A Numerical Study of the Transient Behaviour of a Retrial Queue with Orbital Search and Balking of Customers

Retrial queuing systems occurs naturally in call centers, cellular networks and random access protocols in local area networks. Here we consider a single-server queuing system into which primary customers arrive for service. On finding the server busy, serving a primary customer, the customers join an orbit from where they retry for service. On the other hand finding the server busy, serving a retrial customer the customer decides not to join the system. This behaviour of the customer is called balking. The server serves the primary customers and retrying customers at two different rates. Immediately after service of a primary customer the server picks a customer from the orbit for service with a certain probability and remains idle with a complimentary probability. This is referred to as orbital search. The search time is assumed to be negligible. The analysis of the model is carried out and the transient behavior of the system is studied numerically.