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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

[1] Franceschetti, M., Dousse, O., Tse, D. N. C. and Thiran, P. (2007). {Closing the gap in the capacity of wireless networks via percolation theory}. IEEE Trans. Inf. Theory 53, 1009–1018.CrossRefGoogle Scholar
[2] Ganti, R. K. and Haenggi, M. (2008). The transport capacity of a wireless network is a subadditive Euclidean functional. In Proc. IEEE Trans. Conf. Mobile Ad Hoc and Sensor Systems (Atlanta, GA), pp. 784–789.CrossRefGoogle Scholar
[3] Gupta, P. and Kumar, P. R. (2000). {The capacity of wireless networks}. IEEE Trans. Inf. Theory 46, 388–404.CrossRefGoogle Scholar
[4] Kumar, P. R. and Xue, F. (2006). {Scaling laws for ad hoc wireless networks: an information theoretic approach}. In Foundations and Trends in Networking, Now Publishers, Hanover, MA, pp. 145–270.Google Scholar
[5] Rhee, W. T. (1993). {A matching problem and subadditive Euclidean functionals}. Ann. Appl. Prob. 3, 794–801.CrossRefGoogle Scholar
[6] Steele, J. M. (1981). {Subadditive Euclidean functionals and nonlinear growth in geometric probability}. Ann. Prob. 9, 365–376.CrossRefGoogle Scholar