Bounds on the throughput of congestion controllers in the presence of feedback 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 (possibly) 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 (peak) total rate grows linearly with increase in system size, i.e., the fraction of overprovisioning required is constant with respect to N, the number of flows in the system. 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. Earlier results by Johari and Tan have given conditions for a linearized model of the network to be (locally) stable. We show that even when the linearized model is not stable, the nonlinear model is upper bounded, i.e., the total rate at the bottleneck link is upper bounded, and the upper bound is close to the equilibrium rate for TCP.