Asymptotic optimally of the static frequency caching in the presence of correlated requests

Abstract

Renewed interest in caching algorithms stems from their application to content distribution on the Web. When documents are of equal size and their requests are independent and equally distributed, it is well known that static algorithm that keeps the most frequently requested documents in the cache is optimal. However, there are no explicit caching algorithms that are provably optimal when the requests are statistically correlated. In this paper, we show, maybe somewhat surprisingly, that keeping the most frequently requested documents in the cache is still optimal for large cache sizes even if the requests are strongly correlated. We model the statistical dependency of requests using semi-Markov modulated processes that can capture strong statistical correlation, including the empirically observed long-range dependence in the Web access sequences. Although frequency algorithm and its practical version least-frequently-used policy is not commonly used in practice due to their complexity and static nature, our result provides a benchmark for evaluating the popular heuristic schemes. In particular, an important corollary of our main theorem and recent result from [9] is that the widely used least-recently-used heuristic is asymptotically near-optimal under the semi-Markov modulated requests and generalized Zipf's law document frequencies.