A Refined Mean Field Approximation for Synchronous Population Processes

Nicolas Gast (1) , Diego Latella (2) , Mieke Massink (2)

1 POLARIS - Performance analysis and optimization of LARge Infrastructures and Systems
2 CNR | ISTI - CNR Istituto di Scienza e Tecnologie dell’Informazione “A. Faedo” [Pisa]

Mean field approximation is a popular method to study the behaviour of stochastic models composed of a large number of interacting objects. When the objects are asynchronous, the mean field approximation of a population model can be expressed as an ordinary differential equation. When the objects are synchronous the mean field approximation is a discrete time dynamical system. In this paper, we focus on the latter. We show that, similarly to the asynchronous case, the mean field approximation of a synchronous population can be refined by a term in 1/N. Our result holds for finite time-horizon and steady-state. We provide two examples that illustrate the approach and its limit.

Domaines: Réseaux et télécommunications [cs.NI]; Performance et fiabilité [cs.PF]; Mathématiques [math]; Optimisation et contrôle [math.OC]; Probabilités [math.PR]

Nicolas Gast, Diego Latella, Mieke Massink. A Refined Mean Field Approximation for Synchronous Population Processes. MAMA 2018Workshop on MAthematical performance Modeling and Analysis, Jun 2018, Irvine, United States. pp.1-3. ⟨hal-01891629⟩