A single server queueing system with Markov flow of principal customers and background customers arriving from infinite reserve source is studied. The Markov service processes of customers of both types are considered. The system has a finite buffer for principal customers. The service discipline is characterized by non-preemptive priority of principal customers respect to background customers. An effective matrix-recurrent algorithm for the calculation of the stationary state probabilities of the underlying Markov process is derived. © ECMS 2005.