# Mean Field Methods for Computer and Communication Systems

Jean-Yves Le Boudec, EPFL

**Time: ** Mon 2012-05-28 13.15

**Location: **
Lindstedtsvägen 5 Entreplan (D2) Seminarium

## 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 talk we explain the meaning of these concepts, how they are related to Ordinary Differential Equations and how a fast simulation method 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.

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**Biography**

Jean-Yves Le Boudec is full professor at EPFL and fellow of the IEEE. He graduated from Ecole Normale Superieure de Saint-Cloud, Paris, where he obtained the Agregation in Mathematics in 1980 (rank 4) and received his doctorate in 1984 from the University of Rennes, France. From 1984 to 1987 he was with INSA/IRISA, Rennes. In 1987 he joined Bell Northern Research, Ottawa, Canada, as a member of scientific staff in the Network and Product Traffic Design Department. In 1988, he joined the IBM Zurich Research Laboratory where he was manager of the Customer Premises Network Department. In 1994 he joined EPFL as associate professor.

His interests are in the performance and architecture of communication systems. In 1984, he developed analytical models of multiprocessor, multiple bus computers. In 1990 he invented the concept called "MAC emulation" which later became the ATM forum LAN emulation project, and developed the first ATM control point based on OSPF. He also launched public domain software for the interworking of ATM and TCP/IP under Linux. He proposed in 1998 the first solution to the failure propagation that arises from common infrastructures in the Internet. He contributed to network calculus, a recent set of developments that forms a foundation to many traffic control concepts in the internet.

He earned the Infocom 2005 Best Paper award, with Milan Vojnovic, for elucidating the perfect simulation and stationarity of mobility models, the 2008 IEEE Communications Society William R. Bennett Prize in the Field of Communications Networking, with Bozidar Radunovic, for the analysis of max-min fairness and the 2009 ACM Sigmetrics Best Paper Award, with Augustin Chaintreau and Nikodin Ristanovic, for the mean field analysis of the age of information in gossiping protocols.

He is or has been on the program committee or editorial board of many conferences and journals, including Sigcomm, Sigmetrics, Infocom, Performance Evaluation and ACM/IEEE Transactions on Networking. He co-authored the book "Network Calculus" (2001) with Patrick Thiran and is the author of the book "Performance Evaluation of Computer and Communication Systems" (2010).

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