Asymptotics of a time bounded cylinder model

2021/05/28 by Nils Aschenbruck, Aschenbruck, Nils, Stephan Bussmann +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #60D05 #60F05 #Diffusion and Search Dynamics #FOS: Mathematics #Gene Regulatory Network Analysis #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2105.13916

openalex publication_date 2021/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ℝ^d and a random direction movement scheme. Given a fixed time horizon T>0, we model these movements via cylinders in ℝ^d × [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.

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• Coverage of the unit cube by dynamic Boolean models

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