A Lyapunov analysis of LRU

Caches are segments of memory that store requested information in a system subject to a set of decision rules, defined as the caching algorithm. One of the most popular caching algorithms is the least recently used algorithm (LRU) due to its simplicity and effectiveness in a multitude of applications. LRU caches operate by storing objects in the order that they were most recently requested. Further, whenever an item is requested that is not currently in the cache, the requested item is placed at the head of the cache, and the least recently requested item is evicted. Many have suggested a tie between the performance of an LRU cache and a time to live (TTL) cache. In this thesis, we present a unique Lyapunov based proof for an asymptotically exact TTL approximation for the steady state distribution of our LRU Markov model. We further present ongoing theoretical extensions to other variants of LRU, as well as simulations that validate our model. We conclude by proposing a variance corrected model to better approximate hit rate over time.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Electrical & Computer Engr

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2020

Author dc:creator

• Brenner, Michael

Contributors dc:contributor

• Srikant, Rayadurgam

• Lyapunov
• Control Thoery
• Stochastic Systems
• Cache
• LRU
• Least recently used
• Markov Chain
• TTL

Statement dc:rights

• Copyright 2020 Michael Brenner

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/107992

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/107992