Cache Miss Estimation for Non-Stationary Request Processes

TL;DR

This paper develops a mathematical framework to accurately estimate cache miss probabilities for non-stationary request processes, improving existing approximation methods like the Che approximation.

Contribution

It introduces a Palm theory-based approach and derives an asymptotic expansion for miss probability in large cache regimes, enhancing estimation accuracy.

Findings

Derived a general integral formula for expected cache misses.

Provided an asymptotic expansion improving the Che approximation.

Quantified the accuracy of cache miss estimates in non-stationary settings.

Abstract

The aim 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 general 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 proportionally, 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.