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Ascending Runs in Dependent Uniformly Distributed Random Variables: Application to Wireless Networks

Author

Listed:
  • Nathalie Mitton

    (Université de Lille 1)

  • Katy Paroux

    (Université de Franche-Comté
    INRIA Rennes—Bretagne Atlantique)

  • Bruno Sericola

    (INRIA Rennes—Bretagne Atlantique)

  • Sébastien Tixeuil

    (Université Paris VI)

Abstract

We analyze in this paper the longest increasing contiguous sequence or maximal ascending run of random variables with common uniform distribution but not independent. Their dependence is characterized by the fact that two successive random variables cannot take the same value. Using a Markov chain approach, we study the distribution of the maximal ascending run and we develop an algorithm to compute it. This problem comes from the analysis of several self-organizing protocols designed for large-scale wireless sensor networks, and we show how our results apply to this domain.

Suggested Citation

  • Nathalie Mitton & Katy Paroux & Bruno Sericola & Sébastien Tixeuil, 2010. "Ascending Runs in Dependent Uniformly Distributed Random Variables: Application to Wireless Networks," Methodology and Computing in Applied Probability, Springer, vol. 12(1), pages 51-62, March.
    • Handle: RePEc:spr:metcap:v:12:y:2010:i:1:d:10.1007_s11009-008-9088-0
    DOI: 10.1007/s11009-008-9088-0
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    References listed on IDEAS

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    1. Frolov, Andrei N. & Martikainen, Alexander I., 1999. "On the length of the longest increasing run in d," Statistics & Probability Letters, Elsevier, vol. 41(2), pages 153-161, January.
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    Cited by:

    1. Alexandru Amarioarei & Cristian Preda, 2020. "One Dimensional Discrete Scan Statistics for Dependent Models and Some Related Problems," Mathematics, MDPI, vol. 8(4), pages 1-11, April.

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