Asymptotics of a time bounded cylinder model

TL;DR

This paper develops central limit theorems for functionals of a time-bounded cylinder model representing mobile nodes in telecommunication networks, providing insights into throughput, node availability, and network topology.

Contribution

It introduces a novel asymptotic analysis of a dynamic Boolean model with cylinders, capturing node mobility effects in network performance evaluation.

Findings

Central limit theorems for volume and Euler characteristic

Quantitative insights into network throughput and topology

Analysis of node availability over time

Abstract

One way to model telecommunication networks are static Boolean models. However, dynamics such as node mobility have a significant impact on the performance evaluation of such networks. Consider a Boolean model in $\mathbb{R}^d$ and a random direction movement scheme. Given a fixed time horizon $T>0$, we model these movements via cylinders in $\mathbb{R}^d \times [0,T]$. In this work, we derive central limit theorems for functionals of the union of these cylinders. The volume and the number of isolated cylinders and the Euler characteristic of the random set are considered and give an answer to the achievable throughput, the availability of nodes, and the topological structure of the network.