Open Access
Research Article
Large deviations for spatial telecommunication systems : The Boolean model
Andrew K. Boahenaboahen@aims.edu.ghAfrican Institute of Mathematical Sciences Kasa Global Villa – 1 Shoppers Street ManetSpintex Accra, GhanaView full profile → , *Thomas KatsekporCorresponding authortkatsekpor@ug.edu.ghDepartment of Mathematics College of Basic and Applied Sciences University of Ghana P. O. Box LG 62 AccraLegon, GhanaView full profile → , Kwabena Doku-Amponsahkdoku-amponsah@ug.edu.ghDepartment of Statistics and Actuarial Science College of Basic and Applied Sciences University of Ghana Box LG 115 AccraLegon Accra, GhanaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 08 Jun 2022
- Accepted:
- 04 Oct 2022
- Published Online:
- 01 Jul 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIOS-1338
- Pages:
- 1385–1400
Abstract
There have been some concerns that telecommunication companies are facing today which are spatial in nature. Systems operated by these telecommunication companies have evolved along the years. The main concern of these companies is the ability to provide quality service to customers or users in a dense regime. Therefore, they sought to answer questions such as (i) what is the best possible configurations of base stations and users that maximizes quality service? (ii) can one estimate and control the probability of bad service, which may be seen as a rare event? and many more which may arise during companies operations. To answer these questions one will often have to estimate the tail distribution of events, which may be considered under the realm of large deviations. In this article, we define the empirical marked measure of the Boolean model, which will serve estimate the intensity measure of the Marked Poisson Point Process of devices or users, and the empirical connectivity measure of the Boolean Model which will serve estimate the coverage probability density of the spatial telecommunication area. For these empirical measures, we establish large deviation principle (LDP) in the τ – topology.
Keywords
Subject Classifications
60F1005C8068Q87
References
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