## 4 Evaluation
### Experimental Results  
In this subsection, the results of the average SFD-to-controller latency and the loss rate of the messages from the SFDs to their assigned controllers are shown with different traffic load, number of controllers and SDN deployment ratio. Figures 4 and 5 show the performance of 20 experiments that had different and random loads (arrive rates) of LFDs. Three controllers were deployed in this network. The characteristics of the experiment are shown in Table 2. The arrive rate \(\lambda\) of all LFDs was assumed to follow a normal distribution. The mean of the normal distribution was randomly selected from 4 to 5 M packets/ms and the standard deviation was from 0.5 to 1.5. Compared with the LIA, the proposed LBA had lower average SFD-to-controller latency and message loss rate in all experiments. Figure 3: Topology of TA2 network. Figures 6 and 7 show average latency and average message loss rate with 2-7 SDN controllers. For each case (number of controllers), we used 20 sets of random traffic, whose load of each switch was generated from the normal distribution with mean parameter 10 M packets/ms and standard deviation parameter 1.5. These two figures show the 95% confidence interval. In these cases, 20% of switches were assumed to be SDN randomly. Firstly, we can see that the LBA had and obviously lower average latency and message loss rate relative to the LIB. Secondly, in Figure 6, we can easily see that, with more SDN controllers deployed in the network, lower average latency can be obtained because deploying more controllers offers more choices to SFDs and the more chances to reduce the average SFD-to-controller latency. Besides, Figure 7 shows that more controllers deployed in hybrid SDNs have an overall reduction trend, but not for all cases. For example, when three controllers are deployed, the average packet loss rate is slightly increased relative to that when two controllers are deployed. The reason is that our controller assignment scheme and path scheduler consider the packet loss rate, but it is not the only factor in this problem. The objective of our model is to minimize the average SFD-to-controller latency. Thus, there are chances to choose paths with low latency, but with slightly higher packet loss rate. \begin{table}
\begin{tabular}{c c c} \hline \hline Link transmission speed & 5 \(\mathrm{\SIUnitSymbolMicro s/km}\) & LFD service rate & 5 M packets/ms \\ \hline Queue length of LFD & 40 M packets & Mean arrive rate of LFD & 4–5 M packets/ms \\ \hline Standard deviation of arrive rate & 0.5–1.5 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Characteristics of experiments. Figure 4: Average SFD-to-controller latency with different traffic. SFD: SDN-enabled Forwarding Device. LBA: Legacy Based Assignment. LIA: Legacy Ignored Assignment. Figure 5: Loss rate with different traffic. Figure 8 shows the average SFD-to-controller latency improvement compared with LIA. In this figure, two different topologies are used: the TA2 and the INDIA35. The traffic and deployment ratio are the same as Figure 6. The topology of INDIA35 is shown in Figure 1, which has 35 nodes and 80 links. On the one hand, in this figure, these two broken lines are the average latency improvement percentage compared to LBA and LIA of INDIA35 and TA2. The average improvement is from 4.5% to 14% for INDIA35, and from 2.8% to 9% for TA2. On the one hand, the box plot is a method for graphically depicting numerical dataset through their quartiles. In this figure, the box plots show latency improvement percentage data compared LBA and LIA of INDIA35 and TA2. This figure shows that, with more controllers deployed, the improvement is in an increasing trend overall. As INDIA35 has fewer nodes than TA2, with the same number of controller deployment, the latency improvement of INDIA35 is more obvious than TA2. Figures 9 and 10 show average latency and packet loss rate with 20%, 40%, 60% and 80% SDN devices deployment ratios.