λα . The service of a customer is independent of the services of the other customers and of the arrival process. The busy period of a queuing system begins when a customer arrives there, finding it empty, and ends when a customer leaves the system letting it empty. During the busy period there is always at least one customer in the system. Therefore in a queuing system there is a sequence of idle and busy periods. For these systems with infinite servers the busy period length distribution is difficult to derive, except for a few exceptions. But formulae that allow the calculation of some of the busy period length parameters for the M|G|∞ queuing system are presented. These results can be applied in logistics (see, for instance, Ferreira [4,5] and Ferreira, Andrade and Filipe [9]). For instance, they can be applied to the failures which occur in the operation of an aircraft, shipping or trucking fleet. The customers are the failures. And their service time is the time that goes from the instant at which they occur till the one at which they are completely repaired. Here a busy period is a period in which there is at least one failure waiting for reparation or being repaired. The formulae referred allow the determination of measures of the system performance.Slovak University of Technology2013-10-02T13:36:35Z2010-01-01T00:00:00Z2010info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10071/5684eng1337-6365Ferreira, Manuel Alberto M.Filipe, José Antónioinfo: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:RCAAP2023-11-09T17:41:33Zoai:repositorio.iscte-iul.pt:10071/5684Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:19:20.355117Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Solving logistics problems using M|G|∞ queue systems busy period
title Solving logistics problems using M|G|∞ queue systems busy period
spellingShingle Solving logistics problems using M|G|∞ queue systems busy period
Ferreira, Manuel Alberto M.
M|G|∞
Busy period
Failures
title_short Solving logistics problems using M|G|∞ queue systems busy period
title_full Solving logistics problems using M|G|∞ queue systems busy period
title_fullStr Solving logistics problems using M|G|∞ queue systems busy period
title_full_unstemmed Solving logistics problems using M|G|∞ queue systems busy period
title_sort Solving logistics problems using M|G|∞ queue systems busy period
author Ferreira, Manuel Alberto M.
author_facet Ferreira, Manuel Alberto M.
Filipe, José António
author_role author
author2 Filipe, José António
author2_role author
dc.contributor.author.fl_str_mv Ferreira, Manuel Alberto M.
Filipe, José António
dc.subject.por.fl_str_mv M|G|∞
Busy period
Failures
topic M|G|∞
Busy period
Failures
description In the M|G|∞ queuing systems customers arrive according to a Poisson process at rate λ . Each of them receives immediately after its arrival a service whose length is a positive random variable with distribution function G(.) and mean value α . An important parameter of the system is the traffic intensity ρ = λα . The service of a customer is independent of the services of the other customers and of the arrival process. The busy period of a queuing system begins when a customer arrives there, finding it empty, and ends when a customer leaves the system letting it empty. During the busy period there is always at least one customer in the system. Therefore in a queuing system there is a sequence of idle and busy periods. For these systems with infinite servers the busy period length distribution is difficult to derive, except for a few exceptions. But formulae that allow the calculation of some of the busy period length parameters for the M|G|∞ queuing system are presented. These results can be applied in logistics (see, for instance, Ferreira [4,5] and Ferreira, Andrade and Filipe [9]). For instance, they can be applied to the failures which occur in the operation of an aircraft, shipping or trucking fleet. The customers are the failures. And their service time is the time that goes from the instant at which they occur till the one at which they are completely repaired. Here a busy period is a period in which there is at least one failure waiting for reparation or being repaired. The formulae referred allow the determination of measures of the system performance.
publishDate 2010
dc.date.none.fl_str_mv 2010-01-01T00:00:00Z
2010
2013-10-02T13:36:35Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
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dc.identifier.uri.fl_str_mv http://hdl.handle.net/10071/5684
url http://hdl.handle.net/10071/5684
dc.language.iso.fl_str_mv eng
language eng
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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 reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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