A Closed-Form Method for LRU Replacement under Generalized Power-Law Demand

TL;DR

This paper derives a closed-form, efficient method to compute the per object steady-state hit ratio of the LRU cache replacement algorithm under generalized power-law demand, enabling faster analysis without simulations.

Contribution

It provides the first analytic, constant-time formula for LRU hit ratios under generalized power-law demand, improving efficiency over numeric and simulation methods.

Findings

Closed-form expression for per object hit ratio under power-law demand

First analytic derivation of LRU hit ratio in constant time

Applicable to multiple cache scenarios for practical analysis

Abstract

We consider the well known \emph{Least Recently Used} (LRU) replacement algorithm and analyze it under the independent reference model and generalized power-law demand. For this extensive family of demand distributions we derive a closed-form expression for the per object steady-state hit ratio. To the best of our knowledge, this is the first analytic derivation of the per object hit ratio of LRU that can be obtained in constant time without requiring laborious numeric computations or simulation. Since most applications of replacement algorithms include (at least) some scenarios under i.i.d. requests, our method has substantial practical value, especially when having to analyze multiple caches, where existing numeric methods and simulation become too time consuming.