Output analysis of multiclass fluid models with static priorities

We consider a stochastic fluid flow model with a single server and KK infinite capacity buffers. The input to the kk-th buffer is a Markovian on-off process that transmits fluid at a constant rate pkpk while it is on and at rate 0 while it is off. The fluid is emptied from the buffers by a single server at a constant rate μμ according to a static priority service discipline   in which class 1 fluid has the highest and class KK fluid has the lowest priority. The output process of class kk is defined to be on   if fluid of class kk is leaving the buffer at a positive rate and off   otherwise. In this paper we derive an exact method for computing the mean on-time and the mean off-time of the output process of class kk. We illustrate the method with a numerical example.