## 5 Performance Analysis
### Verification of Analytical Models and Their Throughput and Fairness Analysis  
We developed an event-driven simulator in MATLAB, which almost mimicked the situation assumed by Section 4, to verify the proposed analytical model for multi-link operation. The simulation lasted 30 s. As shown in Figure 10a,b, we can confirm that our analytical model fitted the target multi-link environment. The notable thing is that the analytical model of MLA-A was slightly underestimated because the number of remaining slots was approximated in the process of calculation, as shown in Equation (38). Figure 10a shows sums of saturated throughputs per one link, including MLD and single-link device, when RTS/CTS exchange was disabled when simultaneously varying both the number of MLDs and single-link devices from 5 to 50. Hence, the total number of stations on a link varied from 10 to 100. In this figure, the difference in throughput between the synchronous multi-link DCFs was not significant because most of the transmission trials collide without RTS/CTS exchange. In the case of MLA-S, the probability of channel access trial tended to be higher due to its aggressive manner, and it made higher collision probability compared to the other schemes. In the same manner, asynchronous transmission scheme aside, MLA-L outperformed the other DCF schemes since MLD gave way to single-link devices through its infrequent channel access. It is clear that analyzed throughput decreased as the number of stations increased due to congestion. In addition, we can see that asynchronous transmission outperformed other synchronous DCF schemes. This is because there were no restrictions on accessing the channel, and thus it could perform as if there were two separate single-link DCFs. Figure 9: Topology for the simulation. Figure 10b shows average per-station per-link throughputs, including MLD and single-link device, with RTS/CTS exchange enabled. Excluding asynchronous transmission, when there were few numbers of stations, MLA-S outperformed other schemes because the MLD of MLA-S occupied most of the time by using a prioritized channel access method. This is rare in a Wi-Fi environment, but the throughput of MLA-S was significantly reduced when the number of stations exceeded 100. In order to investigate the effects on each MLD and single-link device further, we depict throughputs for each MLD and single-link device in Figure 11a,b. ML and SL indicate the throughput of MLDs and single-link devices, respectively. As seen in Figure 11a, throughput in all DCF cases, whether ML or SL, tended to decrease gradually. In detail, the ML throughput of MLA-S was much higher than the SL throughput of MLA-S, especially when there were small number of stations. The link was likely to be spacious until there were about 50 stations. Then most of the channel was occupied by MLD that had a smaller backoff counter, and thus the MLDs had prioritized channel access opportunities over the single-link devices. For that reason, single-link devices had less opportunity to access the channel, and SL throughput underperformed SL throughputs of the other DCF schemes. As the number of stations increased, all DCF schemes' performances decreased, but in the case of MLA-S, the performance decreased more rapidly due to its aggressive channel access manner. Figure 11b shows analyzed throughput in the same environment as in Figure 11a when RTS/CTS exchange was enabled. We can see that the asynchronous transmission scheme's throughput decreased more slowly than those of the other multi-link DCF schemes. This is because the asynchronous transmission scheme was insensitive with regard to the station number variation since it had a double opportunity to access the channel. Specifically, MLD of MLA-S occupied most of the channel. Hence the single-link devices' throughput of MLA-S consistently underperformd other schemes.