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.
@article{arxiv.2108.02458,
title = {Proof of convergence of LoRaWAN model},
author = {Davide Magrin and Martina Capuzzo and Andrea Zanella and Michele Zorzi},
journal= {arXiv preprint arXiv:2108.02458},
year = {2021}
}