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International Journal of Stochastic Analysis
Volume 2014 (2014), Article ID 358529, 8 pages
Research Article

A Discrete-Time Queue with Balking, Reneging, and Working Vacations

School of Computer Application, KIIT University, Bhubaneswar 751024, India

Received 21 May 2014; Accepted 9 October 2014; Published 29 October 2014

Academic Editor: Onesimo Hernandez-Lerma

Copyright © 2014 Veena Goswami. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents an analysis of balking and reneging in finite-buffer discrete-time single server queue with single and multiple working vacations. An arriving customer may balk with a probability or renege after joining according to a geometric distribution. The server works with different service rates rather than completely stopping the service during a vacation period. The service times during a busy period, vacation period, and vacation times are assumed to be geometrically distributed. We find the explicit expressions for the stationary state probabilities. Various system performance measures and a cost model to determine the optimal service rates are presented. Moreover, some queueing models presented in the literature are derived as special cases of our model. Finally, the influence of various parameters on the performance characteristics is shown numerically.