Advances in Applied Probability

Large deviation principles for connectable receivers in wireless networks

Christian Hirsch, Benedikt Jahnel, Paul Keeler, and Robert I. A. Patterson

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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.

Article information

Adv. in Appl. Probab., Volume 48, Number 4 (2016), 1061-1094.

First available in Project Euclid: 24 December 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F10: Large deviations
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Wireless network signal-to-interference-and-noise ratio large deviation principle importance sampling


Hirsch, Christian; Jahnel, Benedikt; Keeler, Paul; Patterson, Robert I. A. Large deviation principles for connectable receivers in wireless networks. Adv. in Appl. Probab. 48 (2016), no. 4, 1061--1094.

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