Applying Mean-Field Approximation to Continuous Time Markov Chains

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

doi:10.1007/978-3-662-45489-3_7

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 proceeding › Chapter › Academic › peer-review

4 Citations (Scopus)

603 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 language	English
Title of host publication	Stochastic Model Checking. Rigorous Dependability Analysis Using Model Checking Techniques for Stochastic Systems
Subtitle of host publication	Advanced Lectures of the International Autumn School ROCKS 2012
Editors	Anne Remke, Mariëlle Stoelinga
Place of Publication	Berlin
Publisher	Springer
Pages	242-280
Number of pages	39
ISBN (Electronic)	978-3-662-45489-3
ISBN (Print)	978-3-662-45488-6
DOIs	https://doi.org/10.1007/978-3-662-45489-3_7
Publication status	Published - Oct 2014
Event	International Autumn School, ROCKS 2012 - Vahrn, Italy Duration: 22 Oct 2012 → 26 Oct 2012

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer Verlag
Volume	8453
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	International Autumn School, ROCKS 2012
Country/Territory	Italy
City	Vahrn
Period	22/10/12 → 26/10/12

Keywords

Application
Mean-field approximation
Model checking

Access to Document

10.1007/978-3-662-45489-3_7

Kolesnichenko15applyingAccepted author version, 880 KB

Cite this

Kolesnichenko, A. V., Senni, V., Pourranjabar, A., & Remke, A. (2014). Applying Mean-Field Approximation to Continuous Time Markov Chains. In A. Remke, & M. Stoelinga (Eds.), Stochastic Model Checking. Rigorous Dependability Analysis Using Model Checking Techniques for Stochastic Systems: Advanced Lectures of the International Autumn School ROCKS 2012 (pp. 242-280). (Lecture Notes in Computer Science; Vol. 8453). Springer. https://doi.org/10.1007/978-3-662-45489-3_7

Kolesnichenko, A.V. ; Senni, Valerio ; Pourranjabar, Alireza et al. / Applying Mean-Field Approximation to Continuous Time Markov Chains. Stochastic Model Checking. Rigorous Dependability Analysis Using Model Checking Techniques for Stochastic Systems: Advanced Lectures of the International Autumn School ROCKS 2012. editor / Anne Remke ; Mariëlle Stoelinga. Berlin : Springer, 2014. pp. 242-280 (Lecture Notes in Computer Science).

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Kolesnichenko, AV, Senni, V, Pourranjabar, A & Remke, A 2014, Applying Mean-Field Approximation to Continuous Time Markov Chains. in A Remke & M Stoelinga (eds), Stochastic Model Checking. Rigorous Dependability Analysis Using Model Checking Techniques for Stochastic Systems: Advanced Lectures of the International Autumn School ROCKS 2012. Lecture Notes in Computer Science, vol. 8453, Springer, Berlin, pp. 242-280, International Autumn School, ROCKS 2012, Vahrn, Italy, 22/10/12. https://doi.org/10.1007/978-3-662-45489-3_7

Applying Mean-Field Approximation to Continuous Time Markov Chains. / Kolesnichenko, A.V.; Senni, Valerio; Pourranjabar, Alireza et al.

Stochastic Model Checking. Rigorous Dependability Analysis Using Model Checking Techniques for Stochastic Systems: Advanced Lectures of the International Autumn School ROCKS 2012. ed. / Anne Remke; Mariëlle Stoelinga. Berlin : Springer, 2014. p. 242-280 (Lecture Notes in Computer Science; Vol. 8453).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

TY - CHAP

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AU - Kolesnichenko, A.V.

AU - Senni, Valerio

AU - Pourranjabar, Alireza

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AB - 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.

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BT - Stochastic Model Checking. Rigorous Dependability Analysis Using Model Checking Techniques for Stochastic Systems

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CY - Berlin

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Y2 - 22 October 2012 through 26 October 2012

ER -

Kolesnichenko AV, Senni V, Pourranjabar A, Remke A. Applying Mean-Field Approximation to Continuous Time Markov Chains. In Remke A, Stoelinga M, editors, Stochastic Model Checking. Rigorous Dependability Analysis Using Model Checking Techniques for Stochastic Systems: Advanced Lectures of the International Autumn School ROCKS 2012. Berlin: Springer. 2014. p. 242-280. (Lecture Notes in Computer Science). doi: 10.1007/978-3-662-45489-3_7

Applying Mean-Field Approximation to Continuous Time Markov Chains

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