On the approximation error of mean-field models

Lei Ying

Research output: Chapter in Book/Report/Conference proceedingConference contribution

17 Scopus citations

Abstract

Mean-field models have been used to study large-scale and complex stochastic systems, such as large-scale data centers and dense wireless networks, using simple deterministic models (dynamical systems). This paper analyzes the approximation error of mean-field models for continuous-time Markov chains (CTMC), and focuses on mean-field models that are represented as finite-dimensional dynamical systems with a unique equilibrium point. By applying Stein's method and the perturbation theory, the paper shows that under some mild conditions, if the mean-field model is glob- Ally asymptotically stable and locally exponentially stable, the mean square difference between the stationary distribution of the stochastic system with size M and the equilibrium point of the corresponding mean-field system is O(1/M). The result of this paper establishes a general theorem for establishing the convergence and the approximation error (i.e., the rate of convergence) of a large class of CTMCs to their mean-field limit by mainly looking into the stability of the mean-field model, which is a deterministic system and is often easier to analyze than the CTMCs. Two applications of mean-field models in data center networks are presented to demonstrate the novelty of our results.

Original languageEnglish (US)
Title of host publicationSIGMETRICS/ Performance 2016 - Proceedings of the SIGMETRICS/Performance Joint International Conference on Measurement and Modeling of Computer Science
PublisherAssociation for Computing Machinery, Inc
Pages285-297
Number of pages13
ISBN (Electronic)9781450342667
DOIs
StatePublished - Jun 14 2016
Event13th Joint International Conference on Measurement and Modeling of Computer Systems, ACM SIGMETRICS / IFIP Performance 2016 - Antibes Juan-les-Pins, France
Duration: Jun 14 2016Jun 18 2016

Publication series

NameSIGMETRICS/ Performance 2016 - Proceedings of the SIGMETRICS/Performance Joint International Conference on Measurement and Modeling of Computer Science

Other

Other13th Joint International Conference on Measurement and Modeling of Computer Systems, ACM SIGMETRICS / IFIP Performance 2016
CountryFrance
CityAntibes Juan-les-Pins
Period6/14/166/18/16

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Computational Theory and Mathematics
  • Hardware and Architecture

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  • Cite this

    Ying, L. (2016). On the approximation error of mean-field models. In SIGMETRICS/ Performance 2016 - Proceedings of the SIGMETRICS/Performance Joint International Conference on Measurement and Modeling of Computer Science (pp. 285-297). (SIGMETRICS/ Performance 2016 - Proceedings of the SIGMETRICS/Performance Joint International Conference on Measurement and Modeling of Computer Science). Association for Computing Machinery, Inc. https://doi.org/10.1145/2896377.2901463