Least Recently Used Caches Under the Shot Noise Model

In this paper we develop an analytical framework, based on Che's approximation [2], for the analysis of Least Recently Used (LRU) caches operating under the Shot Noise requests Model (SNM). The SNM was recently proposed in [12] to better capture the main characteristics of today Video on Demand (Vod) traffic. In this context, Che's approximation is derived as the application of a mean field principle to the cache eviction time. We investigate the validity of this approximation through an asymptotic analysis of the cache eviction time. Particularly, we provide a large deviation principle and a central limit theorem for the cache eviction time, as the cache size grows large. Furthermore, we obtain a non-asymptotic analytical upper bound on the error entailed by Che's approximation of the hit probability, and discuss the extension to tandem of caches.