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The Discrete-Time GI/Geo/1 Queue with Multiple Vacations |
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| Authors: | Tian Naishuo Zhang Zhe George |
| Affiliation: | (1) Department of Mathematics, Yanshan University, Qinhuangdao, 066004;(2) Department of Finance, Marketing, and Decision Sciences, College of Business and Economics, Western Washington University, Bellingham, WA 98225-9077, USA;(3) Faculty of Business Administration, Simon Fraser University, Canada |
| Abstract: | We study a discrete-time GI/Geo/1 queue with server vacations. In this queueing system, the server takes vacations when the system does not have any waiting customers at a service completion instant or a vacation completion instant. This type of discrete-time queueing model has potential applications in computer or telecommunication network systems. Using matrix-geometric method, we obtain the explicit expressions for the stationary distributions of queue length and waiting time and demonstrate the conditional stochastic decomposition property of the queue length and waiting time in this system. |
| Keywords: | discrete-time GI/Geo/1 queue vacation model matrix geometric solutions stochastic decomposition |
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