  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.
