Lebiedź Jacek, Cofta Piotr, Orłowski Cezary
Faculty of ETI, Gdansk University of Technology, 80-233 Gdańsk, Poland.
Institute of Management and Finance, WSB University in Gdansk, 80-266 Gdańsk, Poland.
Sensors (Basel). 2021 Sep 16;21(18):6211. doi: 10.3390/s21186211.
Uncertainty in dense heterogeneous IoT sensor networks can be decreased by applying reputation-inspired algorithms, such as the EWMA (Exponentially Weighted Moving Average) algorithm, which is widely used in social networks. Despite its popularity, the eventual convergence of this algorithm for the purpose of IoT networks has not been widely studied, and results of simulations are often taken in lieu of the more rigorous proof. Therefore the question remains, whether under stable conditions, in realistic situations found in IoT networks, this algorithm indeed converges. This paper demonstrates proof of the eventual convergence of the EWMA algorithm. The proof consists of two steps: it models the sensor network as the UOG (Uniform Opinion Graph) that enables the analytical approach to the problem, and then offers the mathematical proof of eventual convergence, using formalizations identified in the previous step. The paper demonstrates that the EWMA algorithm converges under all realistic conditions.
通过应用受声誉启发的算法，如在社交网络中广泛使用的指数加权移动平均（EWMA）算法，可以降低密集异构物联网传感器网络中的不确定性。尽管该算法很受欢迎，但针对物联网网络的最终收敛性尚未得到广泛研究，模拟结果常被用来替代更严格的证明。因此问题依然存在，即在物联网网络中发现的现实情况下，在稳定条件下该算法是否真的收敛。本文证明了EWMA算法的最终收敛性。证明包括两个步骤：将传感器网络建模为均匀意见图（UOG），这使得能够采用分析方法解决该问题，然后使用上一步中确定的形式化方法提供最终收敛的数学证明。本文证明了EWMA算法在所有现实条件下都会收敛。
