A queueing system of finite capacity with the server requiring a priority search for customers

A single-server queueing system with two independent Poisson flows of customers is considered. The customers are located in a pool of limited capacity. The service times of customers of each type are generally distributed. Each service completion is followed by a search phase to seek for the next customer for service. The customers of the first type possess a non-preemptive priority over the second type. The search processes for both classes of customers are of Markov'stype and have different intensities. Recurrent formulas are derived for computing the stationary distribution of the Markov process that describes the queueing process. Some useful system performance indices are also given.