Analysis of Finite Unreliable Sensor Grids

Asymptotic analysis of unreliable sensor grides has been studied previously. Some analytic results for sensor grids have been reported for the case where the number of nodes n in the network tends to infinity (large-scale grids). This includes connectivity, coverage, and diameter of the networks. These results have not been extended for small or moderate values of n, although in many practical sensor grids, n might not be very large. In this paper, we first show that previous asymptotic results may provide poor approximations for the finite grids (small-scale grids). We then aim to develop a methodology to analytically study unreliable sensor grids properties without assuming that n is large. We prove some properties of finite sensor grids. We show that a large class of network parameters can be expressed as piecewise constant functions of communication and sensing radii. We obtain simple analytic expressions for connectivity and coverage probabilities of finite sensor grids. Using simulations, we show that the expressions give good estimates of these probabilities.