LRU Caching with Moderately Heavy Request Distributions

Majority of practical caching algorithms, in particular those used in the World Wide Web applications, are based on the so-called Least-Recently-Used (LRU) cache replacement heuristic whose desirable attributes include low complexity, quick adaptability and high cache hit (low fault) probability. Recent studies have developed asymptotic characterization of the LRU fault probability for the generalized Zipf’s (power) law request distributions. In this paper, we extend these results to include the distributions that decay faster than power laws but slower than exponential, hence named moderately heavy distributions. Informally, for these types of distributions and the independent reference model, the main result of this paper shows that the ratio between the cache fault probabilities of the LRU heuristic and the optimal static algorithm is, for large caches, equal to e ≈ 1.78, where γ is Euler’s constant. Interestingly enough, this limiting ratio is constant, i.e., it is invariant to the underlying characteristics of the request distributions.