On the giant component of wireless multihop networks in the presence of shadowing

Ta, X; Mao, G; Anderson, BDO

On the giant component of wireless multihop networks in the presence of shadowing

Ta, X Mao, G

Anderson, BDO

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Publication Type:: Journal Article
Citation:: IEEE Transactions on Vehicular Technology, 2009, 58 (9), pp. 5152 - 5163
Issue Date:: 2009-11-01

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Field	Value	Language
dc.contributor.author	Ta, X	en_US
dc.contributor.author	Mao, G https://orcid.org/0000-0002-3598-4949	en_US
dc.contributor.author	Anderson, BDO	en_US
dc.date.issued	2009-11-01	en_US
dc.identifier.citation	IEEE Transactions on Vehicular Technology, 2009, 58 (9), pp. 5152 - 5163	en_US
dc.identifier.issn	0018-9545	en_US
dc.identifier.uri	http://hdl.handle.net/10453/28435
dc.description.abstract	In this paper, we study transmission power to secure the connectivity of a network. Instead of requiring all nodes to be connected, we require that only a large fraction (e.g., 95%) be connected, which is called the giant component. We show that, with this slightly relaxed requirement on connectivity, significant energy savings can be achieved for a large-scale network. In particular, we assume that a total of n nodes are randomly independently uniformly distributed in a unit square in ℛ2, that each node has uniform transmission power, and that any two nodes are directly connected if and only if the power that was received by one node from the other node, as determined by the log-normal shadowing model, is larger than or equal to a given threshold. First, we derive an upper bound on the minimum transmission power at which the probability of having a giant component of order above qn for any fixed q ∈ (0, 1) tends to one as n →∞. Second, we derive a lower bound on the minimum transmission power at which the probability of having a connected network tends to one as n →∞. We then show that the ratio of the aforementioned transmission power that was required for a giant component to the transmission power that was required for a connected network tends to zero as n →∞. This result implies significant energy savings if we require that only most nodes (e.g., 95%) be connected rather than requiring all nodes to be connected. This result is also applicable for any other arbitrary channel model that satisfies certain intuitively reasonable conditions. © 2009 IEEE.	en_US
dc.relation.ispartof	IEEE Transactions on Vehicular Technology	en_US
dc.relation.isbasedon	10.1109/TVT.2009.2026480	en_US
dc.subject.classification	Automobile Design & Engineering	en_US
dc.title	On the giant component of wireless multihop networks in the presence of shadowing	en_US
dc.type	Journal Article
utslib.citation.volume	9	en_US
utslib.citation.volume	58	en_US
utslib.for	1005 Communications Technologies	en_US
utslib.for	08 Information and Computing Sciences	en_US
utslib.for	09 Engineering	en_US
utslib.for	10 Technology	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Electrical and Data Engineering
pubs.organisational-group	/University of Technology Sydney/Strength - CRIN - Realtime Information Networks
utslib.copyright.status	closed_access
pubs.issue	9	en_US
pubs.publication-status	Published	en_US
pubs.volume	58	en_US

Abstract:

In this paper, we study transmission power to secure the connectivity of a network. Instead of requiring all nodes to be connected, we require that only a large fraction (e.g., 95%) be connected, which is called the giant component. We show that, with this slightly relaxed requirement on connectivity, significant energy savings can be achieved for a large-scale network. In particular, we assume that a total of n nodes are randomly independently uniformly distributed in a unit square in ℛ2, that each node has uniform transmission power, and that any two nodes are directly connected if and only if the power that was received by one node from the other node, as determined by the log-normal shadowing model, is larger than or equal to a given threshold. First, we derive an upper bound on the minimum transmission power at which the probability of having a giant component of order above qn for any fixed q ∈ (0, 1) tends to one as n →∞. Second, we derive a lower bound on the minimum transmission power at which the probability of having a connected network tends to one as n →∞. We then show that the ratio of the aforementioned transmission power that was required for a giant component to the transmission power that was required for a connected network tends to zero as n →∞. This result implies significant energy savings if we require that only most nodes (e.g., 95%) be connected rather than requiring all nodes to be connected. This result is also applicable for any other arbitrary channel model that satisfies certain intuitively reasonable conditions. © 2009 IEEE.

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http://hdl.handle.net/10453/28435