Hysteretic Optimality of Container Warming Control in Serverless Computing Systems

Keeping containers warm for prompt service responses and reducing warm containers for light-weight system management exhibit a fundamental tradeoff in serverless computing systems. In this letter, we investigate the problem of container warming control for serverless computing, and we formulate it as a Markov decision process (MDP). By observing that the value functions corresponding to the MDP are partially submodular, we show that the derived optimal policy is hysteretic and partially non-decreasing. Our numerical results show that the derived optimal policy exhibits a hysteretic structure, which can be realized via switching-up/-down thresholds in practice.