  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. 
Towards Optimal Serverless Function Scaling in Edge Computing Network