- Coverage of Random Discs Driven by a Poisson Point Process

被引：1

作者：

Lan, Guo-Lie ^{[1
]}

Ma, Zhi-Ming ^{[2
]}

Sun, Su-Yong ^{[2
]}

机构：

[1] Guangzhou Univ, Guangzhou 510006, Guangdong, Peoples R China

[2] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China

来源：

PROBABILITY APPROXIMATIONS AND BEYOND | 2012年 / 205卷

关键词：

APPROXIMATION; CONNECTIVITY;

D O I：

10.1007/978-1-4614-1966-2_4

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

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页码：43 / +

页数：3

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