Coverage, connectivity, and fault tolerance measures of wireless sensor networks

Connectivity and sensing coverage are two fundamental concepts in the design of wireless sensor networks (WSNs). In this paper, we investigate the relationship between coverage and connectivity for k-covered WSNs (kCWSN), where every point in a field of interest is covered by at least k sensors. Furthermore, we compute the connectivity of kCWSN based on the degree of sensing coverage. We also propose measures of fault tolerance for kCWSN based on network connectivity and sensing coverage. Random distributions of the sensors in a field have been widely used in most of sensor networking protocols, in spite of the fact that these deployment techniques do not always provide complete, void-free coverage. On the contrary, we consider both deterministic and random sensor deployment strategies to meet coverage degree requirements of sensing applications. Using our Augmented Equilateral Triangle (AET) model, we prove that if the sensing coverage degree is k and R >= 2 x r, the network connectivity is higher than k. Precisely, our analysis of the geometric properties of deterministic sensor deployment strategies, demonstrates that sensing k-coverage and R >= root 3 x r yield kCWSN connectivity that is higher than k. These findings are of practical use for network designers to build up sensing applications with prescribed degrees of sensing coverage, network connectivity and fault tolerance.