# MEC Server Sleep Strategy for Energy Efficient Operation of an MEC System
## 2 Related Works  
### Preliminary: Graph Neural Networks  
Graph neural network (GNN) is a term used to represent the artificial neural networks designed to process data represented as graphs. The key tasks of GNN include node level tasks, edge level tasks, and graph-level tasks. In the node level tasks, GNN learns the features of individual graph nodes by considering their attributes and connectivity. The learned features can be used for new node classification. For the edge level tasks, a GNN embeds edge features and uses them to predict possible links and weights indicating the strength of each connection in a graph. Graph-level tasks involve predicting or classifying features of the entire graph. For example, it can be used to identify communities within the entire social graph and create new protein molecules. In general, a computation module in a GNN is composed of a message function, aggregation function, update function, and readout function. Depending on the configuration of these functions in the computational module, various GNNs can be built [16; 17]. In [18], according to the primary objectives and architectural differences of various GNNs, the authors categorize a set of GNNs into RecGNN (Recurrent GNN), ConvGNN (Convolutional GNN), GAE (Graph AutoEncoder), and STGNN (Spatial-Temporal GNN). RecGNNs aim to learn node representations via recurrent structures, introducing the concept of message passing, where nodes exchange information with neighboring nodes until reaching a stable state. This message passing idea is adopted by ConvGNNs. ConvGNNs generalize the convolution from Euclidean data space to non-Euclidean data space, providing a foundation for constructing other complex GNNs. GAEs are an unsupervised learning model that encodes nodes or graphs into a latent vector space and generates new graphs using embedded graph information. STGNNs focus on learning hidden patterns of graphs that change spatio-temporally, considering the spatio-temporal correlations of graph information simultaneously. We summarize the GNN categories in Table 1. For a further review of graph neural networks, we refer the readers to [16; 17; 18] and the references therein. In this paper, we aim to predict the workload of each MECS by considering the relationship among the MECSs both in the time domain and the space domain. An MEC system consists of MECSs, which are deployed at the network edge. In an MEC system, control messages are exchanged between geographically adjacent MECSs for the efficient operation of the system. Therefore, by considering MECSs as nodes and the geographical relationships between adjacent MECSs as links, the MEC system can be modeled as a graph. Since an MECS serves tasks offloaded by users, the load of an MECS is determined by the number of users and their task-offloading patterns within the MECS service area. Additionally, the locations of users change over time, and the mobility of users is physically constrained within a certain distance over a specified period. Consequently, changes in the user set for each MECS over time impact the user set of neighboring MECSs, influencing the load of each MECS based on the load of neighboring MECSs. In other words, the load of each MECS is closely related with the load of its neighboring MECSs over time and space. Due to its ability to consider spatio-temporal correlations among the related entities, STGNN is being applied to various applications. For example, in [19], STGNN is used for road traffic prediction by exploiting complex spatio-temporal correlation of traffic flow. In [20], STGNN is used for skeleton-based human action cognition by making use of the skeleton topology information. Motivated by these research trends and the characteristics of the load distribution in an MEC system, we chose STGCN which belongs to the STGNN category for predicting the load distribution in an MEC system. Specifically, we extract node features by representing the spatio-temporal relationships among the loads of each MECS by adopting STGCN.