Numerical Algebra, Control and Optimization (NACO)

Markovian characterization of node lifetime in a time-driven wireless sensor network

Pages: 763 - 780, Volume 1, Issue 4, December 2011      doi:10.3934/naco.2011.1.763

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Sebastià Galmés - Department of Mathematics and Computer Science, University of Balearic Islands, 07122, Palma, Spain (email)

Abstract: While feeling honoured for being invited to write a paper dedicated to Prof. Yutaka Takahashi, I was enthusiastically wondering how to connect my current research on sensor networks to his excellent professional profile. The question or, better, the answer, was not simple. Considering, for instance, the field of Markov chains, as far as I know there are hardly works in literature that use this well-known modelling paradigm to represent the operational states of a sensor network. However, in a very recent work on time-driven sensor networks, I proposed the exponential randomization of the sense-and-transmit process, in order to avoid tight synchronization requirements while preserving good expectations in terms of lifetime and reconstruction quality. But$\ldots{}$oh, I said exponential, that's the connection! $\ldots{}$ So, specifically, in this paper a Markov chain is constructed to characterize the activity of a node in a time-driven sensor network based on stochastic (exponential) sampling. Since this activity can be translated to energy consumption, the exact solution to the Markov chain yields the complete statistical distribution of node lifetime. The effects of several parameters on the average and variance of this lifetime are also analyzed in detail.

Keywords:  Wireless sensor network, multi-dimensional sampling theorem, continuous-time Markov chain, embedded discrete-time Markov chain, squared coefficient of variation.
Mathematics Subject Classification:  Primary: 90B18; Secondary: 60J10.

Received: June 2011;      Revised: August 2011;      Available Online: November 2011.