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Large deviation principles for connectable receivers in wireless networks

Part of: Special processes Limit theorems

Published online by Cambridge University Press:  11 January 2017

Christian Hirsch ,
Benedikt Jahnel ,
Paul Keeler  and
Robert I. A. Patterson
Christian Hirsch*
Affiliation:
Weierstrass Institute for Applied Analysis and Stochastics
Benedikt Jahnel*
Affiliation:
Weierstrass Institute for Applied Analysis and Stochastics
Paul Keeler*
Affiliation:
Weierstrass Institute for Applied Analysis and Stochastics
Robert I. A. Patterson*
Affiliation:
Weierstrass Institute for Applied Analysis and Stochastics
*
* Postal address: Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany.
* Postal address: Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany.
* Postal address: Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany.
* Postal address: Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany.
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Abstract

We study large deviation principles for a model of wireless networks consisting of Poisson point processes of transmitters and receivers. To each transmitter we associate a family of connectable receivers whose signal-to-interference-and-noise ratio is larger than a certain connectivity threshold. First, we show a large deviation principle for the empirical measure of connectable receivers associated with transmitters in large boxes. Second, making use of the observation that the receivers connectable to the origin form a Cox point process, we derive a large deviation principle for the rescaled process of these receivers as the connection threshold tends to 0. Finally, we show how these results can be used to develop importance sampling algorithms that substantially reduce the variance for the estimation of probabilities of certain rare events such as users being unable to connect.

Keywords

Wireless networksignal-to-interference-and-noise ratiolarge deviation principleimportance sampling

MSC classification

Primary: 60F10: Large deviations
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Type
Research Article
Information
Advances in Applied Probability , Volume 48 , Issue 4 , December 2016 , pp. 1061 - 1094
Copyright
Copyright © Applied Probability Trust 2017 

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