Analysis of large scale interacting systems by mean field method

Andrea Bobbio, Marco Gribaudo, Miklós Telek

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

38 Citations (Scopus)

Abstract

Modeling and analysing very large stochastic systems composed of interacting entities is a very challenging and complex task. The usual approach, relying on the generation of the whole state space, is bounded by the state space explosion, even if symmetry properties, often included in the model, allow to apply lumping techniques and building the overall model by means of tensor algebra operations. In this paper we resort to the mean field theory. The main idea of the mean field theory is to focus on one particular tagged entity and to replace all interactions with the other entities with an average or effective interaction. The reduction of a multibody problem into an effective one-body problem makes the solution easier while at the same time taking into account the contribution of an averaged interdependence of the whole system on the specific entity. We apply the mean field approach to very large systems of interacting continuous time Markov chains, in which the averaged interaction depends on the distribution of the entity population in each state. We report several examples of interacting Markovian queues, showing the potentialities of the proposed technique.

Original languageEnglish
Title of host publicationProceedings - 5th International Conference on the Quantitative Evaluation of Systems, QEST 2008
Pages215-224
Number of pages10
DOIs
Publication statusPublished - Nov 28 2008
Event5th International Conference on the Quantitative Evaluation of Systems, QEST 2008 - St. Malo, France
Duration: Sep 14 2008Sep 17 2008

Publication series

NameProceedings - 5th International Conference on the Quantitative Evaluation of Systems, QEST 2008

Other

Other5th International Conference on the Quantitative Evaluation of Systems, QEST 2008
CountryFrance
CitySt. Malo
Period9/14/089/17/08

Keywords

  • Continuous time Markov chain
  • Mean field method
  • Performance Evaluation

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Hardware and Architecture
  • Control and Systems Engineering

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  • Cite this

    Bobbio, A., Gribaudo, M., & Telek, M. (2008). Analysis of large scale interacting systems by mean field method. In Proceedings - 5th International Conference on the Quantitative Evaluation of Systems, QEST 2008 (pp. 215-224). [4634974] (Proceedings - 5th International Conference on the Quantitative Evaluation of Systems, QEST 2008). https://doi.org/10.1109/QEST.2008.47