How Many Wireless Sensors are Needed to Guarantee Connectivity of a One-Dimensional Network with Random Inter-Node Spacing? - Kurlin, Vitaliy; Mihaylova, Lyudmila (Journal of applied probability and statistics., 2013)
An important problem in wireless sensor networks is to nd 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 dierent piece-wise constant densities. Explicit estimates for a number of sensors to guarantee connectivity of the network are found for constant and normal densities.
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Keywords: Wireless sensor network; Connectivity; Probability; Density.