Abstract

Set associative page mapping algorithms have become widespread for the operation of cache memories for reasons of cost and efficiency. We show how to calculate analytically the effectiveness of standard bit-selection set associative page mapping or random mapping relative to fully associative (unconstrained mapping) paging. For two miss ratio models, Saltzer's linear model and a mixed geometric model, we are able to obtain simple, closed-form expressions for the relative LRU fault rates. We also experiment with two (infeasible to implement) dynamic mapping algorithms, in which pages are assigned to sets either in an LRU or FIFO manner at fault times, and find that they often yield significantly lower miss ratios than static algorithms such as bit selection. Trace driven simulations are used to generate experimental results and to verify the accuracy of our calculations. We suggest that as electronically accessed third-level memories composed of electron-beam tubes, magnetic bubbles, or charge-coupled devices become available, algorithms currently used only for cache paging will be applied to main memory, for the same reasons of efficiency, implementation ease, and cost.