This paper deals with the stationary analysis of a fluid queue driven by anM/M/1queueing 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.

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In this paper, we analyse a fluid queue modulated by a computer system with two processors. The modulating process is modelled as a quasi birth and death process and the steady state probabilities are determined by standard methods. Further, for the fluid model the explicit expression for the joint steady state distribution of the content of the buffer and the number of tasks in the computer system is presented using matrix analytic methods as a tool to solve the underlying system of governing equations.