The maximum achievable capacity from source to destination in a network is limited by the min-cut max-flow bound; this serves as a converse limit. In practice, link capacities often fluctuate due to dynamic network conditions. In this work, we introduce a novel analytical framework that leverages tools from computational geometry to analyze throughput in heterogeneous networks with variable link capacities in a finite regime. Within this model, we derive new performance bounds and demonstrate that increasing the number of links can reduce throughput variability by nearly $90\%$. We formally define a notion of network stability and show that an unstable graph can have an exponential number of different min-cut sets, up to $O(2^{|E|})$. To address this complexity, we propose an algorithm that enforces stability with time complexity $O(|E|^2 + |V|)$, and further suggest mitigating the delay-throughput tradeoff using adaptive rateless random linear network coding (AR-RLNC).

翻译：网络中从源节点到目的节点的最大可达容量受限于最小割最大流界；这构成了一个逆极限。在实际应用中，链路容量常因动态网络条件而波动。本文提出了一种新颖的分析框架，该框架利用计算几何工具，在有限域内分析具有可变链路容量的异构网络吞吐量。在此模型中，我们推导出新的性能界，并证明增加链路数量可将吞吐量波动降低近$90\%$。我们形式化定义了网络稳定性的概念，并证明不稳定图可能具有指数级数量的不同最小割集，可达$O(2^{|E|})$。为应对此复杂性，我们提出一种强制稳定性的算法，其时间复杂度为$O(|E|^2 + |V|)$，并进一步建议采用自适应无速率随机线性网络编码（AR-RLNC）来缓解延迟与吞吐量的权衡。