Stationary probabilities of the states of the MAP/G/1/r retrial system with priority servicing of primary customers

The queue with Markov input flow, retrying customers, and limited queues both of the primary and retrying customers was discussed. A new arriving customer is queued with the primary customers, or is sent to the queue of retrying customers if all places on the queue of primary customers are occupied, or leaves the system if the Queue of retrying customers also has no vacant places. A customer from the queue of retrying customers can be sent only to a free server. For this system, the stationary probabilities of states, as well as the stationary time distributions of the numbers of retrying and primary customers in the system were determined for the embedded Markov chain which is generated by the instants of server release.