## 5 Performance Evaluation
### Impact of Prediction Error  
To compare the performance of each method in a real operating scenario where \(\tilde{\lambda}_{i}(t)\)s are not known in advance, we conduct simulation experiments using the workload distribution across the MEC system during a time slot \(t\), which is predicted by the controller at the beginning of the time slot. In other words, instead of \(\tilde{\lambda}_{i}(t)\)s, we use \(\tilde{\lambda}_{i}(t)\)s predicted by STGCN. In addition, to focus on comparing how each method determines \(\eta(t)\) when the same \(s(t)\) is given, we apply the same state information to all methods, which is derived from \(\eta(t)\) selected by the \(ES_{R}\) at the beginning of each time slot \(t\). To analyze the impact of prediction errors, we also experiment with the \(ES_{P}\) method that determines \(\eta(t)\) by using \(\tilde{\lambda}_{i}(t)\)s predicted by STGCN. We measure the \(\zeta(t)\) and the maximum \(\delta_{i}(t)\) in each time slot when each method is used. We draw the distribution of \(\zeta(t)\) in Figure 7 and the distribution of the longest \(\delta(t)\) in Figure 8. In Table 4, we also show the average energy consumed by the MEC system, the average service delay provided in a time slot, the maximum service delay violation rate, and \(\eta(t)\) decision time when each method is applied. In these figures and the table, we observe that \(ES_{P},GA_{A}\), and our method achieve similar distributions to those obtained when \(ES_{R}\) is used. Analysis of the \(\zeta(t)\) distribution reveals that while the proposed method exhibits a shorter tail distribution compared with \(ES_{P}\) and \(GA_{A}\), it shows a slightly higher number of MECSs in the active state. Specifically, the percentage of cases where four or more MECSs become active is 11.8% for \(ES_{R}\), 10.4% for \(ES_{P}\), 11.8% for \(GA_{A}\), 17.7% for \(GA_{T}\), and 18.1% for the proposed method. Consequently, our experimental results indicate that our method incurs slightly higher average energy consumption compared with \(ES_{P}\) and \(GA_{A}\) while achieving a little lower average delay characteristics. However, when we inspect the violation rate, our method achieves the smallest violation rate. When \(GA_{A}\) is used, the violation rate is 14%, and it is 15% when \(GA_{T}\) is used. Notably, even when ES is used to determine \(\eta(t)\), the violation rate is as high as 17%. This is attributed to the way that ES and GA determine solutions. Even though the prediction error caused by STGCN is small, \(\tilde{\lambda}_{i}(t)\) is different from \(\tilde{\lambda}_{i}(t)\). The prediction errors create a discrepancy between the actual and predicted states. Since ES and GA are search methods, they do not learn the similarity between the actual and predicted states but instead treat them independently when they find an optimal solution for each given state. Because they determine the optimal \(\eta(t)\) for the predicted state at the start of a time slot, applying this \(\eta(t)\) to the actual state can increase the probability of violating the maximum service delay constraint. In contrast, DQN is a learning method that can learn intrinsic features of similar states. Specifically, DQN embeds states closer together in the feature space when the similarity between them is high. Therefore, even if a discrepancy arises between the actual and predicted states due to prediction errors, DQN is likely to output the same \(\eta(t)\) for both if the difference is not significant. As a result, our method shows the smallest violation rate. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \(ES_{R}\) & \(ES_{P}\) & \(GA_{T}\) & \(GA_{A}\) &
\begin{tabular}{c} **Our** \\ **Method** \\ \end{tabular} \\ \hline Avg. energy (W) & 38.98 & 38.38 & 46.26 & 38.74 & 42.72 \\ \hline Avg. delay (s) & 0.22 & 0.26 & 0.24 & 0.25 & 0.19 \\ \hline Violation rate (\%) & 0 & 17 & 15 & 14 & 9 \\ \hline Decision time (ms) & 1.22 & 1.22 & 0.45 & 9 & 0.45 \\ \hline \hline \end{tabular}
\end{table}