Quantifying connectivity in wireless sensor networks with grid-based deployments

Measuring network connectivity under grid-based deployment in 3D space is a challenging problem in wireless sensor networks (WSNs). Solving such a problem becomes an even more intricate task with realistic deployment factors such as placement uncertainty and hindrances to wireless communication channels. While much work has been published on optimizing connectivity, only a few papers have addressed such realistic aspects which cause severe connectivity problems in practice. In this paper, we introduce a novel grid-based deployment metric, called Average Connectivity Percentage in order to characterize the deployed network connectivity when sensor placements are subject to random errors around their corresponding grid locations. A generic approach is proposed to assess and evaluate the proposed metric. This generic approach is independent of the grid-shape, random error distributions, and different environment-based channel characteristics. We apply the generic approach in two practical deployment scenarios: the grid-based deployment with bounded uniform errors and with unbounded normal errors. In both cases, the average connectivity percentage is computed numerically and verified via extensive simulations. Based on the numerical results, quantified effects of positioning errors and grid edge length on the average connectivity percentage are outlined.