Homogeneous Finite-Source Retrial Queues with Search of Customers from the Orbit

We consider a retrial queueing system with a finite number of homogeneous sources of calls and a single server. Each source generates a request after an exponentially distributed time. An arriving customer finding the server idle enters into service immediately; otherwise the customer enters into an orbit. The service times are supposed to be exponentially distributed random variables. An orbiting customer competes for service, the inter-retrial times are exponentially distributed. Upon completion of a service, with a certain probability the server searches for an orbiting customer. Assuming the search time to be negligible, the source, service, and retrial times to be independent random variables, we perform the steady-state analysis of the model computing various steady-state performance measures and illustrative numerical examples are presented. The novelty of the investigation is the introduction of orbital search by the server for customers in finite-source retrial queues. The MOSEL-2 tool is used to formulate and solve the problem.