## 5 Evaluated Algorithms
### Carbon- and Power-Efficient Optimal Frequency VM Placement (C-PEF)
In this work, along with initial placement, C-FF is used separately to model the worst possible power consumption. Naturally, the C-FFLE and C-FF algorithms will have worse performance than the power management algorithms. The C-PE algorithm is considered as a fair measure to evaluate power management approaches. * Reduction in Overall Carbon Footprint \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Data Center**} & **Carbon Footprint Rate** & **PUE** \\  & **(CFR) in Tons/MWh** & **2.1** \\ \hline DC\({}_{1}\) & 0.124, 0.147 & 1.56 \\ DC\({}_{2}\) & 0.350, 0.658 & 1.7 \\ DC\({}_{3}\) & 0.466, 0.782 & 1.9 \\ DC\({}_{4}\) & 0.678, 0.730 & 2.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Datacenter features [24]. Figure 4: Processor demand at different intervals

Figure 3: VM Request arrivalThe reduction of grid energy consumption in datacenters is considered as a crucial metric for carbon footprint reduction. Equation (7) formulates the total carbon footprint emission of data centers. The ratio of VM acceptance (RVA)

The RVA is considered as a measure of service level agreement (SLA). The RVA is the ratio between the number of VM requests placed and the number of requests submitted. ### Scenario-I: Energy-Efficient Mapping of VMs to PMs with StaticPUE

The VM placement algorithms are evaluated based on the reduction of the carbon footprint with static PUE, as shown in Table 4. Figure 5 and Table 5 present the number of active PMs for the same utilization level, with 100% RVA for all algorithms. In order to interpret the number of active PMs shown in Table 5, this has to be compared with the minimum and maximum utilization levels given in Table 6 for each interval. In C-PE, for 10% utilization, the number of active PMs is 36 with a minimum utilization 50% and the number of PMs with 100% utilization is 23. These numbers are far greater than C-FFF and C-PEF, for which the number of active PMs is 17, with minimum utilization ranging between 25% and 40.6%. The C-PE placement strategy utilizes a lower number of PMs with the maximum utilization possible for the current workload, but the C-FFF and C-PEF algorithms utilize the maximum number of PMs with the minimum possible utilization level and a lower number of fully utilized PMs. The results show that distribution of the load among the servers using DVFS with C-FFF and C-PE algorithms limits the percentage of load received at each interval. This approach does not lead to optimal results with very low loads. The minimum load required for best result depends on the machine configuration and power model. According to our specifications, repeated execution with different VM requests shows that20% is the minimum load. For the C-PEF algorithm, the optimal load requirement is less than C-FFF, because in spite of DVFS, it uses the greedy approach, which limits load distribution. It can be noticed that the C-FF algorithm achieves a significant improvement over C-FFLE, displaying a trade-off between effective resource utilization and power consumption. The utilization results presented in Table 6 prove the above algorithm strategies. Figure 5(a),b and Table 5 illustrates the power consumption for all algorithms at 100% RVA for the first 8 intervals, the power consumption of the C-PEF algorithm is 3.79% lower than for C-FFF, while the power consumption for C-FFF is 2.26% lower than C-PE, 21.75% lower than C-FFLE, and 12.08% lower than C-FF. Based on the cumulative carbon footprint depicted in Figure 5(b), which is equivalent to the power given in Table 5, the C-PEF reduces the carbon footprint to 4.09%, while C-PE, C-FFLE, and C-FF reduce the carbon footprint to 3.35%, 38.8%, and 17.6%, respectively. Based on Figure 6(a) and Table 7, the total power consumed by the servers using the C-PEF placement algorithm is reduced by 1.61%. The C-FFF algorithm reduces power consumption by2.16%, 13.54%, 2.77% when compared to C-PE, C-FFLE, and C-FF, respectively. Based on Figure 6(b) and Table 7, the C-PEF placement algorithm's carbon emission is 1.64% less than C-FFF.