Bounding a statistical measure of network lifetime for wireless sensor networks

The inherent many-to-one flow of traffic in Wireless Sensor Networks produces a skewed distribution of energy consumption rates leading to the early demise of those sensors that are critical to the ability of surviving nodes to communicate their readings to the data collection center. Numerous previous approaches aimed at balancing the consumption of energy in wireless networks are based on a linear programming-based minmax formulation that seeks to maximize the minimum lifetime of sensors in a network. However, this approach fails to provide a clear picture of the cost at which this optimization is achieved and focuses attention on a single sensor, the minimum lifetime sensor. This paper makes two contributions; 1) it puts forward a new understanding of sensor network lifetime based on statistical measures, mean and variance, of node power consumption rates that provides a more inclusive view of the consumption rates, and 2) it provides an optimal quadratic programming (QP) formulation that provides an upper bound on the lifetime under a given set of topological and energy budgetary constraints. Our results demonstrate that the QP formulation has the ability to provide a soft trade-off between the mean and variance of power consumption rates.