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Percolation in the signal to interference ratio graph

Part of: Equilibrium statistical mechanics Special processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Olivier Dousse ,
Massimo Franceschetti ,
Nicolas Macris ,
Ronald Meester  and
Patrick Thiran
Olivier Dousse
Affiliation:
École Polytechnique Fédérale de Lausanne
Massimo Franceschetti*
Affiliation:
University of California, San Diego
Nicolas Macris*
Affiliation:
École Polytechnique Fédérale de Lausanne
Ronald Meester*
Affiliation:
Vrije Universiteit Amsterdam
Patrick Thiran*
Affiliation:
École Polytechnique Fédérale de Lausanne
*
∗∗Postal address: Electrical and Computer Engineering, University of California, San Diego, 9500 Gilman Drive, Mail Code 0407, La Jolla, CA 92093-0407, USA.
∗∗∗Postal address: School of Computer and Communication Sciences, Laboratoire de Théorie des Communications (LTHC), Station 14, EPFL, 1015 Lausanne, Switzerland.
∗∗∗∗Postal address: Department of Mathematics, Vrije Universiteit Amsterdam, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands.
∗∗∗∗∗Postal address: School of Computer and Communication Sciences, Laboratory for Computer Communication and Applications (LCA), Station 14, EPFL, 1015 Lausanne, Switzerland. Email address: patrick.thiran@epfl.ch
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Abstract

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Continuum percolation models in which pairs of points of a two-dimensional Poisson point process are connected if they are within some range of each other have been extensively studied. This paper considers a variation in which a connection between two points depends not only on their Euclidean distance, but also on the positions of all other points of the point process. This model has been recently proposed to model interference in radio communications networks. Our main result shows that, despite the infinite-range dependencies, percolation occurs in the model when the density λ of the Poisson point process is greater than the critical density value λc of the independent model, provided that interference from other nodes can be sufficiently reduced (without vanishing).

Keywords

Percolationwireless networkinterferencePoisson Boolean model

MSC classification

Primary: 82B43: Percolation
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory 90B18: Communication networks
Type
Research Papers
Information
Journal of Applied Probability , Volume 43 , Issue 2 , June 2006 , pp. 552 - 562
Copyright
© Applied Probability Trust 2006 

Footnotes

∗

Postal address: Deutsche Telekom AG, Laboratories, Ernst-Reuter-Platz 7, D-10587 Berlin, Germany.

References

Daley, D. J. (1971). The definition of a multidimensional generalization of shot noise. J. Appl. Prob. 8, 128–135.CrossRefGoogle Scholar
Dousse, O., Baccelli, F. and Thiran, P. (2005). Impact of interferences on connectivity in ad-hoc networks. {IEEE/ACM Trans. Networking} 13, 425–436.CrossRefGoogle Scholar
Gilbert, E. N. (1961). Random plane networks. J. SIAM 9, 533–543.Google Scholar
Grimmett, G. (1999). Percolation, 2nd edn. Springer, Berlin.CrossRefGoogle Scholar
Meester, R. and Roy, R. (1996). Continuum Percolation. Cambridge University Press.CrossRefGoogle Scholar
Kingman, J. F. C. (1993). Poisson Processes (Oxford Stud. Prob. 3). Clarendon Press, Oxford.Google Scholar