The author considers the economic behavior of a queueing system, operating under a specified linear cost structure, in which the server may be turned on and off. Optimal policies for turning the server on and off are derived for differing assumptions about discounting of future costs, length of the planning horizon, the form of the arrival stream, and the number of servers. The costs imposed are: a server start-up cost, a server shut-down cost, a cost per unit time when the server is turned off, a cost per unit time when the server is turned on, and a holding cost per unit time spent in the system for each customer. It is proven that for the single server queue there is a stationary optimal policy of the form: Turn the server on when n customers are present, and turn it off when the system is empty.