## 4 Analysis and Evaluations
### Comparison between SDN and Legacy Network
#### 4.1.3 Round Trip Time (RTT)  
Next, we compare the delay between nodes in each network. The _PING_ tool was used to obtain the RTT between the source and the destination nodes. The networks are compared on the basis of the variance of RTT, and the minimum and maximum values of RTT.  
Figure 9: Bandwidth capacity for SDN and legacy network.  
Here, the standard deviation of the values of RTT for both the networks are plotted in a graph. This is done for the source and destination nodes within an AS, in a neighbouring AS, and when AS65000 and the SDN network are used as transit networks.  
Standard deviation is simply the average of how far each RTT value is from the mean RTT. This shows how the round trip time varies with time. A higher value of variation in the RTT value results in a more unstable network. As shown in the plots of Figures 11a,b, 12a,b, 13a,b and 14a,b, the standard deviation values with a varying number of packets for SDN is lesser than that of the legacy network. This signifies that SDN can be more reliable and stable than their legacy counterparts.  
The values used in the plots are used as point estimates to provide a rough estimate of the population parameter (i.e., mean RTT variance of the population) within a confidence interval. Two different samples for the legacy (ref. Figures 11a, 12a, and 13a,b) and SDN networks (ref. Figures 11b, 12b, and 14a,b) were taken, respectively. The T-distribution of the samples are determined at a confidence level of 95% as the standard deviation of the population is unknown to us. For the legacy network, a confidence interval of (0.02495, 0.06938) is obtained with a sample mean equal to 0.0472 and a \(t\)-critical value equal to 2.200985. Similarly, for the SDN network, a confidence interval of (0.0304, 0.0551) is obtained with a sample mean equal to 0.042767 and a \(t\)-critical value equal to 2.000995.  
Figure 11: RTT Variance, (**a**) in Legacy (AS65000 as transit) and (**b**) AS65000/SDN as Transit in SDN.  
Figure 10: PTR for AS65000/SDN as a transit network.  
Figure 14: RTT variance for neighbouring AS of SDN, (a) h1 <-> h4 and (b) h2 <-> h3.  
Figure 12: RTT Variance, (a) Within AS65000 in Legacy, and (b) within SDN. RTT, Round Trip Time.  
Figure 13: RTT Variance for Neighbouring AS of Legacy Network, (a) h1 <-> h3 and (b) h2 <-> h4.  
Furthermore, we run the experiments in the virtual machine hosted on the azure and DNS servers of Google and Cloud-flare to demonstrate the presence of variability in RTT values over time and the results are plotted in Figure 15. This shows that the RTT variance of the _PING_ results between machines in a real scenario. We observed the values of RTT with a deviation from 0.1 to 0.8. There are other communications and the protocol's internal signaling (e.g., OpenFlow communication, Host_Location_service_Provider etc.), which affect the RTT values.  
The minimum and maximum values of RTT for both networks are plotted in the graph in Figures 16a-d, 17a-d, and 18a-d. This is done for source and destination nodes within an AS, in a neighbouring AS, and when AS65000 and the SDN network are used as transit networks. The traffic were captured at multiple rounds and more than one plot is provided in Figures 16-18 respectively.  
From the plots of Figures 16a-d, 17a-d, 18a-d and 19a-d, it can be observed that, for a varying number of packets, the minimum and maximum values of RTT are lesser in SDN compared to that of the legacy network. A higher RTT value signifies more time taken for the transmission of packets that can affect the speed and reliability of the network. Thus, it can be concluded that routing in SDN using ONOS/SDN-IP performs much better than the legacy network in terms of speed and reliability.