Unreliable retrial queueing system with a backup server

In this paper we consider an unreliable retrial queueing system consisting of the main unreliable server, the reliable backup server and the orbit of innite size. Customers and breakdowns arrive to the main server according to Markovian arrival processes (MAP). If at the moment of a customer arrival the main server is busy, then the customer goes to the orbit. If at the moment of a primary or an orbital customer arrival the main server is under repair and the backup server is free, then the customer goes to the backup server. If during the service by the backup server the main server restores, the customer goes to this server and is serviced as a new. If at the time of the arrival of a primary or an orbital customer the main server is under repair and the backup one is busy, then the customer goes to orbit. If a breakdown arrives at the busy main server, then the under-served customer is transferred to the backup server and is serviced as a new. Service times and repair times have phase type (PH) distributions. The system under consideration can be used when modeling the hybrid communication system consisting of the main optic channel and the reserve radio channel. We investigate the stable operation of the system, calculate the stationary distribution and a number of performance measures. We also present illustrative numerical examples to show the behavior of the performance measures of the system.