Large Large deviations for spatial telecommunication systems: The boolean model

TL;DR

This paper establishes large deviation principles for empirical measures in the Boolean model of spatial telecommunication systems, aiding in understanding rare events like service failures in dense networks.

Contribution

It introduces and proves large deviation principles for empirical measures related to coverage and connectivity in the Boolean model of spatial telecommunication systems.

Findings

Proves LDP for empirical marked measure of the Poisson process.

Proves LDP for empirical connectivity measure.

Provides tools to estimate probabilities of rare events in dense networks.

Abstract

Spatial telecommunication systems have evolved along the years, leading to some concerns that telecommunication companies are facing today. The main inquietude is the ability to provide quality service to customers or users in a dense regime. Therefore, questions such as : what is the best possible configurations of base stations and users that maximizes quality service? Is it possible to estimate and control the probability of bad service, which may be seen as a rare event? and many more arise. These questions often involve estimating the tail distribution of events, which falls under the scope of large deviation principles. In this article, we associate with the Boolean model, the empirical marked measure which will serve as a statistic for the intensity measure of the Marked Poisson Point Process of devices or users and the empirical connectivity measure which will serve as a statistic for coverage probability density of the spatial telecommunication area. For these empirical measures, prove large deviation principle (LDP) for well-defined empirical measures.