# American Institute of Mathematical Sciences

2011, 1(4): 763-780. doi: 10.3934/naco.2011.1.763

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

 1 Department of Mathematics and Computer Science, University of Balearic Islands, 07122, Palma, Spain

Received  June 2011 Revised  August 2011 Published  November 2011

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.
Citation: Sebastià Galmés. Markovian characterization of node lifetime in a time-driven wireless sensor network. Numerical Algebra, Control & Optimization, 2011, 1 (4) : 763-780. doi: 10.3934/naco.2011.1.763
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