A positive systems model of TCP-like congestion control: asymptotic results
IEEE/ACM Transactions on Networking (TON)
TCP-Illinois: a loss and delay-based congestion control algorithm for high-speed networks
valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
Brief paper: Modelling TCP congestion control dynamics in drop-tail environments
Automatica (Journal of IFAC)
Network optimization and control
Foundations and Trends® in Networking
TCP-Illinois: A loss- and delay-based congestion control algorithm for high-speed networks
Performance Evaluation
Random walk analysis of parallel queueing stations
Mathematical and Computer Modelling: An International Journal
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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.)