Workshop on interdisciplinary systems approach in performance
evaluation and design of computer & communication systems

This talk focuses on the stability analysis of (fluid limits of) systems operating under decentralised control. The first part treats the case of a network whose resources are shared among competing flows according to the proportional fairness criterion. A new characterisation of proportional fairness is proposed, which is then used to prove Lyapunov stability of the system’s fluid limits. This result extends previously known stability results to cover the case of phase-type service time distributions.

The second part of the talk treats the case of broadcasting information in a peer-to-peer network. Scheduling rules based on local information are proposed, and shown to achieve the theoretical broadcasting limit. The proof again relies on Lyapunov function techniques. A classical characterisation, due to Edmonds, of the number of spanning trees that can be packed in a graph is retrieved as a corollary.