## 3 VM Consolidation Model
### Power Consumption Minimization for DC  
The purpose of VM consolidation is to minimize power consumption for energy efficient management of a DC. In the recent operation environment of the DC, accurate power consumption data can be collected through the IoT sensors embedded in a server. However, it is difficult to identify the power consumption of a particular system. Similarly, new PM-VM mapping information obtained by the VM consolidation needs to be estimated since it is a plan that has not yet been implemented.  
[PERSON] et al. presented the power consumption estimation model to estimate the power consumption of a particular system by analyzing the power consumption data from thousands of PMs. The analysis results show strong correlations between power consumption and CPU utilization, and the power consumption tends to increase linearly when utilization of the CPU changes from idle to full utilization [35].  
Based on the model by [PERSON] et al., the estimated power consumption of the PM is calculated as shown in Equation (4).  
\[W(i)=\left\{\begin{array}{l}W_{idle,\;i}+\left(W_{busy,\;i}-W_{busy,\;i} \right)\times\;\epsilon_{i}\;\;\sum\limits_{j=1}^{V}x_{i  
migrated to a destination PM, which is then considered as the primary PM, and the VM that is in the source PM is abandoned. During activation, the VM is activated after appropriate actions for the destination PM, such as connection of the device drivers and change of IP addresses.  
This study calculates the migration cost to avoid VM migration and reflects this in the VM consolidation model. Factors affecting the VM migration are the memory size of the VM, page dirty rate, CPU utilization of the source/destination PM, network bandwidth, and application sensitivity. Accurate calculation of the VM migration considering all of these factors have challenges. Therefore, this study considers the VM migration cost proposed by [PERSON] et al., as shown in Equation (6) [36].  
\[MC_{j}=m_{j}\times dRatio_{j}\times sen_{j} \tag{6}\]  
VM migration sends the memory page, so it correlates with the memory size (\(m_{j}\)) of the VM. Page dirty rate (\(dRatio_{j}\)) is also considered to calculate the migration cost since a higher percentage of the page dirty rate increases the number of memory pages during migration. In addition, migrating a VM to the destination PM is achieved through the network associated with a network bandwidth. Application sensitivity (\(sen_{j}\)) is defined as a variable considering a network-intensive VM with the heavier burden of the migration process from providing streaming services compared to a VM that is not network-intensive.  
The current allocation information of the PM-VM(\(x\)) is changed to \(x^{\prime}\) according to the VM consolidation condition. VM migration cost from VM consolidation \(MC(x^{\prime})\) is  
Figure 4: Procedure of precopy migration.  
calculated by Equation (7). The absolute value of the difference between \(x\) and \(x^{\prime}\) indicates the number of changed VMs when the source and destination PMs are compared, and half of the absolute value represents the number of migrated VMs. The total VM migration cost \(MC(x^{\prime})\) is calculated by multiplying the number of migrated VMs and the migration cost \(MC_{j}\). \(Max(MC)\) represents the cost when all the VMs are migrated.  
\[MC\big{(}x^{\prime}\big{)}=\frac{1}{2}\times\sum_{i=1}^{P}\sum_{j=1}^{V}\lvert x _{ij}-x^{\prime}_{j}\rvert\times MC_{j} \tag{7}\]  
\[Max(MC)=\sum_{j=1}^{V}MC_{j} \tag{8}\]