Lifetime analysis for wireless sensor networks

The sensor nodes of wireless sensor networks (WSNs) have the dual function of gathering information and relaying it to a central collection point, the sink. In this paper, we derive connectivity, as expressed by the probability that a node lies on a path to the sink, as a function of the probability that adjacent cells in a grid are connected. The nodes are assumed to have two modes of operation, the active and sleep states and the energy is consumed only in the active state. For battery powered nodes, lifetime is an important factor. The effect of the demise of nodes on the nodal density and, in turn, on network connectivity is quantified. The novelty of the results is that they determine the degree of connectivity in networks with finite number of nodes, unlike to many results in the literature which are asymptotic and for full connectivity.