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A fluid limit for a cache algorithm with general request processes

Part of: Algorithms - Computer Science Stochastic processes Limit theorems

Published online by Cambridge University Press:  01 July 2016

Takayuki Osogami
Takayuki Osogami*
Affiliation:
IBM Research - Tokyo
*
∗ Postal address: IBM Research - Tokyo, 1623-14 Shimotsuruma, Yamato-shi, Kanagawa 242-8502, Japan. Email address: osogami@jp.ibm.com
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Abstract

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We introduce a formal limit, which we refer to as a fluid limit, of scaled stochastic models for a cache managed with the least-recently-used algorithm when requests are issued according to general stochastic point processes. We define our fluid limit as a superposition of dependent replications of the original system with smaller item sizes when the number of replications approaches ∞. We derive the average probability that a requested item is not in a cache (average miss probability) in the fluid limit. We show that, when requests follow inhomogeneous Poisson processes, the average miss probability in the fluid limit closely approximates that in the original system. Also, we compare the asymptotic characteristics, as the cache size approaches ∞, of the average miss probability in the fluid limit to those in the original system.

Keywords

Fluid limitleast recently usedpoint processnonstationaryhit probabilityinsensitivityapproximation

MSC classification

Primary: 68W40: Analysis of algorithms
Secondary: 60G55: Point processes 60F05: Central limit and other weak theorems
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 42 , Issue 3 , September 2010 , pp. 816 - 833
Copyright
Copyright © Applied Probability Trust 2010 

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