Stochastic equilibria of aimd communication networks

F. Wirth, Rade Stanojevic, R. Shorten, D. Leith

Research output: Contribution to journalArticle

17 Citations (Scopus)


In this paper tools are developed to analyse a recently proposed random matrix model of communication networks that employ additive-increase multiplicative-decrease (AIMD) congestion control algorithms. We investigate 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. ns2 simulation results are discussed to validate the obtained formulae. (The simulation program ns2, or network simulator, is an industry standard for the simulation of Internet dynamics.)

Original languageEnglish
Pages (from-to)703-723
Number of pages21
JournalSIAM Journal on Matrix Analysis and Applications
Issue number3
Publication statusPublished - 2006
Externally publishedYes



  • AIMD congestion control
  • Communication networks
  • Infinite products of positive matrices
  • Law of large numbers
  • Markov e-chain
  • Positive matrices

ASJC Scopus subject areas

  • Analysis

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