Probability of k-Hop Connection under Random Connection Model
Guoqiang Mao, Zijie Zhang, Brian D. O. Anderson · IEEE Communications Letters · 2010
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.