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Model Checking Two Layers of Mean-Field Models

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Principles of Performance and Reliability Modeling and Evaluation

Part of the book series: Springer Series in Reliability Engineering ((RELIABILITY))

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Abstract

Recently, many systems that consist of a large number of interacting objects have been analysed using the mean-field method, which allows a quick and accurate analysis of such systems, while avoiding the state-space explosion problem. To date, the mean-field method has primarily been used for classical performance evaluation purposes. In this chapter, we discuss model-checking mean-field models. We define and motivate two logics, called Mean-Field Continuous Stochastic Logic (MF-CSL) and Mean-Field Logic (MFL), to describe properties of systems composed of many identical interacting objects. We present model-checking algorithms and discuss the differences in the expressiveness of these two logics and their combinations.

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Notes

  1. 1.

    Note that for ease of interpretation, we group the elements of the vector according to the three submodels.

  2. 2.

    A function is called cadlag if it is defined on the real numbers (or a subset of them), if it is everywhere right-continuous and if it has left limits everywhere.

  3. 3.

    Note, however, a global atomic property is not always connected to the properties of the local model (unlike the expectation operator in MF-CSL).

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Acknowledgments

The work in this chapter has been performed when Anna Kolesnichenko was still at the University of Twente. She has been supported through NWO grant 612.063.918, MATMAN (Mean-Field Approximation Techniques for Markov Models), as well as the FP7 Sensation project (see below). Anne Remke has been supported through an NWO VENI grant on Dependability Analysis of Fluid Critical Infrastructures using Stochastic Hybrid Models. Boudewijn Haverkort and Pieter-Tjerk de Boer have been supported through FP7 STREP 318490, Sensation (Self Energy-Supporting Autonomous Computation).

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Authors and Affiliations

  1. UL Transaction Security Division, De Heyderweg 2, 2314 XZ, Leiden, The Netherlands

    Anna Kolesnichenko

  2. Department of Computer Science, University of Münster, Einsteinstrasse 62, 48149, Münster, Germany

    Anne Remke

  3. Department of Computer Science, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    Pieter-Tjerk de Boer & Boudewijn R. Haverkort

Authors
  1. Anna Kolesnichenko
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  2. Anne Remke
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  3. Pieter-Tjerk de Boer
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  4. Boudewijn R. Haverkort
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Corresponding author

Correspondence to Anna Kolesnichenko .

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Editors and Affiliations

  1. University of Massachusetts Dartmou, Dartmouth, Massachusetts, USA

    Lance Fiondella

  2. Università degli studi di Messina, Messina, Italy

    Antonio Puliafito

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Kolesnichenko, A., Remke, A., de Boer, PT., Haverkort, B.R. (2016). Model Checking Two Layers of Mean-Field Models. In: Fiondella, L., Puliafito, A. (eds) Principles of Performance and Reliability Modeling and Evaluation. Springer Series in Reliability Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-30599-8_13

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  • DOI: https://doi.org/10.1007/978-3-319-30599-8_13

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