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Interacting branching processes and linear file-sharing networks

Part of: Markov processes Operations research and management science

Published online by Cambridge University Press:  01 July 2016

Lasse Leskelä ,
Philippe Robert  and
Florian Simatos
Lasse Leskelä*
Affiliation:
Helsinki University of Technology
Philippe Robert*
Affiliation:
INRIA Paris-Rocquencourt
Florian Simatos*
Affiliation:
INRIA Paris-Rocquencourt
*
∗ Current address: Aalto University, Department of Mathematics and Systems Analysis, PO Box 11100, 00076 Aalto, Finland. Email address: lasse.leskela@iki.fi
∗∗ Postal address: INRIA Paris-Rocquencourt, Domaine de Voluceau, BP 105, 78153 Le Chesnay, France.
∗∗ Postal address: INRIA Paris-Rocquencourt, Domaine de Voluceau, BP 105, 78153 Le Chesnay, France.
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Abstract

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File-sharing networks are distributed systems used to disseminate files among nodes of a communication network. The general simple principle of these systems is that once a node has retrieved a file, it may become a server for this file. In this paper, the capacity of these networks is analyzed with a stochastic model when there is a constant flow of incoming requests for a given file. It is shown that the problem can be solved by analyzing the asymptotic behavior of a class of interacting branching processes. Several results of independent interest concerning these branching processes are derived and then used to study the file-sharing systems.

Keywords

Interacting branching processpeer-to-peer algorithm

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60J85: Applications of branching processes
Secondary: 90B18: Communication networks
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 42 , Issue 3 , September 2010 , pp. 834 - 854
Copyright
Copyright © Applied Probability Trust 2010 

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