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Asymptotic critical transmission ranges for connectivity in wireless ad hoc networks with Bernoulli nodes

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2 Author(s)
Peng-Jun Wan ; Dept. of Comput. Sci., Illinois Inst. of Technol., Chicago, IL, USA ; Chih-Wei Yi

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 ρ. Let ρn denote the random variable which is the smallest transmission range at which the active nodes form a connected network, and pn' 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, ρn is referred to as the critical transmission range for connectivity of active modes, and ρn' is referred to as the critical transmission range for connectivity of all nodes. In this paper, we derive the precise asymptotic distributions of ρn and ρn'.

Published in:

Wireless Communications and Networking Conference, 2005 IEEE  (Volume:4 )

Date of Conference:

13-17 March 2005