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Ergodicity aspects of multidimensional Markov chains with application to computer communication system analysis

  • Stationarity And Ergodicity 2
  • Conference paper
  • First Online:
Modelling and Performance Evaluation Methodology

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 60))

Abstract

Ergodicity and nonergodicity of multidimensional Markov chains are discussed. We investigate ergodic and nonergodic Markov chains by the means of Lyapunov function method and so called comparison tests method. In the former case two theorems being a generalization of Pakes and Kaplan theorems are presented. Moreover, for multidimensional Markov chains we propose an explicite form for a simple Lyapunov function. On the other hand, comparison tests investigate ergodicity/nonergodicity of M-dimensional Markov chains by the means of appropriate ergodic/nonergodic K-dimensional Markov chains, where K is smaller than M. These results are applied to analysis of some computer communication systems.

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Authors and Affiliations

  1. Technical University of Gdansk, ul. Majakowskiego 11/12, 80-952, Gdansk, Poland

    Wojciech Szpankowski

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  1. Wojciech Szpankowski
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F. Baccelli G. Fayolle

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© 1984 Springer-Verlag

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Szpankowski, W. (1984). Ergodicity aspects of multidimensional Markov chains with application to computer communication system analysis. In: Baccelli, F., Fayolle, G. (eds) Modelling and Performance Evaluation Methodology. Lecture Notes in Control and Information Sciences, vol 60. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0005179

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  • DOI: https://doi.org/10.1007/BFb0005179

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13288-2

  • Online ISBN: 978-3-540-38838-8

  • eBook Packages: Springer Book Archive

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