Abstract—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 in both single-link and multi-link configurations. The network model and control are based on a continuous-time fluid flow model of network traffic data rates.