Fault Tolerant Sensor Networks with Bernoulli Nodes

Connectivity, power consuming and fault tolerance are three critical issues in sensor networks. In this paper, sensor networks are modeled by the unit disc graph, random point process and Bernoulli nodes. A sensor network is composed of identical nodes randomly located on an unit area disc with uniform distribution. Each node is associated with probability ( ) to be active and with probability to be inactive. is the transmission radius. As goes to infinite and let , then the probability that each node neighbors at least one active node is , the Gumbel extreme-value function, for , and the cardinality of one connected component in the random graph is either or tending to infinite.