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.

电信网络建模的一种方法是静态布尔模型。然而，节点移动性等动态因素对此类网络的性能评估有重大影响。考虑$\mathbb {R}^d$中的布尔模型和随机方向移动方案。给定固定的时间范围$T>0$，我们通过$\mathbb {R}^d \times [0,T]$中的圆柱体对这些运动进行建模。在这项工作中，我们推导出这些圆柱体并集泛函的中心极限定理。考虑了随机集的体积和数量以及欧拉特性，并给出了可实现的吞吐量、节点的可用性以及网络的拓扑结构的答案。