# Dependency Analysis based Approach for Virtual Machine Placement in Software-Defined Data Center
## 5 Simulation Results and Analysis
### Simulation Results of Small Network  
Figure 5 shows a simple leaf-spine data center network, which comprises two spine switches, three leaf switches, and three PMs. Ten VMs are placed among the PMs with a simple placement plan, which enables additional VMs to be placed on other PMs if the remaining resources of the currently used PM are not sufficient to host the additional VMs. The necessary resources for each VM and the resources available on each PM are shown in Tables 1 and 2, respectively. Additionally, the VMs are separated into two traffic-dependency groups: odd-numbered VMs are in dependency Group \(1\) and even-numbered VMs are in dependency Group 2. The data rates between VMs in the same dependency group are randomly selected from values generated according to a Gaussian distribution, and the data rates between VMs in different dependency groups are randomly selected from values generated according to a uniform distribution. Each simulation result reported here is the average values from 100 runs.  
First, the data rates between VMs in dependency Groups 1 and 2 are set according to Gaussian distributions, each having a standard deviation (SD) of 100 Mbps but having different mean values of 1000 and 1500 Mbps, respectively. The data rates between the VMs in different dependency groups are set according to a uniform distribution ranging from 0 to 100 Mbps. The result of a PCA-based traffic-dependency analysis on this configuration is shown in Figure 6. VMs belonging to the same dependency group are placed closely, indicating that the SP algorithm successfully identifies the traffic dependencies of the VMs.  
We analyzed the effectiveness of the SP for different data traffic patterns between the VMs in terms of the resulting data rate in the physical network. Numerical simulations were conducted with  
\begin{table}
\begin{tabular}{l c c c} \hline \hline  & **CPU (cores)** & **Memory (GB)** & **Storage (GB)** \\ \hline PM1 & 10 & 20 & 700 \\ PM2 & 12 & 23 & 420 \\ PM3 & 11 & 27 & 250 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Available resources in each PM.  
Figure 5: Simple data center network topology.  
Figure 6: PCA-based dependency analysis.  
different mean and SD values for the Gaussian distribution used to set the data rates between VMs within the same dependency group and different maximum values for the uniform distribution used to set the data rates between VMs in different dependency groups.  
The simulation results are shown in Figure 7. Figure 7a shows the effect of the mean value of the Gaussian distribution used for setting the data rates between the VMs in dependency Group 2 (in the range of 100-1500 Mbps) on the data rate in the physical network. The result shows that the performance of the proposed SP scheme improves considerably as the mean data rate increases. The effect of the SD of the Gaussian distribution of the data rates between VMs in dependency Group 2 (in the range of 100-1500 Mbps) on the data rate in the physical network is shown in Figure 7b. The result shows that the use of the SP algorithm considerably decreases the data rate in the physical network compared to when the naive scheme is used. Moreover, the effect of the maximum value of the uniform distribution of the data rates between VMs in different dependency groups is shown in Figure 7c. As the maximum value increases, average data rate between the VMs of different dependency groups increases and becomes closer to the data rates between the VMs in the same dependency group.