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The Mean Drift: Tailoring the Mean Field Theory of Markov Processes for Real-World Applications

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Analytical and Stochastic Modelling Techniques and Applications (ASMTA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10378))

Abstract

The statement of the mean field approximation theorem in the mean field theory of Markov processes particularly targets the behaviour of population processes with an unbounded number of agents. However, in most real-world engineering applications one faces the problem of analysing middle-sized systems in which the number of agents is bounded. In this paper we build on previous work in this area and introduce the mean drift. We present the concept of population processes and the conditions under which the approximation theorems apply, and then show how the mean drift can be linked to observations which follow from the propagation of chaos. We then use the mean drift to construct a new set of ordinary differential equations which address the analysis of population processes with an arbitrary size.

The authors would like to thank Erik de Vink, Mieke Massink, Tjalling Tjalkens and Ulyana Tikhonova for their constructive comments and helpful remarks.

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Acknowledgments

The research from DEWI project (www.dewi-project.eu) leading to these results has received funding from the ARTEMIS Joint Undertaking under grant agreement No. 621353.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands

    Mahmoud Talebi & Jan Friso Groote

  2. Department of Electrical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands

    Jean-Paul M. G. Linnartz

Authors
  1. Mahmoud Talebi
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  2. Jan Friso Groote
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  3. Jean-Paul M. G. Linnartz
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Correspondence to Mahmoud Talebi .

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Editors and Affiliations

  1. School of Computing Science, Newcastle University, Newcastle upon Tyne, UK

    Nigel Thomas

  2. School of Computing Science, Newcastle University, Newcastle upon Tyne, UK

    Matthew Forshaw

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Talebi, M., Groote, J.F., Linnartz, JP.M.G. (2017). The Mean Drift: Tailoring the Mean Field Theory of Markov Processes for Real-World Applications. In: Thomas, N., Forshaw, M. (eds) Analytical and Stochastic Modelling Techniques and Applications. ASMTA 2017. Lecture Notes in Computer Science(), vol 10378. Springer, Cham. https://doi.org/10.1007/978-3-319-61428-1_14

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  • DOI: https://doi.org/10.1007/978-3-319-61428-1_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-61427-4

  • Online ISBN: 978-3-319-61428-1

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