On deriving the upper bound of α-lifetime for large sensor networks

In this paper, we explore the fundamental limits of sensor network lifetime that all algorithms can possibly achieve. Specifically, under the assumptions that nodes are deployed as a Poisson point process with density λ in a square region with side length l and each sensor can cover a unit-area disk, we first derive the necessary and sufficient condition of the node density in order to maintain complete k-coverage with probability approaching 1. With this result, we obtain that if #955; = log l2 + (k+2)log log l2 + c(l), c(l) → -∞, as l → +∞, the sensor network lifetime (for maintaining complete coverage) is upper bounded by kT with probability approaching 1 as l → +∞, where T is the lifetime of each sensor. Second, we derive, given a fixed node density in a finite (but reasonably large) region, the upper bounds of lifetime when only α-portion of the region is required to be covered at any time. We also carry out simulations to validate the derived results. Simulation results indicate that the derived upper bounds apply not only to networks of large areas but also to small-area networks.