A Poisson queue under N-policy with a general setup time

This paper deals with a Poisson queue under N-policy with a general setup time, where the server is turned off each time at the end of each busy period. As soon as the queue size becomes 'N', the setup of the service facility begins (during which no work is done), on completion of which service begins. In this paper, the steady state behaviour of the queue size distribution for such a model under fairly general conditions has been studied. The purpose of the present study is to provide meaningful probabilistic interpretation of the queue size distribution. Also we place our emphasis on understanding the operating characteristic of this queueing system. Finally we provide a simple derivation for expected busy period.