On the Path Tracking Properties of Random Sensor Networks
S. Sundhar Ram, Deepika Revankar Manjunath, K. N. Iyer, Dhandapani Yogeshwaran, Mumbai India · 2005
We analyze the ability of a two dimensional sensor network to track targets moving on a one dimensional path. The sensor locations are assumed to form a spatial Poisson process of density and the sensing regions are random circles of i.i.d. radii. We first show that the sensing process induced on a straight line path by the area coverage process is a one dimensional Boolean process which in turn is the same as an M/G/ queue. This is then used to obtain two asymptotic results—a strong law and a central limit theorem for the fraction of a path that is covered by or more sensors. The asymptotic results are obtained under the same limiting regimes as that required for asymptotic coverage by a two dimensional Boolean process. Interestingly, for the asymptotic fraction of the area covered by the sensors is the same as the fraction of a path sensed. It is not clear if this generalizes for . The strong law derived above helps us obtain the sensor density that is necessary to sense a given fraction of an arbitrary path with very high probability is derived. Expectation and variance of the fraction of a path covered for finite are also obtained. We then characterize the ‘length to first sense’, and sensing continuity measures like holes and clumps. Measures that do not depend on the sensing radius like breach and support are also characterized. Finally, we discuss some generalizations of the results like characterization of the coverage process of dimensional ‘straight line paths’ by a dimensional sensor networks.