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On k−coverage in a mostly sleeping sensor network

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Abstract

Sensor networks are often desired to last many times longer than the active lifetime of individual sensors. This is usually achieved by putting sensors to sleep for most of their lifetime. On the other hand, event monitoring applications require guaranteed k-coverage of the protected region at all times. As a result, determining the appropriate number of sensors to deploy that achieves both goals simultaneously becomes a challenging problem. In this paper, we consider three kinds of deployments for a sensor network on a unit square—a √n×√n grid, random uniform (for all n points), and Poisson (with density n). In all three deployments, each sensor is active with probability p, independently from the others. Then, we claim that the critical value of the function npπ r 2/log (np) is 1 for the event of k-coverage of every point. We also provide an upper bound on the window of this phase transition. Although the conditions for the three deployments are similar, we obtain sharper bounds for the random deployments than the grid deployment, which occurs due to the boundary condition. In this paper, we also provide corrections to previously published results. Finally, we use simulation to show the usefulness of our analysis in real deployment scenarios.

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Authors and Affiliations

  1. Department of Computer Science, University of Memphis, Memphis, TN, USA, 38152-3240

    Santosh Kumar

  2. Department of Computer Science and Engineering, Ohio State University Columbus, OH, USA, 43210

    Ten H. Lai

  3. Department of Mathematical Sciences, University of Illinois, Urbana, IL, USA, 61801

    József Balogh

Authors
  1. Santosh Kumar
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  2. Ten H. Lai
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  3. József Balogh
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Corresponding author

Correspondence to Santosh Kumar.

Additional information

An earlier version of this paper appeared in the Tenth Annual International Conference on Mobile Computing and Networking (ACM MobiCom), September 25–October 1, 2004, Philadelphia, PA. Major differences from the conference version are in Sections 5, 6, and 7.

Santosh Kumar is an Assistant Professor in the department of Computer Science at the University of Memphis. He received his Ph.D. in Computer Science and Engineering from the Ohio State University in 2006, where he was the SBC Presidential Fellow in 2006. He also received an M.S. in Computer and Information Science from the Ohio State University in 2002. He received a B.Tech. in Computer Science and Engineering from the Institute of Technology at Banaras Hindu University (IT-BHU) in 1998. His current research focuses on the issues of coverage and connectivity in wireless sensor networks.

Ten-Hwang Lai is a Professor of Computer Science and Engineering at the Ohio State University. A pioneer of Zen Networking, he is interested in the art of applying Zen to the teaching and research of protocol design. He served as the program chair of ICPP'98, the general chair of ICPP'00, the program co-chair of ICDCS'04, and, recently, the general chair of ICDCS'05. He is/was an editor of IEEE Transactions on Parallel and Distributed Systems (TPDS), ACM/Springer Wireless Networks, Academia Sinica's Journal of Information Science and Engineering (JISE), and International Journal of Ad Hoc and Ubiquitous Computing.

József Balogh is an Assistant Professor of Mathematics at the University of Illinois at Urbana-Champaign. He received an M.S. from Szeged University, Hungary in 1995 and a Ph.D. in Mathematics from the University of Memphis in 2001. Before joining the University of Illinois, he held post doctoral positions at AT&T (2001–2002), Princeton (2002), and the Ohio State University (2002–2005). His current research interests include Probabilistic Methods in Discrete Mathematics and Extremal Graph Theory.

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Kumar, S., Lai, T.H. & Balogh, J. On k−coverage in a mostly sleeping sensor network. Wireless Netw 14, 277–294 (2008). https://doi.org/10.1007/s11276-006-9958-8

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