Analysis of a multi-server retrial queue with search of customers from the orbit

We consider a multi-server retrial queueing model in which customers arrive according to a Markovian arrival process (MAP). An arriving customer finding a free server enters into service immediately; otherwise the customer enters into an orbit of infinite size. An orbiting customer competes for service by sending out signals at random times until a free server is captured. The inter-retrial times are exponentially distributed with intensity depending on the number of customers in the orbit. Upon completion of a service, with a certain probability the server searches for an orbiting customer. Assuming the search time to be negligible, and the service and retrial times to be exponentially distributed, we perform the steady state analysis of the model using direct truncation and matrix-geometric approximation. Efficient algorithms for computing various steady state performance measures and illustrative numerical examples are presented.