# MEC Server Sleep Strategy for Energy Efficient Operation of an MEC System
## 5 Performance Evaluation
### Combined Effect  
To evaluate the combined effects of the task arrival rate prediction and the sleep control vector determination, we compare the performance of the proposed method (STGCN-GA) with that of the following two techniques. The first method denoted by True-ES is an ideal method that determines \(\Omega(t)\) via the exhaustive search by using the true task arrival rates \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**STGCN**} & \multicolumn{2}{c}{**LSTM**} \\ \hline
**MECS** & **MAE** & **RMSE** & **MAE** & **RMSE** \\ \hline
3 & 2.94 & 3.85 & 3.26 & 4.23 \\
4 & 2.30 & 2.98 & 2.54 & 3.27 \\
8 & 3.50 & 4.45 & 3.90 & 5.04 \\ Total & 3.00 & 3.88 & 3.38 & 4.36 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of task arrival rate prediction accuracy. MECS 3 is located at the side, MECS 4 is located at the center, and MECS 8 is located at the vertex of the topology. Total represents the case where all the MECSs are considered when calculating MAE and RMSE. \(\{\hat{\lambda}_{i}(t)\}\). The second method uses GA to determine \(\Omega(t)\) by exploiting the task arrival rate predicted by the LSTM model. Henceforth, we denote the second method as LSTM-GA.  
Figure 4: Comparison of task arrival rate error distributions. The term ‘Total’ represent the case where all MECSs are considered. (**a**) LSTM, MECS 3, (**b**) STGCN, MECS 3, (**c**) LSTM, MECS 4, (**d**) STGCN, MECS 4, (**e**) LSTM MECS 8, (**f**) STGCN, MECS 8, (**g**) LSTM, Total, and (**h**) STGCN, Total. We denote the energy consumed at an MECS \(i\) during a time slot \(t\) when True-ES is used as \(e_{i}^{TE}(t)\). We also denote by \(e_{i}^{LG}(t)\) the energy consumed at an MECS \(i\) during a time slot \(t\) when LSTM-GA is used. We represent the energy consumed at an MECS \(i\) by our method during a time slot \(t\) as \(e_{i}^{SG}(t)\). In Figure 7, we show the box plots of \(\delta_{i}^{e,LG}(t)=e_{i}^{TE}(t)-e_{i}^{LG}(t)\) and \(\delta_{i}^{eSG}(t)=e_{i}^{TE}(t)-e_{i}^{SG}(t)\). To facilitate the comparison, the ranges of the y-axis in all subfigures are shown to be the same. We observe that the energy consumed by the proposed method is closer to the ideal value obtained by the True-ES method than the energy consumed by LSTM-GA. Specifically, \(Q_{2}\) of \(\delta_{i}^{e,LG}(\forall i\in\mathcal{M})\) is \(-0.52\) while \(Q_{2}\) of \(\delta_{i}^{e,SG}(\forall i\in\mathcal{M})\) becomes \(-0.28\). In addition, the IQR of \(\delta_{i}^{e,LG}(\forall i\in\mathcal{M})\) is \(14.10\) and the IQR of \(\delta_{i}^{e,SG}(\forall i\in\mathcal{M})\) decreases to \(12.74\). To investigate the difference between the queue length generated by our method and LSTM-GA and the ideal queue length generated by True-ES, we introduce the following symbols. We denote the difference between \(\bar{Q}(t)\) obtained by True-ES and that acquired by our method as \(\delta_{i}^{q,SG}(t)\). We also denote the difference between \(\bar{Q}(t)\) obtained by True-ES and \(\bar{Q}(t)\) when LSTM-GA is used as \(\delta_{i}^{q,LG}(t)\). Then, we show the distribution of \(\delta_{i}^{q,SG}(t)\)  
Figure 5: Distribution of the difference in \(E(t)\) between ES and GA. (**a**) Box plot; (**b**) Histogram. Figure 6: Distribution of the difference in \(\bar{Q}(t)\) between ES and GA. (**a**) Box plot; (**b**) Histogram. and \(\delta_{i}^{q,LC}(t)\) in Figure 8. We observe that \(\delta_{i}^{q,SG}(t)\) is closer to zero than \(\delta_{i}^{q,LC}(t)\), which means that the proposed method makes the queue length more similar to the ideal \(\bar{Q}(t)\) obtained by Tru-ES compared to LSTM-GA. Specifically, the median of \(\delta_{i}^{q,LC}(t)\) is 0.56 while the median of \(\delta_{i}^{q,SG}(t)\) is 0.47, which corresponds to a 16.07% reduction. In addition, the IQR of \(\delta_{i}^{q,LC}(t)\) is 4.20 while the IQR of \(\delta_{i}^{q,SG}(t)\) is 3.87. Thus, the proposed method decreases the IQR of the queue length difference by 7.86%.