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A model is developed which represents the behavior of multiprogrammed computer systems in terms of a network of interdependent queues. This model, which is known as the central server model of multiprogramming, is first analyzed mathematically and then applied to three problems in operating system design. These are: The optimal choice of buffer size for tape-like devices; The optimal allocation of processing requests among a set of functionally equivalent peripheral processors such as disks and drums; The optimal selection of the degree of multiprogramming in demand paging systems. A series of computational algorithms are developed to supplement the analytic work. These algorithms can be used to obtain the marginal distributions and expected queue lengths for a large class of queueing network models.