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A study on one-dimensional k-coverage problem in wireless sensor networks

Authors

  • Lei Li,

    1. Key Laboratory of Wireless Sensor Networks and Communications, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050, China
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  • Baoxian Zhang,

    1. Research Center of Ubiquitous Sensor Networks, Graduate University of Chinese Academy of Sciences, Beijing 100049, China
    2. Research Center of Internet of Things, Institute of Microelectronics of Chinese Academy of Sciences, Beijing 100029, China
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  • Jun Zheng

    Corresponding author
    1. National Mobile Communications Research Laboratory, School of Information Science and Engineering, Southeast University, Nanjing, Jiangsu 210096, China
    • National Mobile Communications Research Laboratory, School of Information Science and Engineering, Southeast University, Nanjing, Jiangsu 210096, China.
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  • This work was partially supported by the National Natural Science Foundation of China under Grant Nos. 60970137, 61070166, and 61071115, the National Key Special Program of China under Grant Nos. 2009ZX03006-001-02 and 2009ZX03006-006, and the Research Fund of National Mobile Communications Research Laboratory, Southeast University, China, under Grant No. 2009B07. B. Zhang's work was also partially supported by SRF for ROCS, SEM. L. Li's work was supported in part by the National Basic Research Program of China (973 Program) under Grant No. 2011CB302901.

ABSTRACT

In this paper, we study the one-dimensional coverage problem in a wireless sensor network (WSN) and consider a network deployed along a one-dimensional line according to a Poisson distribution. We analyze three important parameters that are related to the problem, i.e., expected k-coverage proportion, full k-coverage probability, and partial k-coverage probability, and derive mathematical models that describe the relationships between the node density in the network and these parameters. The purpose is to calculate or estimate the node density required for achieving a given coverage probability, which is useful in the deployment of a one-dimensional network for many applications. We first analyze the expected k-coverage proportion, then analyze the full k-coverage probability for k = 1 and the lower bound to the full k-coverage probability for k > 1, and finally analyze the partial k-coverage probability for k = 1 and give a brief discussion of the partial k-coverage probability for k > 1. The mathematical models are validated through simulation. Copyright © 2011 John Wiley & Sons, Ltd.

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