## 5 Evaluated Algorithms
### Carbon- and Power-Efficient Optimal Frequency VM Placement (C-PEF)
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**RVA% Under Different VM Requests**} \\ \hline
**Algorithm** & **481** & **910** & **1276** & **1591** & **1861** & **2000** \\ \hline
**C-FFF** & 100 & 88.68132 & 81.5047 & 81.58391 & 81.30038 & 81.7909 \\
**C-PE** & 100 & 87.03297 & 80.17241 & 80.32684 & 80.06448 & 80.5903 \\
**C-PEF** & 100 & 88.35165 & 81.03448 & 81.01823 & 80.65556 & 81.14057 \\
**C-FFLE** & 100 & 87.25275 & 80.721 & 81.26964 & 80.60183 & 81.14057 \\
**C-FF** & 100 & 87.03297 & 80.01567 & 80.01257 & 79.36593 & 79.93997 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: RVA for all VM placement algorithms. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**C-FFF**} & \multicolumn{2}{c}{**C-PE**} & \multicolumn{2}{c}{**C-PEF**} & \multicolumn{2}{c}{**C-FFLE**} & \multicolumn{2}{c}{**C-FF**} \\ \hline
**Metric** & \begin{tabular}{c} **\% CPU** \\ **Utilization** \\ \end{tabular} & \begin{tabular}{c} **Power** \\ **(kW)** \\ \end{tabular} & \begin{tabular}{c} **\% CPU** \\ **Utilization** \\ \end{tabular} & \begin{tabular}{c} **Power** \\ **(kW)** \\ \end{tabular} & \begin{tabular}{c} **\% CPU** \\ **Utilization** \\ \end{tabular} & \begin{tabular}{c} **Power** \\ **(kW)** \\ \end{tabular} & \begin{tabular}{c} **\% CPU** \\ **Utilization** \\ \end{tabular} & \begin{tabular}{c} **Power** \\ **(kW)** \\ \end{tabular} & \
\begin{tabular}{c} **\% CPU** \\ **Utilization** \\ \end{tabular} &
\begin{tabular}{c} **Power** \\ **(kW)** \\ \end{tabular} \\ \hline Min & 0.1471 & 1626 & 0.1471 & 1437 & 0.1471 & 1513 & 0.1471 & 2070 & 0.1471 & 1954 \\ Max & 89.12 & \(6.76\times 10^{5}\) & 90.04 & \(6.91\times 10^{5}\) & 88.38 & \(6.65\times 10^{5}\) & 92.46 & \(7.82\times 10^{5}\) & 89.87 & \(6.96\times 10^{5}\) \\ Mean & 48.6 & \(4.49\times 10^{5}\) & 48.91 & \(4.58\times 10^{5}\) & 47.82 & \(4.42\times 10^{5}\) & 50.46 & \(5.17\times 10^{5}\) & 48.97 & \(4.64\times 10^{5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Statistical analysis of different VM placement algorithms. Figures 9 and 10 present the amounts of carbon and power consumed by different power-efficient VM placement algorithms. C-PEF and C-FFF algorithms consume more power initially at lower loads than C-PE, which distributes the loads among all the servers. C-FFLE and C-FF algorithms consume more power as they do not utilize power-efficient allocation. The non-parametric Mann-Whitney U test and Wilcoxon rank sum test are utilized to test whether there is a noteworthy difference in the results obtained. Based on the abovementioned non-parametric tests on two samples for C-PEF with C-PE, C-FFLE, and C-FF, the \(p\)-values obtained are less than 0.0001. Therefore, it can be concluded that DVFS-aware scheduling (C-PEF and C-FFF) makes a significant difference compared with standard power-aware scheduling(C-PE) and other heuristic approaches interms of energy consumption. The difference between the two DVFS-aware algorithms, C-PEF and C-FFF, is not substantial (\(p\)-value of 0.76 \(>\) 0.05). Figure 8: (**a**) Power consumption values with low utilization. (**b**) Carbon footprint values with high utilization. C-PEF and C-FFF are compared with other algorithms in terms of CPU utilization. ### Scenario-II: Energy-Efficient Mapping of VMs to PMs with DynamicPUE

The power usage effectiveness is the metric used to analyze the efficiency of a datacenter. This is the ratio between the total energy requirements of a data center (total facility power) and the power consumed by IT devices. In total, 60% of the energy consumption is due to cooling device power consumption, which has a direct impact on PUE. The proposed power-aware algorithms C-FFF and C-PEF, along with the standard C-PE algorithm, are considered in scenario II to analyze the impact of dynamic PUE on carbon footprint values, based on Equation (11).