How Many Wireless Sensors are Needed to Guarantee Connectivity of A One-Dimensional Network with Random Inter-Node Spacing?

An important problem in wireless sensor networks is to find an optimal number of randomly deployed sensors to guarantee connectivity of the resulting network with a given probability. The authors describe a general method to compute the probabilities of connectivity and coverage for one-dimensional networks with arbitrary densities of inter-node spacings. A closed formula for the probability of connectivity is derived when inter-node spacings have arbitrary di fferent piece-wise constant densities. Explicit estimates for a number of sensors to guarantee connectivity of the network are found for constant and normal densities.