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.