The similarity between queuing and inventory models has long been recognized. Inventory analysis generally includes an explicit cost structure and a solution for optimal policies. Queuing theory, however, has been preoccupied with the underlying stochastic structure. Models of queuing situations including an explicit cost structure have only been studied for rather trivial situations. The interest in this field of study is shifting slowly towards operating policies for queuing situations. D.P. Heyman and C.E. Bell tried to establish stationary operating policies for queuing situations in analogy with inventory models. Assuming a linear cost structure associated with an M/G/1 queue, they could demonstrate the existence of an optimal stationary operating policy that has the form: Turn (or leave) the server on whenever k or more customers are present, turn the server off only when none is present. This decision rule is called a (o,k)-policy. The present research is directed towards exploring (s, S)-policies for queuing systems. The following situation is considered: At a service facility units arrive according to a Poisson process with parameter λ. The service facility may comprise one or several channels. If an arriving unit finds an empty channel, it is served immediately after its arrival. Otherwise units form a queue in front of the service facility. Units are processed individually in their order of arrival. The service times are independent, indentically distributed non-negative random variables with known distribution function. In this queuing system, a manager can excersie partial control over the system's behavior by varying the service rate according to the length of queue. More specifically, he follows an (s, S)-policy: First, arriving units are processed with service rate μ1.
