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A simple model of the storage hierarchies is formulated with the assumptions that the effect of the storage management strategy is characterized by the hit ratio function. The hit ratio function and the device technology-cost function are assumed to be representable by power functions (or piece-wise power functions). The optimization of this model is a geometric programming problem. An explicit formula for the minimum hierarchy access time is derived; the capacity and technology of each storage level are determined. The optimal number of storage levels in a hierarchy is shown to be directly proportional to the logarithm of the systems capacity with the constant of proportionality dependent upon the technology and hit ratio characteristics. The optimal cost ratio of adjacent storage levels is constant, as are the ratios of the device access times and storage capacities of the adjacent levels. An illustration of the effect of overhead cost and level-dependent cost, such as the cost per “box” and cost for managing memory faults is given and several generalizations are presented.
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