On computing conditional fault-tolerance measures for k-covered wireless sensor networks

Traditional connectivity is a graph-theoretic concept that has been widely used as a measure of the fault tolerance in wireless sensor networks. The classical connectivity, however, assumes that any subset of nodes can potentially fail at the same time, including the entire neighbor set of any node. In this paper, we propose a new measure of fault tolerance, called conditional fault-tolerance, for a class of wireless sensor networks, named k-covered wireless sensor networks (kcwsn), using the concept of forbidden faulty set. Our forbidden faulty set analysis of conditional fault-tolerance prohibits having a simultaneous failure of all the neighbors of any node. We characterize kcwsn with either homogeneous or non-homogeneous sensors based on the assumptions of random uniform distribution of the sensors and circular model of their transmission and sensing ranges. In particular, we compute the minimum node degree of kcwsn. We also prove that in general, the relationship between transmission and sensing ranges (R≥2r) does not always imply network connectivity even if sensing coverage is guaranteed. Moreover, we propose two conditional fault-tolerance measures for kcwsn: one based on the concept of conditional connectivity, the other using a new concept that is called conditional coverage. Our results prove that kcwsn can sustain a large number of sensor failures provided that the faulty set does not include the forbidden faulty set.