Optimal number of annuli for maximizing the lifetime of sensor networks

• Maximize the lifetime of a wireless sensor network by optimal network design.
• Represent the network lifetime as a function of the number of annuli.
• Find an expression of the optimal number of annuli for an arbitrary sensor density function.

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 mm of annuli and show that mm has significant impact on network lifetime. We prove that if the energy consumed by data transmission is proportional to dα+cdα+c, where dd is the distance of data transmission and αα and cc are some constants, then for a circular area of interest with radius RR, the optimal number of annuli that maximizes the network lifetime is m=R((α−1)/c)1/αm=R((α−1)/c)1/α for an arbitrary sensor density function.