# MEC Server Sleep Strategy for Energy Efficient Operation of an MEC System
## 1 Introduction
Threshold methods [10; 11], commonly employed in determining the operational mode of an MECS, involve transitioning an MECS into sleep mode when its load falls below a predefined threshold. This approach, wherein each MECS independently decides based on its own workload, is straightforward to implement. However, the uneven distribution of the load across MECSs at each time step prompts the exploration of comprehensive load distribution considerations to optimize system-wide energy efficiency. Addressing this, cooperative sleep decision methods have been proposed [9; 12], where MECSs form clusters, exchange status information, and make sleep decisions, considering the status of other MECSs in the same cluster. Despite the potential enhancement in energy efficiency, such cooperative methods introduce additional signaling overhead, and when MECS decisions differ, an iterative consensus process ensues, potentially leading to delayed decision making. To tackle these challenges, deep learning models have been used [13; 14]. These approaches leverage the current load information of MEC at a specific time point to predict the load of each MECS in the subsequent time step. Subsequently, decisions are made regarding which MECS should sleep based on these predictions. To forecast the MECS load, these techniques often model the MECS load as a time-series sequence and predominantly employ the LSTM (Long Short Term Memory) model as it is suitable for time-series data prediction. In this approach, the accuracy of the determined set of sleep MECS based on predicted values depends on the precision of load prediction for each MECS. Therefore, the optimization of the sleep MECS decision problem can be reframed as a precise workload prediction problem. 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 improve the previous method based on the LSTM predictor in two major aspects. Firstly, we improve the accuracy of the predictedtask arrival rate. The task arrival rate to an MECS varies in time and space. However, LSTM exploits 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 (Spatio-Temporal Graph Convolution Network) [15]. STGCN extends the convolution operations commonly used in graph neural networks to both spatial and temporal dimensions to effectively capture information between neighboring nodes and detects temporal changes, providing enhanced capabilities in modeling spatio-temporal data. Secondly, we reduce the prediction delay. Since LSTM has a recurrent architecture, it processes inputs sequentially. Therefore, the methods based on LSTM are slow in producing predicted values. On the contrary, since we use the STGCN model that can process inputs in parallel, we can reduce the time needed to produce predicted values. We can summarize our contributions as follows. * We propose a framework for the MECS sleep decision by using STGCN. We define an input graph for this framework and enhance the prediction accuracy for the workload distribution in an MEC system by utilizing not only the workload correlations in each MECS in the time domain, but also the relationships among MECSs in the space domain. * Despite the availability of the workload distribution information, determining the operational modes of individual MECS poses a computationally challenging combinatorial optimization problem. To address this, we utilize a genetic algorithm (GA) to fast compute the optimal operation mode for each MECS at the start of each time slot, taking into account both energy consumption and service latency factors for all MECSs in the system. * Comprehensive simulation studies show that our approach is better than the conventional LSTM-based method in terms of both energy efficiency and the time required for determining sleep MECSs.