Wirth, F. and Stanojević, R. and Shorten, Robert N. and Leith, Douglas J. (2006) Stochastic equilibria of AIMD communication networks. SIAM Journal on Matrix Analysis and Applications, 28 (3). pp. 703-723. ISSN 0895-4798

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Abstract

In this paper we develop tools to analyse a recently proposed random matrix model of communication networks that employ AIMD congestion control algorithms. We analyse properties of the Markov process describing the evolution of the window sizes of network users. Using paracontractivity properties of the matrices involved in the model, it is shown that the process has a unique invariant probability and the support of this probability is characterized. Based on these results we obtain a weak law of large numbers for the average distribution of resources between the users of a network. This shows that under reasonable assumptions such networks have a well defined stochastic equilibrium. NS-simulation1 results are given to demonstrate the efficacy of the obtained formulae.

Item Type:	Article
Keywords:	Positive matrices; Infinite products of positive matrices; AIMD Congestion Control; Additive-Increase Multiplicative Decrease; Communication networks; Markov e-chain; weak law of large numbers; Hamilton Institute.
Academic Unit:	Faculty of Science and Engineering > Computer Science Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID:	1791
Identification Number:	https://doi.org/10.1137/040620953
Depositing User:	Hamilton Editor
Date Deposited:	18 Jan 2010 15:59
Journal or Publication Title:	SIAM Journal on Matrix Analysis and Applications
Publisher:	SIAM - Society for Industrial and Applied Mathematics
Refereed:	Yes
URI:	Publisher
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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