Performance Measures of Feedback Batch Arrival Retrial Queue with Optional Second Service and Orbital Search

The steady state behaviour of two phase retrial queue with Bernoulli feedback and orbital search is analysed. Customers arrive in batches of variable size. If the server is free, then one of the arriving customers receives essential service and the others join the orbit. All the customers demand the essential service whereas only some of them opt for optional service. However, after completion of essential or optional service, if the customer is dissatisfied with the service, he can immediately join the orbit as a feedback customer for receiving regular service. After optional service, the server searches for customers in the orbit or remains idle. Retrial times and the service times are arbitrarily distributed. The mean system size and the mean orbit size are derived. The effects of various parameters on the system performances are analysed numerically