@article {IOPORT.05709664,
    author       = {Yi, Chih-Wei and Wan, Peng-Jun and Su, Chao-Min and Lin, Kuo-Wei and Huang, Scott C.-H.},
    title        = {Asymptotic distribution of the number of isolated nodes in wireless ad hoc networks with unreliable nodes and links.},
    year         = {2010},
    journal      = {Discrete Mathematics, Algorithms and Applications},
    volume       = {2},
    number       = {1},
    issn         = {1793-8309},
    pages        = {107-124},
    publisher    = {World Scientific, Singapore},
    doi          = {10.1142/S1793830910000516},
    abstract     = {Summary: We study the connectivity of wireless ad hoc networks that are composed of unreliable nodes and links by investigating the distribution of the number of isolated nodes. We assume that a wireless ad hoc network consists of $n$ nodes distributed independently and uniformly in a unit-area disk or square. All nodes have the same maximum transmission radius $r_{n}$, and two nodes have a link if their distance is at most $r_{n}$. Nodes are active independently with probability $0 < p_{1} \leq 1$, and links are up independently with probability $0 < p_{2} \leq 1$. Nodes are said isolated if they do not have any links to active nodes. We show that if $r_n = \sqrt {\frac {\ln n + \xi}{\pi p_1 p_2 n}}$ for some constant $\xi $, then the total number of isolated nodes (or isolated active nodes, respectively) is asymptotically Poisson with mean $e^{-\xi }$ (or $p_{1} e^{-\xi }$, respectively). In addition, in the secure wireless networks that adopt $m$-composite key predistribution schemes, a node is said isolated if it does not have a secure link. Let $p$ denote the probability of the event that two neighbor nodes have a secure link. If all nodes have the same maximum transmission radius $r_n = \sqrt {\frac {\ln n + \xi}{\pi p n}}$, the total number of isolated nodes is asymptotically Poisson with mean $e^{-\xi }$.},
    identifier   = {05709664},
}