On a Batch Arrival Queuing System Equipped with a Stand-by Server during Vacation Periods or the Repairs Times of the Main Server

We study a queuing system which is equipped with a stand-by server in addition to the main server. The stand-by server provides service to customers only during the period of absence of the main server when either the main server is on a vacation or it is in the state of repairs due to a sudden fail...

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Main Authors: Rehab F. Khalaf, Kailash C. Madan, Cormac A. Lukas
Format: Article
Language:English
Published: Hindawi Limited 2011-01-01
Series:Journal of Probability and Statistics
Online Access:http://dx.doi.org/10.1155/2011/812726
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spelling doaj-1150409d40474d629c7d0f12b6b0b8fa2020-11-24T22:48:56ZengHindawi LimitedJournal of Probability and Statistics1687-952X1687-95382011-01-01201110.1155/2011/812726812726On a Batch Arrival Queuing System Equipped with a Stand-by Server during Vacation Periods or the Repairs Times of the Main ServerRehab F. Khalaf0Kailash C. Madan1Cormac A. Lukas2School of Information Systems Computing and Mathematics, Brunel University, Middlesex UB83PH, UKCollege of Information Technology, Ahlia University, P.O. Box 10878, BahrainSchool of Information Systems Computing and Mathematics, Brunel University, Middlesex UB83PH, UKWe study a queuing system which is equipped with a stand-by server in addition to the main server. The stand-by server provides service to customers only during the period of absence of the main server when either the main server is on a vacation or it is in the state of repairs due to a sudden failure from time to time. The service times, vacation times, and repair times are assumed to follow general arbitrary distributions while the stand-by service times follow exponential distribution. Supplementary variables technique has been used to obtain steady state results in explicit and closed form in terms of the probability generating functions for the number of customers in the queue, the average number of customers, and the average waiting time in the queue while the MathCad software has been used to illustrate the numerical results in this work.http://dx.doi.org/10.1155/2011/812726
collection DOAJ
language English
format Article
sources DOAJ
author Rehab F. Khalaf
Kailash C. Madan
Cormac A. Lukas
spellingShingle Rehab F. Khalaf
Kailash C. Madan
Cormac A. Lukas
On a Batch Arrival Queuing System Equipped with a Stand-by Server during Vacation Periods or the Repairs Times of the Main Server
Journal of Probability and Statistics
author_facet Rehab F. Khalaf
Kailash C. Madan
Cormac A. Lukas
author_sort Rehab F. Khalaf
title On a Batch Arrival Queuing System Equipped with a Stand-by Server during Vacation Periods or the Repairs Times of the Main Server
title_short On a Batch Arrival Queuing System Equipped with a Stand-by Server during Vacation Periods or the Repairs Times of the Main Server
title_full On a Batch Arrival Queuing System Equipped with a Stand-by Server during Vacation Periods or the Repairs Times of the Main Server
title_fullStr On a Batch Arrival Queuing System Equipped with a Stand-by Server during Vacation Periods or the Repairs Times of the Main Server
title_full_unstemmed On a Batch Arrival Queuing System Equipped with a Stand-by Server during Vacation Periods or the Repairs Times of the Main Server
title_sort on a batch arrival queuing system equipped with a stand-by server during vacation periods or the repairs times of the main server
publisher Hindawi Limited
series Journal of Probability and Statistics
issn 1687-952X
1687-9538
publishDate 2011-01-01
description We study a queuing system which is equipped with a stand-by server in addition to the main server. The stand-by server provides service to customers only during the period of absence of the main server when either the main server is on a vacation or it is in the state of repairs due to a sudden failure from time to time. The service times, vacation times, and repair times are assumed to follow general arbitrary distributions while the stand-by service times follow exponential distribution. Supplementary variables technique has been used to obtain steady state results in explicit and closed form in terms of the probability generating functions for the number of customers in the queue, the average number of customers, and the average waiting time in the queue while the MathCad software has been used to illustrate the numerical results in this work.
url http://dx.doi.org/10.1155/2011/812726
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