On the Discrete-Time GeoX/G/1 Queues under N-Policy with Single and Multiple Vacations

We consider the discrete-time GeoX/G/1 queue under N-policy with single and multiple vacations. In this queueing system, the server takes multiple vacations and a single vacation whenever the system becomes empty and begins to serve customers only if the queue length is at least a predetermined thre...

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Bibliographic Details
Published inJournal of applied mathematics Vol. 2013; no. 2013; pp. 1 - 6
Main Authors Kim, Sung J., Kim, Nam K., Park, Hyun-Min, Chae, Kyung Chul, Lim, Dae-Eun
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Puplishing Corporation 2013
Hindawi Publishing Corporation
Hindawi Limited
Subjects
Customers
Decomposition
Mathematical models
Queues
Queuing theory
Servers
Software
Stochasticity
Studies
Thresholds
Vacations
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Summary:We consider the discrete-time GeoX/G/1 queue under N-policy with single and multiple vacations. In this queueing system, the server takes multiple vacations and a single vacation whenever the system becomes empty and begins to serve customers only if the queue length is at least a predetermined threshold value N. Using the well-known property of stochastic decomposition, we derive the stationary queue-length distributions for both vacation models in a simple and unified manner. In addition, we derive their busy as well as idle-period distributions. Some classical vacation models are considered as special cases.
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ISSN:1110-757X
1687-0042
DOI:10.1155/2013/587163