A Generic Mean Field Convergence Result for Systems of Interacting Objects

We consider a model for interacting objects, where the evolution of each object is given by a finite state Markov chain, whose transition matrix depends on the present and the past of the distribution of states of all objects. This is a general model of wide applicability; we mention as examples: TCP connections, HTTP flows, robot swarms, reputation systems. We show that when the number of objects is large, the occupancy measure of the system converges to a deterministic dynamical system (the ``mean field") with dimension the number of states of an individual object. We also prove a fast simulation result, which allows to simulate the evolution of a few particular objects imbedded in a large system. We illustrate how this can be used to model the determination of reputation in large populations, with various liar strategies.

Published in:
4th International Conference on the Quantitative Evaluation of SysTems (QEST) 2007
Presented at:
QEST'07, Edinburgh, UK, 16-19 September 2007
Keynote Speaker

 Record created 2007-06-16, last modified 2018-03-18

Rate this document:

Rate this document:
(Not yet reviewed)