A batch service queueing system with multiple vacations, setup time and server's choice of admitting reservice

In this paper, a bulk queueing system with server's choice of admitting reservice, multiple vacations and setup time is considered. At a service completion, the leaving batch may request for reservice with probability π and it is not mandatory to accept it; the server admits this request with a probability α. After the reservice or service completion without request for reservice, if the queue length is less than a, the server leaves for a vacation of random length. After this vacation, if the queue length is still less than 'a', the server leaves for another vacation, etc., until he finally finds at least 'a' customers waiting for service. At a vacation completion epoch, if the server finds at least 'a' customers waiting for service, he requires a setup time to start the service. After a setup time or on service completion or on reservice completion, if the server finds at least 'a' customers waiting for service say, ξ, he serves a batch of min (ξ, b) customers, where b ≥ a . The probability generating function of the queue size is obtained. Various performance measures are derived. A cost model is developed.