Asymptotic insensitivity of least-recently-used caching to statistical dependency

We investigate a widely popular least-recently-used (LRU) cache replacement algorithm with semiMarkov modulated requests. SemiMarkov processes provide the flexibility for modeling strong statistical correlation, including the broadly reported long-range dependence in the World Wide Web page request patterns. When the frequency of requesting a page n is equal to the generalized Zipf´s law c/n^α, α > 1, our main result shows that the cache fault probability is asymptotically, for large cache sizes, the same as in the corresponding LRU system with i.i.d. requests. This appears to be the first explicit average case analysis of LRU caching with statistically dependent request sequences. The surprising insensitivity of LRU caching performance demonstrates its robustness to changes in document popularity. Furthermore, we show that the derived asymptotic result and simulation experiments are in excellent agreement, even for relatively small cache sizes. The potential of using our results in predicting the behavior of Web caches is tested using actual, strongly correlated, proxy server access traces.