Cache Miss Estimation for Non-Stationary Request Processes

Felipe Olmos (1, 2) , Carl Graham (1) , Alain Simonian (2)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 Orange Labs [Issy les Moulineaux]

The goal of the paper is to evaluate the miss probability of a Least Recently Used (LRU) cache, when it is offered a non-stationary request process given by a Poisson cluster point process. First, we construct a probability space using Palm theory, describing how to consider a tagged document with respect to the rest of the request process. This framework allows us to derive a fundamental integral formula for the expected number of misses of the tagged document. Then, we consider the limit when the cache size and the arrival rate go to infinity in proportion, and use the integral formula to derive an asymptotic expansion of the miss probability in powers of the inverse of the cache size. This enables us to quantify and improve the accuracy of the so-called Che approximation.

Keywords: performance evaluation; Poisson cluster process; Che approximation; Cox process; LRU cache policy; scaling limit expansion

Domains: Probability [math.PR]

Felipe Olmos, Carl Graham, Alain Simonian. Cache Miss Estimation for Non-Stationary Request Processes. Stochastic Systems, 2018, 8 (1), pp.75-90. ⟨10.1287/stsy.2017.0009⟩. ⟨hal-01232173v2⟩