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Advances in Operations Research
Volume 2016, Article ID 2673017, 11 pages
Research Article

Fluid Queue Driven by an Queue Subject to Bernoulli-Schedule-Controlled Vacation and Vacation Interruption

Department of Mathematics, Anna University, Chennai 600025, India

Received 30 November 2015; Revised 12 March 2016; Accepted 16 March 2016

Academic Editor: Yi-Kuei Lin

Copyright © 2016 Kolinjivadi Viswanathan Vijayashree and Atlimuthu Anjuka. 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 deals with the stationary analysis of a fluid queue driven by an queueing model subject to Bernoulli-Schedule-Controlled Vacation and Vacation Interruption. The model under consideration can be viewed as a quasi-birth and death process. The governing system of differential difference equations is solved using matrix-geometric method in the Laplacian domain. The resulting solutions are then inverted to obtain an explicit expression for the joint steady state probabilities of the content of the buffer and the state of the background queueing model. Numerical illustrations are added to depict the convergence of the stationary buffer content distribution to one subject to suitable stability conditions.