## 5 Evaluated Algorithms
### Carbon- and Power-Efficient Optimal Frequency VM Placement (C-PEF)
The C-FFF placement algorithm consumes 2%, 15%, and 2.8% less power than C-PE, C-FFLE, and C-FF, respectively. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Reservation**} & \multicolumn{4}{c}{**Minimum CPU Utilization \%**} & \multicolumn{4}{c}{**Number of Hosts with 100\% CPU Utilization**} \\ \cline{2-11}
**Interval** & **C-PEF** & **C-PE** & **C-FFF** & **C-FFE** & **C-FF** & **C-PEF** & **C-FFF** & **C-FFE** & **C-FFF** \\ \hline
1 & 40.625 & 50 & 25 & 50 & 50 & 17 & 23 & 17 & 35 & 33 \\
2 & 31.25 & 62.5 & 25 & 50 & 62.5 & 19 & 42 & 27 & 62 & 56 \\
3 & 40.625 & 50 & 40.625 & 62.5 & 62.5 & 56 & 75 & 64 & 96 & 91 \\
4 & 62.5 & 62.5 & 40.625 & 50 & 62.5 & 91 & 101 & 94 & 127 & 118 \\
5 & 62.5 & 50 & 50 & 50 & 62.5 & 113 & 121 & 117 & 152 & 138 \\
6 & 50 & 40.625 & 40.625 & 62.5 & 62.5 & 125 & 146 & 135 & 173 & 159 \\
7 & 62.5 & 62.5 & 40.625 & 50 & 40.625 & 142 & 162 & 153 & 188 & 172 \\
8 & 31.25 & 62.5 & 31.25 & 40.625 & 62.5 & 156 & 176 & 164 & 204 & 189 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Processor utilization for 100% RVA. Figure 5: Active PMs with 100% RVA (first 8 reservation cycles). Figure 6: _Cont._

Figure 6: (a)Power consumption and (b) carbon footprint of all algorithms with 100% RVA. Figure 7: (a)Power consumption and (b) carbon footprint comparisons of all algorithms. In Table 5, the carbon footprint values for C-FFF and C-PEF are about 2.30% and 3.18% lower than for C-PE, respectively, with an increased RVA of 1.2%. C-FFLE and C-FF algorithms have 19.89% and 1.23% greater carbon footprints than C-PE, respectively. Table 8 depicts the substantial improvement in VM request acceptance for C-PEF and C-FFF algorithms compared with other heuristic approaches with different numbers of VM requests. The C-FFF and C-PEF algorithms have approximately 1% higher RVA percentage than other counterparts. The statistical analysis presented in Table 9 supports the fact that the C-FFLE algorithm, which is based on resource utilization, operates with maximum utilization compared to other approaches. The C-FFF, C-PE, and C-PEF algorithms have approximately 1% variation in maximum CPU utilization rates, with similar average utilization rates. With regard to power, the C-PEF placement algorithm's power consumption is 1.64% less than C-FFF. C-FFF consumes 2%, 15%, and 2.8% less power than C-PE, C-FFLE, and C-FF, respectively. The results in Figure 8a,b were obtained by varying the system load with respect to the number of requests in order to measure the power consumption of different algorithms for a single interval with a common initial state. This was done so as to rank the performance of the algorithms from lowest to highest in terms of CPU utilization. Figure 8a displays the power consumption values for all the algorithms, with CPU utilization rates ranging between 40% and 90%. It can be noticed that the C-PEF algorithm shows significant performance improvement between 40%and 85% utilization. Figure 8b presents the carbon footprint values for all of the algorithms for utilization rates above 85%. Above 90% utilization, C-PEF and C-FFF are in close proximity to each other. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Placement Algorithm** & **Power (kW)** & **Carbon Footprint(Tons)** & **Number of VMs Placed** \\ \hline C-FFF & 676,296.2775 & 48.72382575 & 1634 \\ C-PE & 691,256.2894 & 49.87335009 & 1611 \\ C-PEF & 665,341.0031 & 48.28496006 & 1623 \\ C-FFLE & 782,225.6419 & 59.79732901 & 1622 \\ C-FF & 695,623.92 & 50.4902789 & 1598 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Power and carbon footprint for different VM placement algorithms.