# Dependency Analysis based Approach for Virtual Machine Placement in Software-Defined Data Center
## 6 Emulation Results and Analysis
### Emulation Results  
The first emulation was conducted to evaluate the effect of the number of dependency groups on the data rate in the physical network. The VMs were distributed randomly but equally to each dependency group. Since there were 120 VMs, the numbers of VMs in the dependency groups  
Figure 10: Amount of traffic in the physical network with respect to number of VMs.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline  & **CPU (Cores)** & **Memory (GB)** & **Storage (TB)** \\ \hline PM1 & 39 & 101 & 3.0 \\ PM2 & 31 & 70 & 2.7 \\ PM3 & 29 & 44 & 1.8 \\ PM4 & 27 & 56 & 1.2 \\ PMS5 & 34 & 57 & 2.0 \\ PM6 & 39 & 91 & 3.0 \\ PM7 & 34 & 72 & 2.4 \\ PM8 & 50 & 89 & 3.0 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Available resource in each PMwere 60:60, 40:40:40, 30:30:30:30, 24:24:24:24:24, and 20:20:20:20:20 when there were 2-6 dependency groups, respectively. With one dependency group, all VMs belonged to the same dependency group. The second emulation was conducted to measure the performance of the SP in terms of the traffic amount in the physical network when VMs were assigned unevenly to two dependency groups in various ratios. Within two dependency groups, the ratio of the numbers of VMs in the groups was varied as 12:0, 11:1, 10:2, 9:3, 8:4, 7:5, and 6:6. For example, with a ratio of 9:3, the first group included 90 VMs and the second group included 30 VMs.  
Figure 11 shows the effects of the number of dependency groups and the ratio of the dependency groups with respect to the amount of data traffic in the physical network. The emulation results indicate that the use of SP considerably reduces the amount of data traffic volume in the physical network compared to that with the naive, GP, and SWP placements. The reason for more traffic volume in the data center with the naive and GP placements is that they do not consider the traffic dependency between the VMs. Additionally, the proposed SP method outperforms SWP even though SWP groups highly dependent VMs to make the traffic between different PMs to be minimum. The reason is that SWP does not minimize the number of running PMs. SWP splits a VM group into two small groups based on the Stoer-Wagner minimum cut algorithm if a resource for a specific group does not satisfy the resource constraints of its mapped PM. Thus, more VM groups are created with the SWP, and most of them are placed on different PMs. Therefore, the traffic amount in the physical network is increased as compared with SP.  
Moreover, the time complexity of SWP is considerably high compared to the proposed method. For instance, if required resources for a VM group do not satisfy the resource constraints of its mapped PM, it is necessary to remove less dependent VMs until the VM group satisfies the resource constraints. For removing the less dependent VMs from the group, the proposed method finds a farthest node from a center node of the cluster and removes the node. Therefore, it only takes \(O(|V|)\) time for SP. However, SWP needs to split the group using the Stoer-Wagner algorithm, and its complexity is \(O(|V||E|+|V|^{2}\log|V|)\)[53].