Simple analysis of a fluid queue driven by an M/M/1 queue

In this note we consider the fluid queue driven by an M/M/1 queue as analysed by Virtamo and Norros. We show that the stationary buffer content in this model can be easily analysed by looking at embedded time points. This approach gives the stationary buffer content distribution in terms of the modified Bessel function of the first kind of order one. By using a suitable integral representation for this Bessel function we show that our results coincide with the ones of Virtamo and Norros.