TY - GEN

T1 - On the asymptotic connectivity of random networks under the random connection model

AU - Mao, Guoqiang

AU - Anderson, Brian Do

PY - 2011

Y1 - 2011

N2 - Consider a network where all nodes are distributed on a unit square following a Poisson distribution with known density ρand a pair of nodes separated by an Euclidean distance x are directly connected with probability g(x/rρ ), where g : [0,∞ρ+b/cp) [0,1] satisfies three conditions: rotational invariance, qnon-increasing monotonicity and integral boundedness, √ρ+b/Cp = ∫R2g(∥x∥)dx and bis a constant, independent of the event that another pair of nodes are directly connected. In this paper, we analyze the asymptotic distribution of the number of isolated nodes in the above network using the Chen-Stein technique and the impact of the boundary effect on the number of isolated nodes as ρ. On that basis we derive a necessary condition for the above network to be asymptotically almost surely connected. These results form an important link in expanding recent results on the connectivity of the random geometric graphs from the commonly used unit disk model to the more generic and more practical random connection model.

AB - Consider a network where all nodes are distributed on a unit square following a Poisson distribution with known density ρand a pair of nodes separated by an Euclidean distance x are directly connected with probability g(x/rρ ), where g : [0,∞ρ+b/cp) [0,1] satisfies three conditions: rotational invariance, qnon-increasing monotonicity and integral boundedness, √ρ+b/Cp = ∫R2g(∥x∥)dx and bis a constant, independent of the event that another pair of nodes are directly connected. In this paper, we analyze the asymptotic distribution of the number of isolated nodes in the above network using the Chen-Stein technique and the impact of the boundary effect on the number of isolated nodes as ρ. On that basis we derive a necessary condition for the above network to be asymptotically almost surely connected. These results form an important link in expanding recent results on the connectivity of the random geometric graphs from the commonly used unit disk model to the more generic and more practical random connection model.

KW - Isolated nodes

KW - connectivity

KW - random connection model

UR - http://www.scopus.com/inward/record.url?scp=79960863796&partnerID=8YFLogxK

U2 - 10.1109/INFCOM.2011.5935242

DO - 10.1109/INFCOM.2011.5935242

M3 - Conference contribution

SN - 9781424499212

T3 - Proceedings - IEEE INFOCOM

SP - 631

EP - 639

BT - 2011 Proceedings IEEE INFOCOM

T2 - IEEE INFOCOM 2011

Y2 - 10 April 2011 through 15 April 2011

ER -