On the minimum node degree and connectivity of a wireless multihop network
Proceedings of the 3rd ACM international symposium on Mobile ad hoc networking & computing
Fault tolerant deployment and topology control in wireless networks
Proceedings of the 4th ACM international symposium on Mobile ad hoc networking & computing
The coverage problem in a wireless sensor network
WSNA '03 Proceedings of the 2nd ACM international conference on Wireless sensor networks and applications
Understanding packet delivery performance in dense wireless sensor networks
Proceedings of the 1st international conference on Embedded networked sensor systems
Integrated coverage and connectivity configuration in wireless sensor networks
Proceedings of the 1st international conference on Embedded networked sensor systems
On deriving the upper bound of α-lifetime for large sensor networks
Proceedings of the 5th ACM international symposium on Mobile ad hoc networking and computing
Energy-efficient surveillance system using wireless sensor networks
Proceedings of the 2nd international conference on Mobile systems, applications, and services
Introduction to Probability Models, Ninth Edition
Introduction to Probability Models, Ninth Edition
Sentry-based power management in wireless sensor networks
IPSN'03 Proceedings of the 2nd international conference on Information processing in sensor networks
Topography-aware sensor deployment optimization with CMA-ES
PPSN'10 Proceedings of the 11th international conference on Parallel problem solving from nature: Part II
Coverage problems in sensor networks: A survey
ACM Computing Surveys (CSUR)
Providing and finding k-road-coverage efficiently in wireless sensor networks
Wireless Communications & Mobile Computing
Design of wireless sensor networks for mobile target detection
IEEE/ACM Transactions on Networking (TON)
Results on finite wireless sensor networks: Connectivity and coverage
ACM Transactions on Sensor Networks (TOSN)
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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 r2/ 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.