## 5 Experimental Results
### Simulation Setup
These graphical results represent a comparison of the SA-MCSDN algorithm proposed in this work with the HSA-PSO MCSDN algorithm proposed in [24] and SA-FFCCPP. The algorithm results were compared based on metrics, such as propagation delay, average round-trip time (RTT), matrix of TS, average delay, reliability, throughput, cost, and fitness value, as shown in the figures below. These figures show comparisons of the proposed SA-MCSDN algorithm and the previous HSA-PSO approach with respect to a number of SA-FFCCPP validation metrics. These graphical representations show that the proposed SA-MCSDN-based multi-controller placement approach in an SDN achieved improved results with respect to multiple metrics relative to the previous work using the hybrid HSA-PSO algorithm and SA-FFCCPP. The reason for the superior results is that SA-MCSDN enables a short execution time with considerable convergence, whereas the HSA-PSO algorithm requires a longer execution time with lower convergence and local optima traps, in addition to lacking robust management of exploitation and exploration. Our comparison of the SA-MCSDN algorithm with the previous hybrid HS-PSO algorithm revealed that the proposed SA-MCSDN performed better than the hybrid HS-PSO algorithm in terms of latency, propagation time, delay rate, reliability, defects, convergence, and cost. Table 2 presents a comparison of the average numerical results of the proposed method with those obtained in the previous work. The following is a summary of the effects of the metrics through analysis and comparison with reference to the following figures and extracted results of the proposed algorithm. Figure 6 shows the tradeoff between the algorithms, demonstrating the superiority of the proposed SA-MCSDN algorithm in terms of the impact of propagation delay. Latency is an important metric that is used to evaluate the delay between switches and controllers during propagation. It is calculated according to Equation (13):  
\[\mathbb{P}_{d}=\frac{\uplambda}{\mathrm{q}} \tag{13}\]  
where propagation delay (\(\mathbb{P}_{d}\)) is defined as the ratio between the distance (\(\mathrm{q}\)) (\(\mathrm{m}\)) and the propagation speed (\(\mathrm{d}\)) (\(\mathrm{m}\)/s). Figure 6 shows a comparison of the \((\mathbb{P}_{d})\) of the proposed SA-MCSDN method with the hybrid HSA-PSO and SA-FFCCP methods in terms of the number of iterations. An SDN network with low propagation delay attains efficient communication between S2 Cs. The propagation delay decreases with an increasing number of iterations. Controller placement  
Figure 6: Comparison of propagation delay. (CP) was performed by considering only the distance between S2 Cs. In addition, poor tuning of algorithms leads to poor CP, which increases the \((\mathcal{P}_{d})\). In the proposed SA-MCSDN method, CP is performed by considering the (\(\chi\)) using an optimization algorithm that increases the performance and reduces the \((\mathcal{P}_{d})\). Figure 6 shows that the proposed SA-MCSDN method achieves a low propagation latency (4 to 15 ms) of 4.80 ms, compared with the hybrid HSA-PSO (11 to 20 ms; 15.6) and SA-FFCCPP (22 to 40 ms; 31.3) methods. Figure 7 illustrates the tradeoffs between the algorithms listed above. The proposed SA-MCSDN algorithm achieves better performance than the HS-PSO and SA-FFCCP algorithms in terms of the impact of round-trip time (RTT; 6.05 ms). Figure 8 shows a comparison of the algorithms listed above. The proposed SA-MCSDN algorithm achieves better performance than the HS-PSO and SA-FFCCP algorithms in terms of the effect of session time matrix (TS; 113.13). Figure 7: Comparison of average RTT. Figure 9 illustrates a comparison of the algorithms listed above. The proposed SA-MCSDN algorithm achieves better performance than the HS-PSO and SA-FFCCP algorithms in terms of the average delay (42.57 ms). Figure 10 illustrates a comparison of the algorithms listed above.