On the path coverage by a non homogeneous sensor field
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We analyze the statistical properties of the coverage of a one-dimensional path induced by a two dimensional non homogeneous random sensor network. Sensor locations form a non homogeneous Poisson process and coverage area of each sensor is a circle of random i.i.d. radius. We first describe the one-dimensional coverage process on the line and describe an equivalent time-inhomogeneous Mt/Gt/8 queue whose busy period statistics will be equal to the coverage statistics of the line. We also obtain properties like conditional forward and backward hole-lengths. Additional results for the case of fixed coverage radius are obtained. We also obtain some numerical results for a deployment that has a 'Laplacian' intensity function.
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