Stationary analysis of a fluid queue driven by an M/M/1 queue with working vacation

This paper studies a fluid queueing model driven by an M/M/1 queue subject to working vacation. The underlying system of differential difference equations that governs the process is solved using continued fraction and generating function methodologies. Explicit expressions for the joint steady-state probabilities of the state of the background queueing model and the content of the buffer are obtained in terms of modified Bessel function of the first kind. Numerical illustrations are added to depict the variations of the state probabilities and the buffer content distributions against varying values of the parameters subject to the stability conditions.