Probability of k-hop connection under random connection model

Authors:
Guoqiang Mao;Zijie Zhang;Brian D. O. Anderson
Affiliations:
University of Sydney and National ICT, Australia;University of Sydney and National ICT, Australia;Australian National University and National ICT Australia
Venue:
IEEE Communications Letters
Year:
2010

Citing 5
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Abstract

Consider a wireless sensor network with i.i.d. 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 → [0, 1]. The recursive formula is accurate for k = 1, 2 and provides an approximation for Pr (k|x) for k k|x) can be used in a number of areas in sensor networks.