Using congestion graphs to analyze the stability of network congestion control

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In this paper we apply the analysis of delay differential systems to congestion control of computer networks. We represent the congestion of the network as a set of graphs and use that structure to define a matrix equation that represents the queue dynamics of a computer network. We first apply the technique to analytical analysis of first-order delay differential dynamics and then show how the method can be extended to numerical analysis of higher-order dynamics. The network model and control are based on a continuous-time fluid flow model of network traffic data rates.

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