Serverless computing has emerged as a new execution model which gained a lot of attention in cloud computing thanks to the latest advances in containerization technologies. Recently, serverless has been adopted at the edge, where it can help overcome heterogeneity issues, constrained nature and dynamicity of edge devices. Due to the distributed nature of edge devices, however, the scaling of serverless functions presents a major challenge. We address this challenge by studying the optimality of serverless function scaling. To this end, we propose Semi-Markov Decision Process-based (SMDP) theoretical model, which yields optimal solutions by solving the serverless function scaling problem as a decision making problem. We compare the SMDP solution with practical, monitoring-based heuristics. We show that SMDP can be effectively used in edge computing networks, and in combination with monitoring-based approaches also in real-world implementations.

翻译：无服务器计算作为一种新兴的执行模型，借助容器化技术的最新进展，在云计算领域引起了广泛关注。近年来，无服务器计算被引入边缘环境，有助于克服异构性问题、边缘设备的资源受限特性及动态性。然而，由于边缘设备具有分布式特性，无服务器函数的伸缩面临重大挑战。针对这一问题，我们通过研究无服务器函数伸缩的最优性来加以应对。为此，我们提出了一种基于半马尔可夫决策过程（Semi-Markov Decision Process, SMDP）的理论模型，将无服务器函数伸缩问题建模为决策问题进行求解，从而得到最优方案。我们将SMDP求解结果与基于监控的实用启发式方法进行了比较，结果表明SMDP可有效应用于边缘计算网络，并且与基于监控的方法结合后，也能在实际部署中发挥作用。