## 5 Performance Analysis  
In this analysis, we assumed that there were two stations attached to an MLD, each of which formed a link to the AP. Since this study considers appropriate multi-link DCF, we assumed that every data frame was delivered without errors. Used parameters are enumerated in Table 1 and other parameters that are not mentioned followed the IEEE 802.11 ax standard, which is the latest standard for WLANs, both for the MLDs and the single-link devices.  
We depict an illustrative topology for ease of understanding in Figure 9. We assumed two types of physical devices: MLD and single-link device. In this scenario, an MLD consisted of two stations, and a single-link device had only one station naturally. There were two links where the stations of MLDs and single-link are residing. We assumed that there were the same number of stations on each link, that is, \(N_{SLD}=N_{MLD}\), as shown in Figure 9. Since we were considering that \(N_{SLD}\) and \(N_{MLD}\) were the same on each link, the performance on each link was also the same.  
Numerical analysis and simulation experiments were carried out with MATLAB R2020a. Each number of the MLDs and the single-link devices was variable, ranging from 5 to 50, with a step size of 5. All stations were in a saturated condition, and they had a variable size of PPDUs, ranging from 1500 to 82,872 bytes, which made PPDU duration maximized according to the 802.11 ax standard. Initial CW of each MLD varied from 7 to 127, supported in the current 802.11 ax standard. Throughout this analysis, a hidden node problem was not considered. In other words, there were only \(N_{SLD}+N_{MLD}\) devices on a link, and there were no other devices adjacent to them. In addition, each device could sense and receive frames within the corresponding devices. Additionally, we utilized a nonlinear system solver supported by an optimization toolbox in MATLAB to solve a nonlinear system with two unknown variables, \(\tau\) and \(p\), as shown in Equations (3) and (4).  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Number of links & 2 \\ Number of MLD stations & 5–50 \\ Number of single-link devices on a link & 5–50 \\ Initial CW value & 15 \\ Maximum retry limit & 6 \\ Channel bandwidth per one link & 20 MHz \\ Number of spatial streams & 1 \\ Control frame rate & 8.1 Mbps (MCS 0) \\ Data frame rate & 135.4 Mbps (MCS 11) \\ Slot time & 9 us \\ SIFS duration & 16 us \\ DIFS duration & 34 us \\ Length of RTS frame & 20 Bytes \\ Length of CTS frame & 14 Bytes \\ Length of BlockAck frame & 32 Bytes \\ PPDU duration & 5.484 ms \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulation parameters.  
We compared the asynchronous transmission scheme along with SLA, MLA-S, MLA-L, and MLA-A, which are specified in the above section. On top of this, we also present the simulation results when asynchronous transmission scheme was used in the non-STR case to clarify the importance of adopting synchronous transmission in the non-STR. Asynchronous transmission was that channel access on each link occurred without any restriction. The asynchronous transmission could be allowed if all MLDs could nullify in-device interference, which can be called an STR case.