In our paper, "An analytical model for designing memory hierarchies" (see ibid., vol. 45, no. 10, p. 180-1, 194 (1996)), we made the following statement: "Failing to apply a specific model of workload locality makes it impossible to provide an easily used, closed-form solution for the optimal cache configuration, and so the results from these papers have contained dependencies on the cache configuration-the number of levels, or the sizes and hit rates of the levels." Our description did not accurately reflect the contents of the paper by J.E. MacDonald and K.L. Sigworth (1975), and we regret any false impressions caused by the inaccuracy.

Memory hierarchies have long been studied by many means: system building, trace driven simulation, and mathematical analysis. Yet little help is available for the system designer wishing to quickly size the different levels in a memory hierarchy to a first order approximation. We present a simple analysis for providing this practical help and some unexpected results and intuition that come out of the analysis. By applying a specific, parameterized model of workload locality, we are able to derive a closed form solution for the optimal size of each hierarchy level. We verify the accuracy of this solution against exhaustive simulation with two case studies: a three level I/O storage hierarchy and a three level processor cache hierarchy. In all but one case, the configuration recommended by the model performs within 5% of optimal. One result of our analysis is that the first place to spend money is the cheapest (rather than the fastest) cache level, particularly with small system budgets. Another is that money spent on an n level hierarchy is spent in a fixed proportion until another level is added.