## 5 Performance Evaluation
### Impact of Prediction Error

Table 4: Performance comparison in the presence of \(\tilde{\lambda}_{i}(t)\) prediction error. To analyze these reasons more deeply, we measure the rate at which \(\eta(t)\)s determined by each method are the same as those obtained by \(ES_{R}\) for the Euclidean distance between \(\tilde{\lambda}(t)\) and \(\tilde{\lambda}(t)\). We denote this Euclidean distance by \(d_{\lambda}(t)\) and show the results in Figure 9. In this figure, we observe that the proposed method determines the same \(\eta(t)\) as \(ES_{R}\) more frequently than the other methods. The rate at which \(ES_{P}\) outputs the same \(\eta(t)\) as \(ES_{R}\) is 60.49%; for \(GA_{A}\), it is 60.84%, and for \(GA_{T}\), it is 8.74%. In contrast, 84.27% of the \(\eta(t)\)s determined by the proposed method are the same as those decided by \(ES_{R}\), which is the highest among the methods. Figure 7: Comparison of the distribution of \(\zeta(t)\). When we compare our method to \(GA_{T}\), the \(\eta(t)\) decision time of our method is the same as that of \(GA_{T}\). However, as we can see in Figures 7 and 8 and Table 4, the results obtained by our method are closer to the optimal results acquired by \(ES_{R}\). To analyze the underlying causes, in Table 5, we show the rates at which each server is selected to be in an active state by \(ES_{R}\), our method, and \(GA_{T}\). We can see that when the proposed method is applied, the rate at which each server is selected to be active is more similar to the rate when \(ES_{R}\) is applied compared with \(GA_{T}\). Especially when \(GA_{T}\) is used, the rate at which each server is selected to be active is almost uniform. The result indicates that given that the load status of the MEC system dynamically varies over time, the proposed method adapts by activating only the necessary servers as \(ES_{R}\). In contrast, because \(GA_{T}\) has insufficient search time, it tends to select each server uniformly and fails to accurately reflect the load status of the MEC system. Consequently, compared with \(GA_{T}\), our method reduces both the amount of energy consumed by the MEC system and the average delay  
Figure 8: Comparison of the distribution of the longest \(\delta_{i}(t)\). that the system provides in each time slot. Additionally, the proposed method reduces the violation rate of the maximum service delay by 6% compared with \(GA_{T}\). We also note that from Tables 3 and 4, the difference in the violation rate is 2% when our method is used, which is the smallest among the methods. Because of the feature representation capability of DQN that embeds similar states in closer proximity within the feature space, our method is more robust against the prediction error than other methods. The collective findings from these simulation investigations lead to the following conclusions. In the presence of prediction errors in the workload distribution, the proposed method shows superior performance compared with both \(ES_{P}\) and \(GA_{A}\) in terms of the maximum service delay violation rate and \(\eta(t)\) decision time. Additionally, the proposed method outperforms \(GA_{T}\) across all metrics, including energy consumption, average service delay, and the violation rate. Furthermore, compared with other methods, the proposed approach is less sensitive to workload prediction errors.