Reliable density estimates for coverage and connectivity in thin strips of finite length

Abstract

Deriving the critical density (which is equivalent to deriving the critical radius or power) to achieve coverage and/or connectivity for random deployments is a fundamental problem in the area of wireless networks. The probabilistic conditions normally derived, however, have limited appeal among practitioners because they are often asymptotic, i.e., they only make high probability guarantees in the limit of large system sizes. Such conditions are not very useful in practice since deployment regions are always finite. Another major limitation of most existing work on coverage and connectivity is their focus on thick deployment regions (such as a square or a disk). There is no existing work (including traditional percolation theory) that derives critical densities for thin strips (or annuli).In this paper, we address both of these shortcomings by introducing new techniques for deriving reliable density estimates for finite regions (including thin strips). We apply our techniques to solve the open problem of deriving reliable density estimates for achieving barrier coverage and connectivity in thin strips, where sensors are deployed as a barrier to detect moving objects and phenomena. We use simulations to show that our estimates are accurate even for small deployment regions. Our techniques bridge the gap between theory and practice in the area of coverage and connectivity, since the results can now be readily used in real-life deployments.

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].…”

On Minimizing the Sum of Sensor Movements for Barrier Coverage of a Line Segment

“…In [4] the problem of local barrier coverage is introduced and it is shown that it is possible for individual sensors to locally determine the existence of local barrier coverage, even when the region of deployment is arbitrarily curved. Techniques for deriving density estimates for achieving barrier coverage and connectivity in thin strips are introduced in [1], where sensors are deployed as a barrier to detect moving objects and events. In all these instances the problem studied concerns static optimal sensor deployment patterns and there is no concept of mobility of the sensors.…”

On Minimizing the Maximum Sensor Movement for Barrier Coverage of a Line Segment

“…It shows that it is possible for individual sensors to locally determine the existence of local barrier coverage, even when the region of deployment is arbitrarily curved. Techniques for deriving density estimates for achieving barrier coverage and connectivity in thin strips are studied in [1], where sensors are deployed as a barrier to detect moving objects. In all these instances the problem studied concerns static optimal sensor deployment patterns and there is no concept of movement of the sensors.…”