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 Title: On Deriving the Upper Bound of α-Lifetime for Large Sensor Networks Author(s): Zhang, Honghai Contributor(s): Hou, Jennifer C. Subject(s): sensor networks networking Abstract: In this paper, we explore the fundamental limits of sensor network lifetime that all algorithms can possibly achieve. Specifically, under the assumptions that nodes are deployed as a Poisson point process with density $\lambda$ in a square region with side length $\ell$ and each sensor can cover a unit-area disk, we first derive the necessary and sufficient condition of the node density in order to maintain complete $k$-coverage with probability approaching 1. With this result, we obtain that if $\lambda = \log \ell^2 + (k+2)\log\log \ell^2 + c(\ell), c(\ell) \to -\infty$, as $\ell\to +\infty$, the sensor network lifetime (for maintaining complete coverage) is upper bounded by $kT$ with probability approaching 1 as $\ell \to +\infty$, where $T$ is the lifetime of each sensor. Second, we derive, given a fixed node density in a finite (but reasonably large) region, the upper bounds of lifetime when only $\alpha$-portion of the region is required to be covered at any time. We also carry out simulations to validate the derived results. Simulation results indicate that the derived upper bounds apply not only to networks of large sizes and homogeneous nodal distributions but also to small-size networks with clustering nodal distributions. Issue Date: 2004-02 Genre: Technical Report Type: Text URI: http://hdl.handle.net/2142/10782 Rights Information: You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) days from the most recent time that you verified that this technical report is still available from the University of Illinois at Urbana-Champaign Computer Science Department under terms that include this permission. All other rights are reserved by the author(s). Date Available in IDEALS: 2009-04-14
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