## 5 Evaluated Algorithms
### Carbon- and Power-Efficient Optimal Frequency VM Placement (C-PEF)
### Physical Machine and VM Reservation Modeling

Table 1 shows model of physical machines with varying power models to simulate heterogeneity and configurations of heterogeneous systems taken from the SPEC power benchmark [53] used in the simulation. Table 2 presents the power consumption, with equal CPU utilization distribution ranging from 0% to 100%. The power calculation for the periods in between intervals is estimated based on Equation (4). For example, the power consumption with 13% CPU utilization for power model 1 is between 10% and 20%,while the resulting power is 64.14 W based on ((13%-10%)/(20%-10%) \(\times\)(66-63)) + 63 with reference to Table 2.

To evaluate the proposed algorithms, 4 small-scale data centers with 100 heterogeneous systems are used to model infrastructure-as-a-service(IaaS).The VM characteristics for elastic compute units (ECU) shown in Table 3 are used to model the virtual machine reservations. Each data center is assumed to have 2 clusters with varying values for carbon footprint rates. The carbon footprint rates of clusters and PUE values of data centers are considered based on [55; 56], as presented in Table 4. The workload is generated based on the Lublin-Feitelson model [57]. By taking advantage of the arrival rate, gamma, and hyper-gamma Lublin parameters, the bag-of-tasks and web requests are generated, which have long and short holding times, respectively, as compared to the VM types given in Table 3 (shown in Figures 3 and 4). Figure 3 depicts the variation in the numbers of requests in each reservation cycle. Figure 4 presents the total number of CPU utilization requests received from the VMs concerning different reservation cycles. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Machines**} & **Frequency** & **No. of** & **Power** & **Memory** & **Storage** & **Network** \\  & **(GHz)** & **Cores** & **Model** & **(GB)** & **(GB)** & **Bandwidth (Mbps)** \\ \hline M1 & 2 & 2 & 1 & 16 & 2000 & 1000 \\ M2 & 4 & 4 & 1 & 32 & 6000 & 1000 \\ M3 & 4 & 8 & 2 & 32 & 7000 & 2000 \\ M4 & 8 & 8 & 2 & 64 & 7000 & 4000 \\ M5 & 16 & 8 & 2 & 128 & 9000 & 4000 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Physical machine characteristics [24]. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Power Model** & **Idle** & **10\%** & **20\%** & **30\%** & **40\%** & **50\%** & **60\%** & **70\%** & **80\%** & **90\%** & **100\%** \\ \hline
1 & 60 & 63 & 66.8 & 71.3 & 76.8 & 83.2 & 90.7 & 100 & 111.5 & 125.4 & 140.7 \\
2 & 41.6 & 46.7 & 52.3 & 57.9 & 65.4 & 73 & 80.7 & 89.5 & 99.6 & 105 & 113 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Power (in watts) model of physical machines (PMs) [24]. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Name** & **ECU** & \begin{tabular}{c} **Core Speed** \\ **(GHz)** \\ \end{tabular} & \begin{tabular}{c} **Memory** \\ **(MB)** \\ \end{tabular} & \
\begin{tabular}{c} **Storage** \\ **(GB)** \\ \end{tabular} &
\begin{tabular}{c} **Network Band** \\ **Width (Mbps)** \\ \end{tabular} & **Probability** \\ \hline M1.small & 1 & 1 & 1740 & 160 & 500 & 0.25-BT \\ M1.large & 2 & 4 & 7680 & 850 & 500 & 0.25-BT/0.12-WR \\ M1.xlarge & 4 & 8 & 15,360 & 1000 & 1000 & 0.08-WR \\ M2 xlarge & 2 & 6.5 & 17,510 & 1000 & 1000 & 0.12-WR \\ M22.xlarge & 4 & 13 & 35,020 & 1000 & 1000 & 0.08-WR \\ C1.median & 2 & 5 & 1740 & 500 & 500 & 0.1-BT \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Virtual machine request types [24]. ## 7 Results and Discussions

The workload data described above are used to evaluate the proposed VM placement algorithms C-PEF and C-FFF against C-PE, C-FF, and C-FFLE approaches. The C-FFLE algorithm is used to show the impact on power consumption when only resource usage is considered as a parameter in the heuristic approach. The C-FF is the first-fit placement algorithm, which is used for initial placement for all algorithms in this work. The other algorithms improve the placement strategy for power reduction as an extension of C-FF.