A batch service queueing system with multiple vacations, setup time and server's choice of admitting reservice (Q2627293)

Summary: 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 \(\pi\) and it is not mandatory to accept it; the server admits this request with a probability \(\alpha\). 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, \(\xi\), he serves a batch of \(min (\xi, b)\) customers, where \(b<a\). The probability generating function of the queue size is obtained. Various performance measures are derived. A cost model is developed.