Output analysis of multiclass fluid models with static priorities

We consider a stochastic fluid flow model with a single server and K infinite capacity buffers. The input to the k-th buffer is a Markovian on-off process that transmits fluid at a constant rate p_k 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 μ according to a static priority service discipline in which class 1 fluid has the highest and class K fluid has the lowest priority. The output process of class k is defined to be on if fluid of class k 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 k. We illustrate the method with a numerical example.