Bulk Arrival Queueing Model Delayed Service With Restricted Vacation, Variant Arrival Rate And Setup Times

In this paper, a bulk arrival general bulk service queueing model delayed service with restricted vacation policy, variant arrival rate and setup time is considered. The server starts the service only if at least ‘a’ customers are waiting in the queue, and renders the service according to the general bulk service rule with minimum of ‘a’ customers and maximum of ‘b’ customers, then the server will avail of multiple vacations, Also after serving M batches continuously even if sufficient number of customers are there in the queue, the server goes for a vacation with probability or resume service with probability (1. After completing the M th vacation, if the queue length is still less than a then the server remains idle. In addition the server requires a setup time R to start the service, after the setup the server serves a batch of b customers, b ≥ a. It is considered that the variant arrival rate dependent on the state of the server.