# MEC Server Sleep Strategy for Energy Efficient Operation of an MEC System
## 2 Related Works
### Sleep Control Methods
They employ the LSTM model to predict the long-term workload and adjust the number of active MECSs in a heuristic manner based on the predicted workloads. For the joint optimization of task latency and energy consumption, the authors in [37] adopt a reinforcement learning approach. After casting a joint optimization problem that minimizes the weighted sum of latency and energy, they develop a solver for the formulated problem by integrating DDQN (Deep Reinforcement Learning with Double Q-learning) with the multi-knapsack algorithm. Centralized methods leverage existing state information of the MEC system to estimate its future state and use the estimated state to control the mode of MECSs. Therefore, the precision of the predicted state information becomes the major factor that influences the performance. The Lyapunov optimization framework transforms the optimization problem of long-term average cost into a per-time-slot cost optimization problem. In general, the optimality gap caused by the problem modification is not marginal. To enhance the accuracy of future state predictions, deep learning models such as LSTM are widely employed. However, since LSTM was originally developed for the prediction of Euclidean data, its performance may degrade when applied to non-Euclidean data with graph structures like MEC systems. Therefore, in this paper, we enhance the previous method based on the LSTM predictor in two major aspects. Firstly, we improve the accuracy of the predicted task arrival rate. The task arrival rate to an MECS varies in time and space. However, the previous methods that predict the task arrival rate for each MECS by using LSTM exploit only the correlation in the time domain, neglecting the valuable correlation information in the space domain. We enhance the accuracy of task arrival rate prediction by using STGCN. STGCN extends the convolution operations commonly used in graph neural networks to both spatial and temporal dimensions. This convolutional layer effectively captures information between neighboring nodes and detects temporal changes, providing enhanced capabilities in modeling spatio-temporal data. Secondly, we reduce the prediction delay. LSTM has a recurrent architecture which processes the input sequentially. Therefore, the methods based on LSTM are slow in producing the predicted values. On the contrary, we use the STGCN model that can process inputs in parallel. Therefore, compared to the methods based on LSTM, we can reduce the time needed to produce the predicted values. For easy comparison of the techniques that have been proposed to control the sleep mode of MECSs, we summarize their main feature by adding Table 2. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Technique** & **Control** & **Operation** & **Weakness** & **Ref.** \\ \hline PSO & AP selection & Iterative & Long decision time & [33] \\ \hline ICS & Relative load level & Iterative & Long decision time & [12] \\ \hline MG & Offload decision & Iterative & Long decision time & [34] \\ \hline LOF & MECS working mode & On-demand & Optimality gap & [9; 35; 36] \\ \hline LR & Load distribution prediction & On-demand & Optimality gap & [13] \\ \hline DDQN & Cost (sum of delay and energy) & On-demand & Optimality gap & [37] \\ \hline LSTM & Load distribution prediction & On-demand & Optimality gap & [14] \\ \hline Proposed & Load distribution prediction & On-demand & Fast and near-optimal & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of sleep control methods in an MEC system (PSO: Particle Swarm Optimization, ICS: Inter-Cell Signaling, MG: Minority Game, LOF: Lyapunov Optimization Framework, LR: Linear Regression, DDQN: Deep Reinforcement Learning with Double Q-Learning, and LSTM: Long Short Time Memory).