Analysis of a Retrial Bulk Arrival Queue with Secondary Optional Service Subject to Bernoulli Vacation, Server Breakdown and Customer Balking

A bulk arrival retrial queueing model with two service levels, the second of which is optional, and the server undergoing Bernoulli vacation (BV) and breakdown has been investigated in this paper. Further, the client has the option to decline service and exit the service area (balking) if the server is unable to immediately fulfil the demand upon arrival. The probability generating function (PGF) of the no. of clients in the system and orbit has been calculated by utilizing the supplementary variable approach. Key metrics have been presented, including the avg. no. of clients in the system/orbit along with a few distinctive cases. The impact of various characteristics on the system’s functionality is demonstrated with a few numerical examples.