A refined mean field approximation of synchronous discrete-time population models

• Published in: Performance evaluation 2018-10, Vol.126, p.1-21
• Main Authors: Gast, Nicolas, Latella, Diego, Massink, Mieke
• Format: Article
• Language: English
• Subjects: Accuracy of approximation; Computer Science; Discrete time population models; Mathematics; Mean field approximation; Networking and Internet Architecture; Optimization and Control; Probability
• ISSN: 0166-5316; 1872-745X
• DOI: 10.1016/j.peva.2018.05.002

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 (clock-) synchronous the mean field approximation is a discrete time dynamical system. We focus on the latter. We study the accuracy of mean field approximation when this approximation is a discrete-time dynamical system. We extend a result that was shown for the continuous time case and we prove that expected performance indicators estimated by mean field approximation are O(1∕N)-accurate. We provide simple expressions to effectively compute the asymptotic error of mean field approximation, for finite time-horizon and steady-state, and we use this computed error to propose what we call a refined mean field approximation. We show, by using a few numerical examples, that this technique improves the quality of approximation compared to the classical mean field approximation, especially for relatively small population sizes.