Markov Chain Analysis of Self-organizing Mobile Nodes

Self-organization of autonomous mobile nodes using bio-inspired algorithms in mobile ad hoc networks (manets) has been presented in earlier work of the authors. In this paper, the convergence speed of our force-based genetic algorithm (called fga) is provided through analysis using homogeneous Markov chains. The fga is run by each mobile node as a topology control mechanism to decide a corresponding node's next speed and movement direction so that it guides an autonomous mobile node over an unknown geographical area to obtain a uniform node distribution while only using local information. The stochastic behavior of fga, like all ga-based approaches, makes it difficult to analyze the effects that various manet characteristics have on its convergence speed. Metrically transitive homogeneous Markov chains have been used to analyze the convergence of our fga with respect to various communication ranges of mobile nodes and also the number of nodes in various scenarios. The Dobrushin contraction coefficient of ergodicity is used for measuring convergence speed for Markov chain model of our fga. Two different testbed platforms are presented to illustrate effectiveness of our bio-inspired algorithm in terms of area coverage.