Probability of k-hop connection under random connection model

Publication Type:
Journal Article
IEEE Communications Letters, 2010, 14 (11), pp. 1023 - 1025
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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 ε A is directly connected to a sensor located at {x}-{1} ε A with probability g(2-1), 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 ε 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>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. © 2010 IEEE.
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