Ascending runs in dependent uniformly distributed random variables: Application to wireless networks

Details Ascending runs in dependent uniformly distributed random variables: Application to wireless networks Ascending runs in dependent uniformly distributed random variables: Application to wireless networks

2008-02-11

arxiv.org/abs/0802.1387v2

Computer Science

Discrete Mathematics

Scientific paper

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.

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