Fluid Queue Driven by an M/M/1 Queue Subject to Working Vacation and Impatience

In recent years, fluid queueing modelling proves to be very effective in the analysis of computer and communication systems, production inventory systems and many other scenarios. This paper studies a fluid queueing model driven by an M/M/1 queue subject to working vacation and customer impatience. The fluid in the infinite capacity buffer is assumed to decrease when the background queueing model is empty and increase otherwise. The underlying system of differential difference equations that governs the process are 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 fluid buffer are obtained in terms of modified Bessel function of the first kind.