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.
The authors would like to thank the referees for their encouragement and valuable suggestions. Zhi-Ming Ma would like to thank the organizers for inviting him to participate in the stimulating conference in honor of Louis Chen on his 70th birthday.
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