Mostly-Sleeping Wireless Sensor Networks: Connectivity, k-Coverage, and -Lifetime

In this paper, we explore the fundamental limits of a wireless sensor network’s lifetime under the guarantee of both connectivity and k-coverage. We consider a wireless sensor network with n sensors deployed independently and uniformly in a square region of unit area. Each sensor is active with probability p, independently from the others, and can sense a disk of radius rs when active. Two active sensors can communicate with each other if and only if the distance between them is less than communication radius rc. However, due to the variation of the environment and sensors’ characteristics, we model the sensing radius rs as a random variable with mean r0 and variance r 0σ 2 s . We first derive the sufficient and necessary condition on the sensing radius in order to maintain the k-coverage with probability one as the number of sensors goes to infinity. Then, we introduce a new definition of network’s lifetime, namely α-lifetime, from a probabilistic perspective, which is the expectation of the entire interval during which the probability of guaranteeing connectivity and k-coverage simultaneously is at least α. Finally, we propose a near-optimal scheduling algorithm to maximize the network’s α-lifetime, which is verified by simulation results.