Modeling LEAST RECENTLY USED caches with Shot Noise request processes

Abstract

In this paper we analyze least recently used (LRU) caches operating under the shot noise requests model (SNM). The SNM was recently proposed in [S. Traverso et al., ACM Comput. Comm. Rev., 43 (2013), pp. 5--12] to better capture the main characteristics of today's video on demand traffic. We investigate the validity of Che's approximation [H. Che, Y. Tung, and Z. Wang, IEEE J. Selected Areas Commun., 20 (2002), pp. 1305--1314] through an asymptotic analysis of the cache eviction time. In particular, we provide a law of large numbers, a large deviation principle, and a central limit theorem for the cache eviction time, as the cache size grows large. Finally, we derive upper and lower bounds for the “hit" probability in tandem networks of caches under Che's approximation.