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

TL;DR

This paper studies the distribution of the longest increasing contiguous sequence in dependent uniform random variables, with applications to analyzing protocols in large-scale wireless sensor networks.

Contribution

It introduces a Markov chain approach to analyze dependent uniform variables and develops an algorithm to compute the distribution of maximal ascending runs.

Findings

Derived the distribution of maximal ascending runs in dependent uniform variables

Developed an efficient algorithm for computing the distribution

Applied results to analyze wireless sensor network protocols

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.