Stationary Distribution of a Generalized LRU-MRU Content Cache

TL;DR

This paper derives a new closed-form stationary distribution for a generalized LRU-MRU cache model, compares its performance with other caching policies, and analyzes cache hit probabilities under Zipf popularity.

Contribution

It introduces a novel analytical expression for the invariant distribution of a generalized LRU-MRU cache, extending prior models and enabling performance comparison.

Findings

Cache hit probabilities vary with caching policy: smaller under MRU, larger under IRP.

The derived distribution applies to a caching tree-network with random eviction.

Numerical results show differences in performance among LRU, MRU, and IRP policies.

Abstract

Many different caching mechanisms have been previously proposed, exploring different insertion and eviction policies and their performance individually and as part of caching networks. We obtain a novel closed-form stationary invariant distribution for a generalization of LRU and MRU caching nodes under a reference Markov model. Numerical comparisons are made with an "Incremental Rank Progress" (IRP a.k.a. CLIMB) and random eviction (a.k.a. random replacement) methods under a steady-state Zipf popularity distribution. The range of cache hit probabilities is smaller under MRU and larger under IRP compared to LRU. We conclude with the invariant distribution for a special case of a random-eviction caching tree-network and associated discussion.