A MARKOV MODULATED FLUID QUEUING SYSTEM WITH STRICT PRIORITY

We investigate a Markov modulated fluid queueing system with strict pr iority. The input process is composed of two fluid flows which are sto red in buffer-1 and buffer-2, respectively. The rates of these fluid f lows depend on the current state of a finite state Markov chain. Buffe r-1 has full assignment of priority (=strict priority) for service and so buffer-2 is served at a residual service rate when buffer-1 is emp ty. We explicitly derive the stationary joint distribution of the two buffer contents in the system by a spectral decomposition method. In t he case of a two-state Markov chain, the joint distribution is explici tly expressed in terms of the system parameters. Also the joint moment s and tail distributions of the two buffer contents are obtained and s ome numerical examples are presented.