Dr Robert Shorten, Hamilton Institute, NUI Maynooth

Positive matrices and the internet
 
In this talk we show how positive matrices can be used to build a dynamic model of communication systems that employ AIMD
(TCP) congestion control strategies. We first build a model under the assumption that each source is informed of congestion at the
same time. We then extend this model to the unsynchronised case and show how common Lyapunov functions can be used to
reveal some fundamental properties of networks. Finally, time permitting, we use our results to design a fair and stable adaptive
congestion control strategy for the internet.