Using congestion graphs to analyze the stability of network congestion control

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.