Fluid Queue Driven by an M/M/1 Queue Subject to Bernoulli-Schedule-Controlled Vacation and Vacation Interruption

Abstract

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