Path coverage by a sensor field

Abstract

We analyze the statistical properties of the coverage of a one-dimensional path induced by a two-dimensional nonhomogeneous random sensor network. Sensor locations form a nonhomogeneous Poisson process and sensing area for the sensors are circles of random independent and identically distributed radii. We first characterize the coverage of a straight-line path by the nonhomogeneous one-dimensional Boolean model. We then obtain an equivalent M t /G t /∞, queue whose busy period statistics is the same as the coverage statistics of the line. We obtain k -coverage statistics for an arbitrary point and a segment on the x -axis. We provide upper and lower bounds on the probability of complete k -coverage of a segment. We illustrate all our results for the case of the sensor deployment having a “Laplacian” intensity function.