Stability of a rate control system with averaged feedback and network delay

We study the stability of a variant of Kelly's rate control scheme in a simple setting with a single flow and a single resource. The feedback signal from the resource is a function of an average rate of the flow obtained using a low pass filter. We derive a sufficient condition for asymptotic stability in the presence of an arbitrary fixed communication delay from the resource to the sender. We show that a sufficient condition derived earlier for a system without averaging suffices.