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Large deviation principles for connectable receivers in wireless networks

Published online by Cambridge University Press:  11 January 2017

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
Corresponding

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.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 2017 

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