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

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 rs. Moreover, considering the inherent irregularity of a sensor's sensing range caused by time-varying environments, we model the sensing radius rs as a random variable with mean r0 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 rc. 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.

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