Optimal Number of Annuli for Maximizing the Lifetime of Sensor Networks

The most effective way to maximize the lifetime of a wireless sensor network (WSN) is to allocate initial energy to sensors such that they exhaust their energy at the same time. The lifetime of a WSN as well as an optimal initial energy allocation are determined by a network design. The main contribution of the paper is to show that the lifetime of a WSN can be maximized by an optimal network design. We represent the network lifetime as a function of the number m of annuli and show that m has significant impact on network lifetime. We prove that if the energy consumed by data transmission is proportional to d^α + c, where d is the distance of data transmission and α and c are some constants, then for a circular area of interest with radius R, the optimal number of annuli that maximizes the network lifetime is m = R((α - 1)/c)^1/α for a uniform sensor distribution.