Optimal Prefetching in Random Trees

Kausthub Keshava,Alain Jean-Marie,Sara Alouf

doi:10.3390/math9192437

Abstract

We propose and analyze a model for optimizing the prefetching of documents, in the situation where the connection between documents is discovered progressively. A random surfer moves along the edges of a random tree representing possible sequences of documents, which is known to a controller only up to depth d. A quantity k of documents can be prefetched between two movements. The question is to determine which nodes of the known tree should be prefetched so as to minimize the probability of the surfer moving to a node not prefetched. We analyzed the model with the tools of Markov decision process theory. We formally identified the optimal policy in several situations, and we identified it numerically in others.

Highlights

Prefetching is a basic technique underlying many computer science applications
The adequate formalism for modeling optimal decisions in such a context is that of Markov Decision Processes (MDPs)
For small values of p, we describe the optimal policy, and we conjecture that this policy is optimal for general values of p

Summary

Introduction

Prefetching is a basic technique underlying many computer science applications. Its main purpose is to reduce the time needed to access some information by loading it in advance and concurrently with the process that needs this information. The issue here is randomness: the entity in charge of prefetching, let us call it the “controller”, does not know in advance what is the precise data access sequence of the process needing the data. It must make decisions based on the current state of said process and its knowledge of the possible evolution. The adequate formalism for modeling optimal decisions in such a context is that of Markov Decision Processes (MDPs). The principle of using Markov decision processes to optimize prefetching in the context of video applications was first demonstrated in [1,2]. The model was extended in [3,4] and further extended in [5]

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Discussion

Conclusion