Lifetime Analysis for Wireless Sensor Networks

The nodes of wireless sensor networks (WSNs) have the dual function of gathering information and relaying it to a central collection point, the sink. For the latter function the key is connectivity involving paths over which data is passed from node to node to the sink. 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. This result is then applied to the typical scenario where nodes are randomly scattered throughout the area being monitored. Useful upper and lower bounds for the probability of adjacent cells being connected are derived as a function of the node density in a cell. 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.