The authors consider a queueing system with N-policy. The server is turned off as soon as the system empties. When the queue length reaches or exceeds a predetermined value (threshold), the server is turned on and begins to serve the customers. The authors place the present emphasis on understanding the operational characteristics of the queueing system. One of the findings is that the system size is the sum of two independent random variables: one has the PGF of the stationary system size of the queueing system without -policy and the other one has the probability generating function , in which is the probability that the system state stays at before reaching or exceeding N during an idle period. Using this interpretation of the system size distribution, the authors determine the optimal threshold under a linear cost structure.
