A class of mean field interaction models for computer and communication systems
By M. Benaim, J. L. Boudec. 2008 6th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks and Workshops, 2008
340 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Computer Networks and Communications
View Paper: https://www.semanticscholar.org/paper/cfeec78aabbdb26f5aa7f47fff5c80e2152a6036
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In Computational Theory and Mathematics
In Computer Networks and Communications
Citations in the corpus
- Voluntary Energy Harvesting Relays and Selection in Cooperative Wireless Networks (2010, methodology): “Similar approximations have been used to good effect to analyze, for example, multiple access protocols [30] and mean field interaction models [31].”