# MEC Server Sleep Strategy for Energy Efficient Operation of an MEC System
## 5 Performance Evaluation
### Simulation Environment Setup  
We deploy nine MECSs uniformly across a grid with dimensions of 600 m by 600 m (Figure 3). The service region of each MECS is configured as the surrounding four grids with itself at the center. At the beginning of the simulation, we uniformly deploy 275 users on the topology. Users move around over time according to a random mobility model. In other words, at the start of each time slot, a user changes its moving direction from \((0,2\pi]\), according to the Uniform distribution, and selects its speed from the Normal distribution with a mean 15 m per time slot and a variance of 2.5 m per time slot. To maintain the number of users in the topology, we assume that the top and bottom, as well as left and right, of the system topology are connected. Therefore, for example, when a user moves to the right and exits the topology, we add a new user to the left side of the topology. Figure 3: Simulation topology. Users offload their tasks to the nearest MECS. Initially, we configure that each user generates one task. After the initialization, we dynamically adjust the task generation rate of each user to change the total load imposed on the system over time. If \(Q_{i}(t)\leq Q_{th}\) for all MECS \(i\in\mathcal{M}\) at the start of each time slot \(t\), we increase the task generation rate of each user. The increase rate is randomly selected from \(\{0.05,0.10,0.15,0.20\}\) for each user. When the load imposed on the MEC system exceeds its capacity, the queue length of at least one MECS exceeds \(Q_{th}\). Then, after randomly choosing the decrease rate from \(\{0.05,0.10,0.15,0.20\}\) for each user, we reduce the task generation rate of each user by the chosen rate. As the task arrival rate decreases, the number of sleeping MECS increases. However, in accordance with the second condition of the problem P1, at least three MECSs must remain active to serve users in the MEC system. Therefore, after the reduction in the task generation rate initiates, we consistently decrease the task arrival rate every time slot. This continues until the active MECS count reaches three. At this point, we resume increasing the user's task generation rate by randomly selecting the increase rate from \(\{0.05,0.10,0.15,0.20\}\) for each user every time slot. After conducting the data generation process over 50,000 time slots, we construct the training dataset using task generation rates observed in the initial 35,000 time slots. The subsequent 7500 time slots are designated as the validation dataset, and the final 7500 time slots are allocated for the test dataset. In each dataset, a data sample is defined as a pair \(([x(t),\ldots,x(t-h+1)],x(t+1))\), where \(x(t)=\{\hat{\lambda}_{i}(t):i\in\mathcal{M}\}\). These datasets are used to train the STGCN. After completing the training of STGCN, we generate \(x(t)\) for 1000 time slots via the same data generation process. We then evaluate the performance of the proposed method by inputting them into the trained STGCN. We set \(P_{m}=20W\), \(\alpha=0.5\), and \(F_{i}=75\) tasks per time slot. We also set the maximum queue length of each MECS (\(Q_{M}\)) to 75 and \(Q_{th}=Q_{M}/2\). We configure the length of the task-load history as \(h=12\). For the genetic algorithm, we set \(n=|X_{c}|=20\) and \(n_{g}=20\). We use the publicly known values of the LSM model and STGCN model for configuring their hyperparameters. Specifically, we use the hyperparameters in [39] to configure the hyperparameters of the LSTM model and employ the hyperparameters in [40] to configure the STGCN model. One hidden layer with 64 units is used for the LSTM model. Since one LSTM model has 16,961 parameters and there are nine MECS, a total of 152,649 parameters are used when the LSTM method is used. The STGCN model is composed of two ST-Conv blocks and one output layer. The units in the first ST-Conv block is (64, 32, 64) and the units in the second ST-Conv block is (64, 32, 128). The output layer has (256,128) units.