Queueing network models have recently been used to model and study computer systems or flexible manufacturing systems. Optimizing such systems has proven difficult. This paper considers a queueing network with finite multiprocessing factor and finite waiting area at the entrance to the network. The entrance is closed whenever the total number of jobs within the system reaches S and opened again as soon as the number of jobs decreases to s<S. By introducing such a control policy, systems will reach steady state even if the original load exceeds the system’s processing capacity. Such models are of importance for the investigation of flexible manufacturing systems, for production-inventory models and other applications. The paper is restricted to problems of optimal (s,S)-control. As in the queueing network the central-server model (CSM), a basic model for flexible manufacturing systems, is introduced. A simple numerical procedure for defining an optimal (s,S)-control policy is given. To this aim the first need is to develop some results on M/M/1/S-queues with state-dependent service rate, given (s,S)-control policy and given cost and gain structure. Some directions for further research are given in the conclusion.
