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

Nathalie Mitton (), Katy Paroux (), Bruno Sericola () and Sébastien Tixeuil ()
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Nathalie Mitton: Université de Lille 1
Katy Paroux: Université de Franche-Comté
Bruno Sericola: INRIA Rennes—Bretagne Atlantique
Sébastien Tixeuil: Université Paris VI

Methodology and Computing in Applied Probability, 2010, vol. 12, issue 1, 51-62

Abstract: 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.

Keywords: Markov chains; Maximal ascending run; Self-stabilization; Convergence time; G.3; G.2; C.2; 60J10; 60J20; 68R05 (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-008-9088-0

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