## 6 Performance Evaluation  
For the performance evaluation, we used a full factorial design with k = 3 factors [52; 53]. The factors we selected were the MMAC protocols, number of stations, and number of channels. Each factor contains different levels to consider. Table 5 shows the factors and the levels considered for the MMAC performance study. \(y_{ijkl}=\) response (observation) in the Ith replication of the experiment with factors A = MMAC protocols, B = No. of channels, and C = No. of stations at levels i = 5, j = 3, and k = 4, respectively. \(\mu=\) mean response  
\(\alpha_{i}=\) effect of factor A at level i  
\(\beta_{j}=\) effect of factor B at level j  
\(\xi_{k}=\) effect of factor C at level k  
\(\gamma AB_{ij}=\) interaction between A and B at levels i and j. \(\gamma AB_{ijk}=\) interaction between A, B, C at levels i, j, k.  
Figure 10: JFI comparison of adaptive MMAC versus others. (**a**) Three, (**b**) four, and (**c**) twelve channels. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Factors’ Levels** & **1** & **2** & **3** & **4** & **5** \\ \hline Protocols & AMMAC & BiMMAC & SA-MMAC & E-SA-MMAC & Max-ESA-MMAC \\ Number of & 3 & 4 & 12 & & MMAC \\ Channels & 5 & 25 & 45 & 65 & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Factors and levels for MMAC performance study. From the analysis of variation (ANOVA), Table 6, of the throughput analysis, we notice the main effect on the throughput variation is mostly due to the number of channels with almost 56% variation and, to a lesser extent, the number of stations with an impact of around 20.6% of the results, with the MMAC protocols having the least impact with a variation of 1.6%. These variations were calculated from the respective ANOVA tables by dividing the sum of squares of each factor by the total. Additionally, the interaction between the number of channels and the number of stations has the most significant effect with a 17.7% variation in the throughput compared to any other interaction combination. This implies that the number of channels and the number of stations match each other in terms of the effect they have on the throughput. The interaction between all three factors accounts for only 1.4% of the variation. Table 7 describes the ANOVA for JFI, which highlights the impact of the MMAC protocols on the variation of the fairness index. The MMAC protocols contribute 58.7% to the variation in the results. The number of stations has the next most impactful effect with 20.3%, but the number of channels has a negligible effect on fairness. Moreover, the table shows that the interaction between MMAC protocols and the number of channels has the largest effect with a 4.7% variation in the fairness from the interacting factors. Interactions between all factors account for 2.4% of the variation. Table 8 describes the ANOVA for channel access delay, which shows that the impact of the number of stations in the collision domain of the network has the most significant effect  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Component** & **Sum of Squares** & **\% Variation** & **Degree of Freedom** & **Mean Square** \\ \hline \(y\) & 860.0205 & & 60 & \\ \(y\dots\) & 599.9749 & & 1 & \\ \(y-y\dots\) & 260.0411 & 100\% & 59 & \\ **Main Effects** & 203.7815 & 78.36\% & 9 & 22.6 \\ No. of Stations & 53.6673 & 20.64\% & 3 & \\ MMAC Protocols & 4.0952 & 1.57\% & 4 & \\ No. of Channels & 146.019 & 56.15\% & 2 & \\
**First Order** & 52.564 & 20.20\% & 26 & 2 \\
**Interactions** & 1.8193 & & 12 & \\ Stations\({}^{\text{\text{\texton the variation of channel access delay with 55.8%. The second most impactful effect is the number of channels with 28.5%, while the MMAC protocols explain the least percentages of variation. Furthermore, the interaction between the number of stations and channels explains the greatest percentage of variation among the interactions of the factors with almost 13%. This implies that the number of stations and channels match each other in terms of the effect they have on the channel access delay.