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Title:  On the path coverage properties of random sensor networks 
Authors:  RAM, SS MANJUNATH, D IYER, SK YOGESHWARAN, D 
Issue Date:  2007 
Publisher:  IEEE COMPUTER SOC 
Citation:  IEEE TRANSACTIONS ON MOBILE COMPUTING, 6(5), 446458 
Abstract:  In a sensor network, the points in the operational area that are suitably sensed are a twodimensional spatial coverage process. For randomly deployed sensor networks, typically, the network coverage of twodimensional areas is analyzed. However, in many sensor network applications, e. g., tracking of moving objects, the sensing process on paths, rather than in areas, is of interest. With such an application in mind, we analyze the coverage process induced on a onedimensional path by a sensor network that is modeled as a twodimensional Boolean model. In the analysis, the sensor locations form a spatial Poisson process of density lambda and the sensing regions are circles of i.i.d. random radii. We first obtain a strong law for the fraction of a path that is ksensed, i.e., sensed by (>= k) sensors. Asymptotic pathsensing results are obtained under the same limiting regimes as those required for asymptotic coverage by a twodimensional Boolean model. Interestingly, the asymptotic fraction of the area that is 1sensed is the same as the fraction of a path that is 1sensed. For k = 1, we also obtain a central limit theorem that shows that the asymptotics converge at the rate of Phi(lambda(1/2)) for k = 1. For finite networks, the expectation and variance of the fraction of the path that is ksensed is obtained. The asymptotics and the finite network results are then used to obtain the critical sensor density to ksense a fraction alpha(k) of an arbitrary path with very high probability is also obtained. Through simulations, we then analyze the robustness of the model when the sensor deployment is nonhomogeneous and when the paths are not rectilinear. Other path coverage measures like breach, support, "length to first sense," and sensing continuity measures like holes and clumps are also characterized. Finally, we discuss some generalizations of the results like characterization of the coverage process of mdimensional " straight line paths" by ndimensional, n > m, sensor networks. 
URI:  http://dx.doi.org/10.1109/TMC.2007.1000 http://dspace.library.iitb.ac.in/xmlui/handle/10054/8148 http://hdl.handle.net/10054/8148 
ISSN:  15361233 
Appears in Collections:  Article

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