# NFV-Enabled Efficient Renewable and Non-Renewable Energy Management: Requirements and Algorithms
## 9 Evaluation
### Analysis for Large-Scale Scenarios  
A set of simulations for large \(N\) values have been conducted in order to demonstrate the scalability of FastTS. These tests have been limited up to \(N=1000\); however, this is by no means a restriction of the applicability of FastTs to larger scenarios. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{\(\rho\)} & \multicolumn{3}{c}{**Case A**} & \multicolumn{3}{c}{**Case B**} & \multicolumn{3}{c}{**Case C**} & \multicolumn{1}{c}{**Case D**} \\ \cline{2-9}  & **Td1** & **Td2** & **Td3** & **Td1** & **Td2** & **Td3** & \(\overline{Td}\) & \(\overline{Td,Pd}\) \\ \hline \(\rho_{P_{\text{Fasts}}}\) & 1 & 0.78 & 0.83 & 1 & 1 & 1 & 0.70 & 0.87 \\ \(\rho_{AR}\) & 1 & 0.78 & 0.83 & 1 & 1 & 1 & 0.73 & 0.97 \\ \(\rho_{P_{LACK}}\) & 1 & 0.92 & 0.98 & 1 & 1 & 1 & 0.71 & 0.95 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Approximation ratio for small-scale scenarios. Figure 17: Example to evaluate the difference between OptTs and FastTs. Parameters: _Case A_, _AR_, and \(T_{d}^{k}=2\) [time slots] for all \(S_{k}\). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Cases** & **Running Time OptTs [s]** & **Running Time FastTs [s]** & \(G_{R}\) \\ \hline _Case A_ & \(5.04\times 10^{5}\) & \(1.00\times 10^{2}\) & \(\sim\)5000\(\times\) \\ _Case B_ & \(9.72\times 10^{5}\) & \(2.20\times 10^{2}\) & \(\sim\)4400\(\times\) \\ Random scenarios, 50 iterations & \(1.87\times 10^{4}\) & \(8\times 10^{1}\) & \(\sim\)230\(\times\) \\ _Case F_ & - & \(3.53\times 10^{0}\) & - \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Average running time in small-scale scenarios. demonstrates that an appropriate value of \(T_{s}^{k}\) for the full utilization of \(P_{ES}\) is the mean size of \(T_{d}^{k}\), since this value represents the complete displacement of the service. However, when considering that the computational complexity depends on \(T_{s}^{k}\), as shown in Equation (30), smaller values of \(T_{s}^{k}\) equal to \(T_{s}^{k}=1\) [time slot] or \(T_{s}^{k}=2\) [time slots] can be used for practical applications. The simulations reveal that the greatest improvements are obtained with small \(T_{s}^{k}\) values. For example, for all random scenarios, with \(T_{s}^{k}=1\) [time slot], the system reaches improvements over the 50%, with \(T_{s}^{k}=2\) [time slots] the improvements are 30% and, as the value of \(T_{s}^{k}\) increases, the percentage of improvement obtained decreases. Thus, this condition demonstrates that, for real implementations, large intervals of \(T_{s}^{k}\) are not required to achieve notable improvements in energy consumption. Regarding the heuristic strategy, the numerical results of the metrics \(P_{RES}\), \(AR\), \(P_{LACK}\) and \(\rho\) (Table 8) indicate that FastTs is able to produce near-optimal or optimal solutions (e.g., in _Case B_) at a very low complexity cost (Table 9). In small scenarios, FastTs offers solutions, which, in the worst case, are within only \(\sim\)1.4 times the optimal result and are at least three orders of magnitude faster than OptTs. In addition, in large-scale scenarios, we have verified that FastTs improves the energy utilization (decrease of \(P_{RES}\) and \(P_{LACK}\) and increase of \(AR\)) and offers improvements of at least 13% for all cases, as long as the strategy considers partitions smaller than six services to guarantee its performance. The simulation results reveal that a controlled increase in the number of partitions can produce high-quality solutions but with a reduced running time, which, in all cases, is of at least an order of magnitude lower than the original partition scheme. Finally, as a final result of the whole paper, Table 11 summarizes the requirements, proposed solutions, and algorithmic strategies in order to carry out an ICT-enabled ecosystem for adaptive energy management restricted to availability.