Affiliation:
1. Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, Grenoble, France
Abstract
Mean field approximation is a powerful technique which has been used in many settings to study large-scale stochastic systems. In the case of two-timescale systems, the approximation is obtained by a combination of scaling arguments and the use of the averaging principle. This paper analyzes the approximation error of this 'average' mean field model for a two-timescale model (X, Y), where the slow component X describes a population of interacting particles which is fully coupled with a rapidly changing environment Y. The model is parametrized by a scaling factor N, e.g. the population size, which as N gets large decreases the jump size of the slow component in contrast to the unchanged dynamics of the fast component. We show that under relatively mild conditions, the 'average' mean field approximation has a bias of order O(1/N) compared to E[X]. This holds true under any continuous performance metric in the transient regime, as well as for the steady-state if the model is exponentially stable. To go one step further, we derive a bias correction term for the steady-state, from which we define a new approximation called the refined 'average' mean field approximation whose bias is of order O(1/N2). This refined 'average' mean field approximation allows computing an accurate approximation even for small scaling factors, i.e., N ~10 -50. We illustrate the developed framework and accuracy results through an application to a random access CSMA model.
Funder
French National Research Agency
Publisher
Association for Computing Machinery (ACM)
Subject
Computer Networks and Communications,Hardware and Architecture,Safety, Risk, Reliability and Quality,Computer Science (miscellaneous)
Reference34 articles.
1. Asymptotic analysis of multiscale approximations to reaction networks
2. M. Benaim and J. . Y. Boudec . 2008. A class of mean field interaction models for computer and communication systems. Performance Evaluation 65 ( 2008 ). https://doi.org/10.1016/j.peva.2008.03.005 10.1016/j.peva.2008.03.005 M. Benaim and J. . Y. Boudec. 2008. A class of mean field interaction models for computer and communication systems. Performance Evaluation 65 (2008). https://doi.org/10.1016/j.peva.2008.03.005
3. Throughput Analysis in Multihop CSMA Packet Radio Networks
4. A particle system in interaction with a rapidly varying environment: Mean field limits and applications
5. The Prelimit Generator Comparison Approach of Stein’s Method
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