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Limit of the Transport Capacity of a Dense Wireless Network

Part of: Miscellaneous applications of functional analysis Geometric probability and stochastic geometry Miscellaneous applications of operator theory

Published online by Cambridge University Press:  14 July 2016

Radha Krishna Ganti  and
Martin Haenggi
Radha Krishna Ganti*
Affiliation:
University of Notre Dame
Martin Haenggi*
Affiliation:
University of Notre Dame
*
∗Current address: Department of Electrical Engineering, University of Texas at Austin, Austin TX, 78712, USA. Email address: rganti@austin.utexas.edu
∗∗Current address: Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA. Email address: mhaenggi@nd.edu
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Abstract

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It is known that the transport capacity of a dense wireless ad hoc network with n nodes scales like √n. We show that the transport capacity divided by √n approaches a nonrandom limit with probability 1 when the nodes are uniformly distributed on the unit square. To show the existence of the limit, we prove that the transport capacity under the protocol model is a subadditive Euclidean functional and use the machinery of subadditive functions in the spirit of Steele.

Keywords

Subadditive Euclidean functionaltransport capacityad hoc network

MSC classification

Secondary: 60D05: Geometric probability and stochastic geometry 46N30: Applications in probability theory and statistics 47N30: Applications in probability theory and statistics
Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 3 , September 2010 , pp. 886 - 892
Copyright
Copyright © Applied Probability Trust 2010 

References

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