This paper presents, using queuing theory and optimization techniques, a methodology for estimating the optimal capacities and speeds of the memory levels in a computer system memory hierarchy operating in the multiprogrammed environment. Optimality is with respect to mean system response time under a fixed cost constraint. It is assumed that the number of levels in the hierarchy as well as the capacity of the lowest level are known. The effect of the storage management strategy is characterized by the hit ratio function which, together with the device technology cost functions are assumed to be representable by power functions. It is shown that as the arrival rate of processes and/or the number of active processes in the system increase, the optimal solution deviates considerably from that under a uniprogrammed environment.
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