Lifetime Maximization of Sensor Networks Under Connectivity and k-Coverage Constraints

Abstract

In this paper, we study the fundamental limits of a wireless sensor network’s lifetime under connectivity and k-coverage constraints. We consider a wireless sensor network with n sensors deployed independently and uniformly in a square field of unit area. Each sensor is active with probability p, independently from others, and each active sensor can sense a disc area with radius r _s . Moreover, considering the inherent irregularity of a sensor’s sensing range caused by time-varying environments, we model the sensing radius r _s as a random variable with mean r ₀ and variance r $_{\rm 0}^{\rm 2}$ σ $_{s}^{\rm 2}$. Two active sensors can communicate with each other if and only if the distance between them is smaller than or equal to the communication radius r _c .

The key contributions of this paper are: (1) we introduce a new definition of a wireless sensor network’s lifetime from a novel probabilistic perspective, called ω-lifetime (0 ≤ ω ≤ 1). It is defined as the expectation of the time interval during which the probability of guaranteeing connectivity and k-coverage simultaneously is at least ω; and (2) based on the analysis results, we propose a near-optimal scheduling algorithm, called PIS (Pre-planned Independent Sleeping), to achieve the network’s maximum ω-lifetime, which is validated by simulation results, and present a possible implementation of the PIS scheme in the distributed manner.

The research reported in this paper was supported in part by the Information Infrastructure Institute (I-Cube) of Iowa State University. The authors would also like to acknowledge the support from the National Science Foundation under Grants No. ECS 0428040, CCF 0431092, and CNS 0520102. Preliminary results of this research were presented at the 43-rd Annual Allerton Conference on Communication, Control, and Computing, Monticello, IL, Sept. 2005.