## 1 Introduction
Specifically, in this paper, we propose a framework that integrates STGCN (spatio-temporal graph convolutional networks) [15] and DQN (Deep Q-Network) [16] to enable fast and accurate continuous determination of optimal MECS states in an environment where the distribution of the workload imposed on the MEC system changes stochastically. Our framework leverages the strengths of STGCN in capturing spatial dependencies among geographically distributed MECSs and recognizing temporal patterns in workload fluctuations in the system. This capability allows us to be precise in workload forecasting across the system. We make use of the ability of DQN that can make sequential decisions in a dynamic environment. By considering the long-term impact of MECS state transitions in uncertain environments with DQN, we devise an optimal policy for dynamically transitioning MEC servers between active and sleep states. Although STGCN can predict the workload imposed on the system with high accuracy, prediction errors cannot be entirely eliminated. However, when the prediction error is sufficiently small, the difference between the actual system state and the predicted state remains minimal. The Q-Network of DQN extracts features from the system state information and positions similar states close to each other in the feature space. Therefore, even if the input state information to DQN contains small prediction errors, the probability that DQN will output the same result as the one obtained when actual system information is fed into DQN is very high. Thus, through the synergistic integration of these two deep-learning models, our proposed framework demonstrates enhanced capabilities in the strategic optimization of server state transitions. This comprehensive approach enables the system to effectively capture and leverage the intricate relationships between dynamic system states and optimal operational decisions. Consequently, the framework achieves substantial improvements in energy efficiency while maintaining service latency within the prescribed threshold value. Our main contributions in this paper include the following:  
* We propose a novel framework that minimizes MECS system energy consumption while maintaining user service delay below a certain threshold through intelligent MECS operational state management by integrating STGCN and DQN. * We carefully design a reward mechanism for our DQN-based controller that balances the trade-off between energy consumption and service latency. * We conduct extensive performance evaluation using real-world datasets to demonstrate the effectiveness of our approach compared with metaheuristic optimization methods. Especially, we show that the proposed method outperforms the metaheuristic optimization method in terms of the amount of saved energy, the service delay satisfaction rate, and the decision time even when prediction errors are involved. The remainder of the paper is organized as follows. In Section 2, related works are presented, followed by the system model and the problem formulation in Section 3. In Section 4, the proposed approach is presented in detail, while Section 5 validates the effectiveness of the proposed method through simulations based on real-world datasets. Finally, Section 6 concludes the paper and outlines potential directions for future research.