Trap Coverage: Allowing Coverage Holes of Bounded Diameter in Wireless Sensor Networks

Abstract

Abstract-Tracking of movements such as that of people, animals, vehicles, or of phenomena such as fire, can be achieved by deploying a wireless sensor network. So far only prototype systems have been deployed and hence the issue of scale has not become critical. Real-life deployments, however, will be at large scale and achieving this scale will become prohibitively expensive if we require every point in the region to be covered (i.e., full coverage), as has been the case in prototype deployments.In this paper we therefore propose a new model of coverage, called Trap Coverage, that scales well with large deployment regions. A sensor network providing Trap Coverage guarantees that any moving object or phenomena can move at most a (known) displacement before it is guaranteed to be detected by the network, for any trajectory and speed. Applications aside, trap coverage generalizes the de-facto model of full coverage by allowing holes of a given maximum diameter (d). From a probabilistic analysis perspective, the trap coverage model explains the continuum between percolation (when coverage holes become finite) and full coverage (when coverage holes cease to exist).We take first steps toward establishing a strong foundation for this new model of coverage. We derive reliable, explicit estimates for the density needed to achieve trap coverage with a given diameter when sensors are deployed randomly. We show by simulation that our analytical predictions of density are quite accurate even for small networks. Next, we investigate optimal deterministic patterns for deployment. We show that for d ≤ 0.5552r, where r is the sensing range, the optimal deployment pattern is a triangular grid and for large d/r, the subdivided hexagonal grid is within 10% of optimal. Proving the exact optimal pattern appears to be an extremely difficult problem, related to several open problems in optimal plane packing. Finally, we propose polynomial-time algorithms to determine the level of trap coverage achieved once sensors are deployed on the ground.

Maximizing the Lifetime of a Barrier of Wireless Sensors

“…The appropriate density that is needed to guarantee a desired probability of coverage is known [7], [25], [26]. As can be seen in Figure 9 of [7] where density estimates for barrier coverage are presented, these estimates are reliable; they closely match the behavior observed in experiments.…”

On full-view coverage in camera sensor networks

“…In trap coverage, coverage holes are allowed to exist as long as the diameters of the holes are bounded. Sensor density estimation for these coverage requirements are derived [14], [4], [16], [5]. The optimal deterministic deployment pattern for 1-coverage is based on triangle lattices, which has been proved in [13].…”

“…Generally, if sensors are deployed in a bounded region, the area very close to the boundary is likely to have fewer sensors than the interior area, and hence less likely to be covered as required. A common method to avoid this boundary effect is to deploy the sensors in a slightly larger region A ′ , e.g., enlarging the side length of A from d to d +r [5]. The difference is negligible if A is sufficiently large.…”

“…As people realized that requiring the whole target field to be kcovered (full coverage) is not always necessary, various models on partial coverage are proposed. Barrier coverage [14] and trap coverage [5] are two such variants. In barrier coverage, the sensing disks of the active sensors form a strip zone which serves as a barrier, and any object crossing the target field is supposed to be detected by the sensors on the barrier.…”

Mobile Geometric Graphs: Detection, Coverage and Percolation

“…only when the expected degree grows with n, while coverage requires the stronger condition that the network be connected. In the absence of coverage, Balister et al [3] determine the maximum diameter of the uncovered regions, while Dousse et al [12] prove that, for any λ > 0, the detection time for a target moving in a fixed direction has an exponential tail. (Note that this is not a mobility result as the nodes are fixed.…”