## 5 Evaluated Algorithms
### Carbon- and Power-Efficient Optimal Frequency VM Placement (C-PEF)
Table 10 presents the power consumption and carbon footprint values observed with dynamic PUE under the same workload used for the observed values in Table 5 for fair comparison. Dynamic PUE reduces the carbon footprint by approximately 50%, as shown in Table 10. The RVA percentages for C-FFF and C-PE displayed in Table 11 show a slight dip at the beginning and then a significant increase of 1%. Table 12 shows the overall statistics for CPU utilization and power consumption related to dynamic PUE. The values in Table 10 confirm the impact of dynamic PUE. The power consumption of the C-PE algorithm is reduced by approximately 55% compared to static PUE. The power consumption for the mean CPU utilization presented in Tables 9 and 12 reveals the impact of dynamic PUE on power reduction. C-FFF, C-PE, and C-PEF algorithms achieve approximately 14%, 9%, and 15% greater reductions than static PUE. The results support the approach of energy reduction by dynamically adjusting the cooling device load based on the active power consumption of the server for the current workload. Figure 10: Power consumption. Figure 9: Carbon footprint. Let \(n,f\), \(m\), and \(c\) represent the number of VM requests, the fixed DVFS levels, the number of nodes, and number of clusters, respectively. The complexity of the C-PE algorithm is expressed by \(O(ncmlog(m))\). Its complexity is dominated by \(mlog(m)\). The complexity of the proposed C-PEF algorithm is expressed by \(O(nfcmlog(m))\). The C-PEF complexity is \(f\) times that of C-PE. The complexity of the C-FFF algorithm \(O(nfcmlog(c))\) is dominated by \(f\) (fixed frequency level) and \(clogc\). As the number of nodes (\(m\)) in the data center increases, the complexity of the C-PE dominates the overhead caused by the constant \(f\) in C-FFF. The proposed C-FFF algorithm with complexity \(O(nfcmlog(c))\) performs load balancing, while maintaining a better tradeoff between utilization and power consumption than the standard C-PE algorithm with complexity \(O(ncmlog(m))\). ## 8 Conclusions

Energy consumption and carbon footprint problems in data centers are handled using different VM placement algorithms with static and dynamic PUE. The data center energy efficiency metric PUE and carbon usage effectiveness are used as important measures for data center selection. The proposed C-FFF and C-PEF placement algorithms perform placement decisions by maintaining the optimal p-state of the servers. In C-PEF, host selection is based on the power-efficient optimal p-state of the servers. In C-FFF, the host selection is based on the optimal p-state of the servers. Both C-FFF and C-PE are compared with a standard power-efficient algorithm (C-PE), where the host selection is based on the highest power-efficient p-state of the servers. Different VM types with varying execution times and arrival rates are used to simulate the system load. The resulting outcomes for scenario I reveal that C-FFF can reduce the carbon footprint by a minimum of 2% more than C-PE, C-FFL, and C-FF. The experimental results illustrate the importance of considering the DVFS of the servers, along with PUE and carbon release of clusters in data centers. The results for the algorithms in scenario II emphasize the impact of dynamic PUE on the carbon footprints. The C-FF algorithm shows significant improvement over C-FFLE in power reduction, displaying a trade-off between effective resource utilization and power consumption. Among the three power-aware algorithms, C-PEF and C-PE have additional computational overhead due to greedy search function. The results support the fact that C-FFF balances computational overhead and utilization, and stands in between C-PEF and C-PE \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Placement Algorithm** & **Power(kW)** & **Carbon Footprint (Tons)** & **Number of VMs Placed** \\ \hline C-PEF & 564,350.9 & 23.631227 & 1617 \\ C-PE & 628,328.4 & 24.191322 & 1636 \\ C-FFF & 582,335.1 & 24.35445 & 1641 \\ \hline \hline \end{tabular}
\end{table}