Large-deviation principles for connectable receivers in wireless networks
- Hirsch, Christian
- Jahnel, Benedikt
- Keeler, Paul
- Patterson, Robert I. A.
2010 Mathematics Subject Classification
- 60F10 60K35
- wireless network, signal-to-interference-and-noise ratio, large-deviation principle, importance sampling
We study large-deviation principles for a model of wireless networks consisting of Poisson point processes of transmitters and receivers, respectively. 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 zero. 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.
- Adv. Appl. Probab., 48 (2016) pp. 1061--1094.