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We study large-deviation principles for a model of wireless networksconsisting of Poisson point processes of transmitters and receivers,respectively. To each transmitter we associate a family of connectablereceivers whose signal-to-interference-and-noise ratio is larger than a certainconnectivity threshold. First, we show a large-deviation principle for theempirical measure of connectable receivers associated with transmitters inlarge boxes. Second, making use of the observation that the receiversconnectable to the origin form a Cox point process, we derive a large-deviationprinciple for the rescaled process of these receivers as the connectionthreshold tends to zero. Finally, we show how these results can be used todevelop importance-sampling algorithms that substantially reduce the variancefor the estimation of probabilities of certain rare events such as users beingunable to connect

Large-deviation principles for connectable receivers in wireless networks