Mean-Field approximation and Quasi-Equilibrium reduction of Markov Population Models

Day - Time: 19 June 2014, h.10:15
Place: Area della Ricerca CNR di Pisa - Room: C-29

Mieke Massink


Markov Population Model (MPM) is a commonly used framework to describe stochastic systems. Their exact analysis is not feasible in most cases because of the so-called state space explosion problem. Approximations are usually sought, often with the goal of reducing the number of variables. Among them, the mean field limit and the quasi-equilibrium reductions stand out. The basic principle of the quasi-equilibrium reduction is separation of temporal scales. Separation of temporal scales is a property that is found in such MPMs, that describe concurrent processes whose turn-over times vary over a wide range of scales. The method of quasi-equilibrium reduction is elimination of fast scales by averaging. Understanding the averaging property is important when a model is nonlinear: sometimes, multiscale effects and nonlinearities add up in unpredictable ways, with possibly damaging outcomes for the underlying system. My goal in this talk is to present these effects in some detail. An informal discussion will be given, supplemented with examples from real life and client-server based modelling, and an emphasis will be placed on potential pitfalls of using mean field reduction and mixing them with quasi-equilibrium reduction in the presence of multiple time scale events.