Boundedness of utility function based congestion controllers in the presence of delay

We consider decentralized congestion control algorithms for low-loss operation of the Internet using the ECN bit. There has been much analysis of such algorithms, but with a few exceptions, these typically ignore the effect of feedback delays in the network on stability. We study a single node with many flows passing through it, with each flow having a different round trip delay. Using a fluid model for the flows, we show that even with delays, the total data rate at the router is bounded; and this bound shows that the total rate grows linearly with increase in system size. Further, for typical user data rates and delays seen in the Internet today, the bound is very close to the data rate at the router without delays. Johari and Tan (2000) have given conditions for a linearized model of the network to be stable. We show that even when the linearized model is not stable, the nonlinear model is bounded, i.e., the total rate at the bottleneck link is bounded. Our most important conclusion is that in the regime of interest, very little over-provisioning is required at the router to have a low-loss, low-queueing-delay network