Hybrid traffics congestion control based on 2-D Hurwitz-Schur stability

Classical network fluid model and RED algorithm are based on TCP flows in internet network, and they have not considered the UDP flows' effects in network. However, in real work of the network, the network link capacity is shared by the hybrid traffics: TCP flows and UDP flows, and UDP flows can occupy the original link capacity of TCP flow. Since there is no feedback control for UDP flows, the classical network fluid model and RED algorithm can not reflect and control the congestion of TCP/UDP networks. To solve the problem, we modify the classical AQM router into multiple queues AQM router with classifier. We express the proposed TCP/UDP AQM router by a linear time-delay system model. Then, by utilizing the 2-D Laplace-Z transform technique, we derive some explicit conditions that establish the relationship between the control parameter p_max and the network stability. This paper first proposes parameter p_max's stability bounds for TCP/UDP routers for congestion control based on 2-D Hurwitz-Schur stability conditions. The simulation results verify that the proposed stability condition can gain the effective congestion control.