Expected k-coverage in wireless sensor networks Li-Hsing Yen * , Chang Wu Yu, Yang-Min Cheng Department of Computer Science and Information Engineering, Chung Hua University, No. 707, Sec. 2, WuFu Road, Hsinchu, Taiwan 300, China Received 2 December 2004; received in revised form 7 May 2005; accepted 22 July 2005 Available online 24 August 2005 Abstract We are concerned with wireless sensor networks where n sensors are independently and uniformly distributed at ran- dom in a finite plane. Events that are within a fixed distance from some sensor are assumed to be detectable and the sensor is said to cover that point. In this paper, we have formulated an exact mathematical expression for the expected area that can be covered by at least k out of n sensors. Our results are important in predicting the degree of coverage a sensor network may provide and in determining related parameters (sensory range, number of sensors, etc.) for a desired level of coverage. We demonstrate the utility of our results by presenting a node scheduling scheme that conserves energy while retaining network coverage. Additional simulation results have confirmed the accuracy of our analysis. Ó 2005 Elsevier B.V. All rights reserved. Keywords: Sensor network; Coverage; Border effect; Node scheduling; Uniform distribution 1. Introduction Rapid progress in wireless communications and micro-sensing MEMS technology has enabled the deployment of wireless sensor networks. A wireless sensor network consists of a large number of sen- sor nodes deployed in a region of interest. Each sensor node is capable of collecting, storing, and processing environmental information, and com- municating with other sensors. The position of sensor nodes need not be engineered or predeter- mined [1] for the reason of the enormous number of sensors involved [2] or the need to deploy sen- sors in inaccessible terrains [1]. Due to technical limitations, each sensor node can detect only events that are within some range from it. A piece of area in the deployment region is said to be cov- ered if every point in this area is within the sensory range of some sensor. In this paper, we are concerned with a fundamental property of such 1570-8705/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.adhoc.2005.07.001 * Corresponding author. Tel.: +886 351 86408; fax: +886 351 86416. E-mail address: lhyen@chu.edu.tw (L.-H. Yen). Ad Hoc Networks 4 (2006) 636–650 www.elsevier.com/locate/adhoc