A positive systems model of TCP-like congestion control: asymptotic results

Abstract

Abstract-We study communication networks that employ drop-tail queueing and Additive-Increase Multiplicative-Decrease (AIMD) congestion control algorithms. It is shown that the theory of nonnegative matrices may be employed to model such networks. In particular, important network properties, such as: 1) fairness; 2) rate of convergence; and 3) throughput, can be characterized by certain nonnegative matrices. We demonstrate that these results can be used to develop tools for analyzing the behavior of AIMD communication networks. The accuracy of the models is demonstrated by several NS studies.

Modelling TCP congestion control dynamics in drop-tail environments

“…We have also derived under simplifying assumptions a number of analytic results that characterise the ensemble-average throughput of such networks. Finally, we note that we have also validated our results against packet-level simulations for networks many flows and the results are presented in Shorten, Wirth, and Leith (2006). (15) are directly deduced from these results by similarity.…”

On linear co-positive Lyapunov functions for sets of linear positive systems

“…The interest in such systems is hardly surprising since they are ubiquitous and can be found in diverse areas such as economics [14,18], biology [12, 6,1], communication networks [20,5,25], and in decentralised control [24] or synchronisation / consensus problems [13]. While both nonlinear and linear positive systems have been studied, much recent attention has focused on both time-varying and time-invariant linear positive systems, and on the Metzler matrices that characterise the properties of such systems.…”

Tools for the analysis and design of communication networks with Markovian dynamics

“…In particular, much of this work has focussed on understanding the manner in which the network allocates available bandwidth among competing network flows (network fairness) and the speed at which this bandwidth allocation takes place (network convergence rate). Recently, a very accurate random matrix model of TCP network dynamics was proposed [10]. This model was shown to be capable of capturing many essential features of networks in which TCP-like network flows compete for bandwidth via a bottleneck router.…”