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Probability of k-Hop Connection under Random Connection Model

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3 Author(s)
Guoqiang Mao ; University of Sydney and National ICT Australia ; Zijie Zhang ; Brian D. O. Anderson

Consider a wireless sensor network with Ltd. sensors following a homogeneous Poisson distribution in a given area A in ℜ2. A sensor located at x2 ∈ A is directly connected to a sensor located at x1 ∈ A with probability g (x2 - x1), independent of any other distinct pair of sensors. In this letter, we provide a recursive formula for computing Pr (k|x), the probability that a node x ∈ A apart from another node is connected to that node at exactly k hops, for a generic random connection function g : ℜ2 → . The recursive formula is accurate for k = 1, 2 and provides an approximation for Pr (k|x) for k > 2. The exact and approximate analytical results are validated by simulations. The knowledge of Pr (k|x) can be used in a number of areas in sensor networks.

Published in:

IEEE Communications Letters  (Volume:14 ,  Issue: 11 )