Title: Analysis of a discrete-time GI/Geo/1 queue with single vacation

Authors: S.K. Samanta

Addresses: School of Business and Economics, Wilfrid Laurier University, Waterloo, Ontario, N2L 3C5, Canada

Abstract: We analyse a discrete-time GI/Geo/1 queue with vacation in which the server takes exactly one Bernoulli vacation after each busy period based on exhaustive service. With the displacement operator method which is used to solve simultaneous non-homogeneous difference equations, we obtain the distributions of queue length at prearrival and arbitrary epochs, and waiting time for an arrival customer. We also explain the stochastic decomposition properties of queue length and waiting time in this system. Finally, some numerical results are presented. The model presented in this paper may be useful in polling systems where the trade-off between service and vacation times is adopted to capture processing and polling times accurately, and control the access to the communication media.

Keywords: discrete-time queueing; single vacation; stochastic decomposition; supplementary variable; queue length; waiting time.

DOI: 10.1504/IJOR.2009.025198

International Journal of Operational Research, 2009 Vol.5 No.3, pp.292 - 310

Published online: 16 May 2009 *

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