### Abstract

Wireless ad hoc networks with Bernoulli nodes provide a unified model of various important problems including fault-tolerance, randomized construction of virtual backbone, randomized broadcast routing, and randomized wake/sleep management. We assume that the wireless ad hoc network consists of n nodes which are distributed independently and uniformly in a unit-area disk and are active (or available) independently with some constant probability p. Let p _{n}, denote the random variable which is the smallest transmission range at which the active nodes form a connected network, and ρ′_{n} denote the random variable which is the smallest transmission range at which the active nodes form a connected network and each inactive node is adjacent to at least one active node. ρ_{n} is referred to as the critical transmission range for connectivity of active nodes, and ρ′_{n} is referred to as the critical transmission range for connectivity of all nodes. In this paper, we derive the precise asymptotic distributions of ρ_{n} and ρ′_{n}.

Original language | English |
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Title of host publication | 2005 IEEE Wireless Communications and Networking Conference, WCNC 2005 |

Subtitle of host publication | Broadband Wireless for the Masses - Ready for Take-off |

Pages | 2219-2224 |

Number of pages | 6 |

DOIs | |

State | Published - 26 Sep 2005 |

Event | 2005 IEEE Wireless Communications and Networking Conference, WCNC 2005: Broadband Wirelss for the Masses - Ready for Take-off - New Orleans, LA, United States Duration: 13 Mar 2005 → 17 Mar 2005 |

### Publication series

Name | IEEE Wireless Communications and Networking Conference, WCNC |
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Volume | 4 |

ISSN (Print) | 1525-3511 |

### Conference

Conference | 2005 IEEE Wireless Communications and Networking Conference, WCNC 2005: Broadband Wirelss for the Masses - Ready for Take-off |
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Country | United States |

City | New Orleans, LA |

Period | 13/03/05 → 17/03/05 |

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## Cite this

*2005 IEEE Wireless Communications and Networking Conference, WCNC 2005: Broadband Wireless for the Masses - Ready for Take-off*(pp. 2219-2224). [NET42-3] (IEEE Wireless Communications and Networking Conference, WCNC; Vol. 4). https://doi.org/10.1109/WCNC.2005.1424861