## 5 Performance Evaluation
### Performance Comparison in the Absence of Prediction Error  
To focus on comparing the MECS status vector determination performance of each method, we remove the prediction errors included in \(\bar{\lambda}_{i}(t)\). In other words, we configure that at the beginning of each time slot \(t\), \(\bar{\lambda}_{i}(t)\) is known to the controller in advance. Furthermore, to ensure a fair comparison, we evaluate all methods by using identical state information determined by \(\eta(t)\), which is selected by ES per time slot. Specifically, the next state is determined by applying \(\eta(t)\) determined by the ES at the beginning of a time slot \(t\). This resulting state is used as input for each respective method.  
Table 3 compares the performance of each method in terms of the average energy consumed by the MEC system, the average delay per time slot that the system provides, the violation rate at which the system's maximum delay exceeds \(\delta_{th}\), and the time required to decide \(\eta(t)\). Because the errors involved in predicting \(\bar{\lambda}(t)\) are removed and \(GA_{A}\) conducts sufficient iterations for solution searching, its results most closely match those of \(ES_{R}\) in all performance metrics. However, the decision time of \(GA_{A}\) is 9 ms, which is 20 times higher than the proposed method's 0.45 ms. When compared with \(GA_{T}\), which has the same decision time as the proposed method, the proposed method reduces system energy consumption and decreases the average delay. To scrutinize the results, we collect the Hamming distance \(d_{h}(t)\) between \(\eta(t)\) obtained by \(ES_{R}\) and that determined by each method and show their box plots in Figure 6.  
In this figure, we observe that the Hamming distance is the smallest when \(GA_{A}\) is used because the probability that GA produces the same \(\eta(t)\) as that of the \(ES_{R}\) increases with its search time. This result leads to the conclusion that \(GA_{A}\) produces the most similar results to those of \(ES_{R}\) in an environment where there is no \(\bar{\lambda}(t)\) prediction error. When we compare \(GA_{T}\) to our method, our method achieves a smaller Hamming distance. Accordingly, the results obtained by our method are closer to those of the \(ES_{R}\) than those of \(GA_{T}\). In other words, compared with \(GA_{T}\), our method reduces both the system energy  
Figure 6: Box plot for the Hanmming distance between \(\eta(t)\) obtained by \(ES_{R}\) and \(\eta(t)\) determined by each method.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \(ES_{R}\) & \(GA_{T}\) & \(GA_{A}\) & **Our Method** \\ \hline Avg. energy (W) & 38.98 & 47.11 & 39.15 & 43.54 \\ \hline Avg. delay (s) & 0.22 & 0.21 & 0.22 & 0.18 \\ \hline Violation rate (\%) & 0 & 2 & 0 & 7 \\ \hline Decision time (ms) & 1.22 & 0.45 & 9 & 0.45 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Influence of \(\eta(t)\) when \(\bar{\lambda}_{i}(t)\)s are known in advance (\(ES_{R}\) represents the case where ES is used for determining \(\eta(t)\)).  
consumption and the average service delay. Regarding the violation rate, \(GA_{A}\) has a rate of 0% because its \(d_{h}(t)\) is almost zero, while \(GA_{T}\) exhibits a rate of 2%, and the proposed method shows a rate of 7%. However, it should be noted that \(GA_{T}\) fails to determine \(\eta(t)\) for a given input in 7% of cases due to insufficient search time. Therefore, considering such error cases, the performance of the proposed method and \(GA_{T}\) is similar in terms of the violation rate in an ideal scenario in which predicting \(\tilde{\lambda}(t)\) is free from any error.