Entangled Gain and Phase Analysis for the Internet

We conduct a local stability analysis of a class of Internet congestion control protocols, approaching the problem from a novel entangled gain and phase perspective. Our approach incorporates a recently revitalized quantitative MIMO phase concept, which we use to reexamine the local version of certain classical stability results. This phase information is entangled with the gain information through the concept of the Davis-Wielandt shell, providing an intuitive graphical interpretation and reducing the conservatism of stability conditions. Leveraging these tools, we derive decentralized stability conditions for the Internet protocols under consideration.