Research Article
A Class Of Mean Field Interaction Models for Computer and Communication Systems
@INPROCEEDINGS{10.4108/ICST.WIOPT2008.3117, author={Michel Benaim and Jean-Yves Le Boudec}, title={A Class Of Mean Field Interaction Models for Computer and Communication Systems}, proceedings={1st International ICST Workshop on Physics Inspired Paradigms for Wireless Communications and Network}, publisher={IEEE}, proceedings_a={PHYSCOMNET}, year={2008}, month={8}, keywords={Approximation algorithms Automata Convergence Differential equations Infinite horizon Media Access Protocol Power system modeling State-space methods Stochastic processes Time measurement}, doi={10.4108/ICST.WIOPT2008.3117} }- Michel Benaim
Jean-Yves Le Boudec
Year: 2008
A Class Of Mean Field Interaction Models for Computer and Communication Systems
PHYSCOMNET
IEEE
DOI: 10.4108/ICST.WIOPT2008.3117
Abstract
In this presentation we review a generic mean field interaction model where N objects are evolving according to an objectpsilas individual finite state machine and the state of a global resource. We show that, in order to obtain mean field convergence for large N to an Ordinary Differential Equation (ODE), it is sufficient to assume that (1) the intensity, i.e. the number of transitions per object per time slot, vanishes and (2) the coefficient of variation of the total number of objects that do a transition in one time slot remains bounded. No independence assumption is needed anywhere. We find convergence in mean square and in probability on any finite horizon, and derive from there that, in the stationary regime, the support of the occupancy measure tends to be supported by the Birkhoff center of the ODE. We use these results to develop a critique of the fixed point method sometimes used in the analysis of communication protocols.