A Markov modulated fluid queueing system with strict priority

We investigate a Markov modulated fluid queueing system with strict priority. The input process is composed of two fluid flows which are stored in buffer-1 and buffer-2, respectively. The rates of these fluid flows depend on the current state of a finite state Markov chain. Buffer-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 empty. We explicitly derive the stationary joint distribution of the two buffer contents in the system by a spectral decomposition method. In the case of a two-state Markov chain, the joint distribution is explicitly expressed in terms of the system parameters. Also the joint moments and tail distributions of the two buffer contents are obtained and some numerical examples are presented.