Analysis of the LRU Cache StartUp Phase and Convergence Time and Error Bounds on Approximations by Fagin and Che

Abstract

We compare exact and approximate performance evaluation methods of the Least Recently Used (LRU) caching strategy, which is widely applied in local caches and in distributed web cache architectures in core and edge networks. Based on the independent reference model (IRM), the LRU startup behaviour and convergence time (CT) is derived. The result is related to hit ratio approximations by Fagin and Che et al. We evaluate the precision of the approximations by identifying maximum errors, which are shown to decrease with the cache size. For different object sizes, we extend the analytical LRU hit ratio formula, which is tractable for small caches. The Che and CT approximations are subject to larger deviations for high variability of the object sizes and small caches due to partially unused cache space. We propose an estimation scheme for the fraction of unused LRU cache space, which is shown to improve the accuracy.