Cache miss behavior: is it √2?

It has long been empirically observed that the cache miss rate decreased as a power law of cache size, where the power was approximately -1/2. In this paper, we examine the dependence of the cache miss rate on cache size both theoretically and through simulation. By combining the observed time dependence of the cache reference pattern with a statistical treatment of cache entry replacement, we predict that the cache miss rate should vary with cache size as an inverse power law for a first level cache. The exponent in the power law is directly related to the time dependence of cache references, and lies between -0.3 to -0.7. Results are presented for both direct mapped and set associative caches, and for various levels of the cache hierarchy. Our results demonstrate that the dependence of cache miss rate on cache size arises from the temporal dependence of the cache access pattern.