Jean-YvesLeBoudec, EPFL

Title: Mean Field Methods for Computer and Communication Systems

Abstract:
We consider a generic model of N interacting objects, where each object has a state and the evolution of the system depends only on the collection of states at any point in time. This is quite a general modeling framework, which was successfully applied to model many forms of distributed systems and communication protocols. When the number of objects N is large, one often uses simplifying assumptions called "mean field approximation", "fluid approximation", "fixed point method" or "decoupling assumption". In this seminar we explain the meaning of these concepts, how they are related to Ordinary Differential Equations and how a fast simulation methods can be derived. We also show that the first two, namely mean field approximation and fluid approximation, are generally valid, whereas the last two, namely fixed point method and decoupling assumption, require more care, and may not hold even in simple cases. We give sufficient conditions under which they are valid. We illustrate the concepts with some easy-to-follow examples.