In this document, we prove the convergence of the model proposed in [1], which aims at estimating the LoRaWAN network performance in a single-gateway scenario. First, we provide an analytical proof of the existence of a fixed point solution for such a system. Then, we report experimental results, showing that the system of the two inter-dependent equations provided by the model can be solved through fixed-point iterations, and that a limited number of iterations is enough to reach convergence.
翻译:在这份文件中,我们证明了[1]中提议的模型的趋同性,该模型的目的是在单一起点假设中估计LoRawAN网络的性能。 首先,我们提供了分析证据,证明这种系统存在固定点解决办法。 然后,我们报告了实验结果,表明该模型所提供的两个相互依存方程式的系统可以通过固定点迭代解决,而数量有限的迭代足以达到趋同。