- Coverage of Random Discs Driven by a Poisson Point Process

Motivated by the study of large-scale wireless sensor networks, in this paper we discuss the coverage problem that a pre-assigned region is completely covered by the random discs driven by a homogeneous Poisson point process. We first derive upper and lower bounds for the coverage probability. We then obtain necessary and sufficient conditions, in terms of the relation between the radius r of the discs and the intensity lambda of the Poisson process, in order that the coverage probability converges to 1 or 0 when lambda tends to infinity. A variation of Stein-Chen method for compound Poisson approximation is well used in the proof.