Applying Mean-Field Approximation to Continuous Time Markov Chains

A.V. Kolesnichenko, Valerio Senni, Alireza Pourranjabar, Anne Remke

    Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

    3 Citations (Scopus)
    386 Downloads (Pure)

    Abstract

    The mean-field analysis technique is used to perform analysis of a system with a large number of components to determine the emergent deterministic behaviour and how this behaviour modifies when its parameters are perturbed. The computer science performance modelling and analysis community has found the mean-field method useful for modelling large-scale computer and communication networks. Applying mean-field analysis from the computer science perspective requires the following major steps: (1) describing how the agent populations evolve by means of a system of differential equations, (2) finding the emergent deterministic behaviour of the system by solving such differential equations, and (3) analysing properties of this behaviour. Depending on the system under analysis, performing these steps may become challenging. Often, modifications of the general idea are needed. In this tutorial we consider illustrating examples to discuss how the mean-field method is used in different application areas. Starting from the application of the classical technique, moving to cases where additional steps have to be used, such as systems with local communication. Finally, we illustrate the application of existing model checking analysis techniques.
    Original languageEnglish
    Title of host publicationStochastic Model Checking. Rigorous Dependability Analysis Using Model Checking Techniques for Stochastic Systems
    Subtitle of host publicationAdvanced Lectures of the International Autumn School ROCKS 2012
    EditorsAnne Remke, Mariëlle Stoelinga
    Place of PublicationBerlin
    PublisherSpringer
    Pages242-280
    Number of pages39
    ISBN (Electronic)978-3-662-45489-3
    ISBN (Print)978-3-662-45488-6
    DOIs
    Publication statusPublished - Oct 2014
    EventInternational Autumn School, ROCKS 2012 - Vahrn, Italy
    Duration: 22 Oct 201226 Oct 2012

    Publication series

    NameLecture Notes in Computer Science
    PublisherSpringer Verlag
    Volume8453
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    OtherInternational Autumn School, ROCKS 2012
    Period22/10/1226/10/12
    Other22-26 October 2012

    Keywords

    • EWI-25578
    • Application
    • METIS-309820
    • Mean-field approximation
    • IR-94300
    • Model Checking

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