Probabilistic Decomposition Method on the ServerIndices of an Mξ/G/1 Vacation Queue

This paper develops a probabilistic decomposition method for an Mξ/G/1 repairable queueing system with multiple vacations, in which the customers who arrive during server vacations enter the system with probability p. Such a novel method is used to analyze the main performance indices of the server,...

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Main Author:	Renbin Liu
Format:	Article
Language:	English
Published:	Hindawi Limited 2014-01-01
Series:	Journal of Applied Mathematics
Online Access:	http://dx.doi.org/10.1155/2014/241636

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spelling	doaj-ae62f70ec6264c96bd791e7c01a303b52020-11-24T22:25:08ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/241636241636Probabilistic Decomposition Method on the ServerIndices of an Mξ/G/1 Vacation QueueRenbin Liu0School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, ChinaThis paper develops a probabilistic decomposition method for an Mξ/G/1 repairable queueing system with multiple vacations, in which the customers who arrive during server vacations enter the system with probability p. Such a novel method is used to analyze the main performance indices of the server, such as the unavailability and the mean failure number during (0,t]. It is derived that the structures of server indices are two convolution equations. Further, comparisons with existing methods indicate that our method is effective and applicable for studying server performances in single-server Mξ/G/1 vacation queues and their complex variants. Finally, a stochastic order and production system with a multipurpose production facility is numerically presented for illustrative purpose.http://dx.doi.org/10.1155/2014/241636
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Renbin Liu
spellingShingle	Renbin Liu Probabilistic Decomposition Method on the ServerIndices of an Mξ/G/1 Vacation Queue Journal of Applied Mathematics
author_facet	Renbin Liu
author_sort	Renbin Liu
title	Probabilistic Decomposition Method on the ServerIndices of an Mξ/G/1 Vacation Queue
title_short	Probabilistic Decomposition Method on the ServerIndices of an Mξ/G/1 Vacation Queue
title_full	Probabilistic Decomposition Method on the ServerIndices of an Mξ/G/1 Vacation Queue
title_fullStr	Probabilistic Decomposition Method on the ServerIndices of an Mξ/G/1 Vacation Queue
title_full_unstemmed	Probabilistic Decomposition Method on the ServerIndices of an Mξ/G/1 Vacation Queue
title_sort	probabilistic decomposition method on the serverindices of an mξ/g/1 vacation queue
publisher	Hindawi Limited
series	Journal of Applied Mathematics
issn	1110-757X 1687-0042
publishDate	2014-01-01
description	This paper develops a probabilistic decomposition method for an Mξ/G/1 repairable queueing system with multiple vacations, in which the customers who arrive during server vacations enter the system with probability p. Such a novel method is used to analyze the main performance indices of the server, such as the unavailability and the mean failure number during (0,t]. It is derived that the structures of server indices are two convolution equations. Further, comparisons with existing methods indicate that our method is effective and applicable for studying server performances in single-server Mξ/G/1 vacation queues and their complex variants. Finally, a stochastic order and production system with a multipurpose production facility is numerically presented for illustrative purpose.
url	http://dx.doi.org/10.1155/2014/241636
work_keys_str_mv	AT renbinliu probabilisticdecompositionmethodontheserverindicesofanmxg1vacationqueue
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Probabilistic Decomposition Method on the ServerIndices of an Mξ/G/1 Vacation Queue

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