## 5 Simulative Assessment
### Simulation Results
#### 5.2.3 Scalability Assessment  
The simulations aimed to evaluate of the scalability of the LBT AFA MAC protocol were run in several scenarios by varying the number of EDs from 100 to 1200, in steps of 100 EDs. For a given number of EDs, three cases (A, B, and C) are considered, each one with a different value for the maximum number of backoffs, i.e., 5, 10, and 15. Moreover, for each of such cases, four backoff unit duration (\(U_{backoff}\)) values are considered, i.e., 5 ms, 10 ms, 15 ms, and 20 ms. The performance metrics used are the average MDelivR and the e2 eDs. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number of EDs** & **50** & **100** & **150** & **200** \\ \hline
**Avg e2 eD (s)** & 0.35 & 0.41 & 0.52 & 0.59 \\
**Max e2 eD (s)** & 2.50 & 2.69 & 2.97 & 2.98 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Average and maximum e2 eD varying the number of EDs. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(MAC_{nBackoff}^{max}\) & **5** & **7** & **9** & **11** & **13** & **15** \\ \hline
**MLossR** & 2\% & 2\% & 2\% & 2\% & 2\% & 2\% \\
**MDropR** & 26\% & 20\% & 12\% & 11\% & 10\% & 6\% \\
**MDelivR** & 72\% & 78\% & 86\% & 87\% & 88\% & 92\% \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Average values of MLossR, MDropR and MDelivR varying the maximum number of backoffs. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Number**} & \multicolumn{2}{c}{**5 ms**} & \multicolumn{4}{c}{**10 ms**} & \multicolumn{4}{c}{**15 ms**} & \multicolumn{4}{c}{**20 ms**} \\  & **Avg e2 eD (s)** & **Max e2 eD (s)** & **Avg e2 eD (s)** & **Avg e2 eD (s)** & **Max e2 eD** (s)** & **Avg e2 eD (s)** & **Max e2 eD** (s)** & **Max e2 eD** (s)** \\ \hline
**100** & 0.41 & 2.48 & 0.49 & 4.08 & 0.67 & 6.16 & 0.69 & 7.69 \\
**200** & 0.60 & 2.71 & 0.81 & 4.68 & 1.04 & 6.48 & 1.30 & 8.28 \\
**300** & 0.60 & 2.60 & 0.94 & 4.81 & 1.23 & 6.64 & 1.60 & 8.52 \\
**400** & 0.63 & 2.55 & 0.95 & 4.74 & 1.34 & 6.72 & 1.70 & 8.60 \\
**500** & 0.67 & 2.53 & 1.00 & 4.63 & 1.35 & 6.99 & 1.73 & 8.51 \\
**600** & 0.65 & 2.43 & 1.01 & 4.24 & 1.39 & 6.25 & 1.81 & 8.58 \\
**700** & 0.66 & 2.41 & 1.01 & 4.16 & 1.39 & 6.24 & 1.81 & 8.33 \\
**800** & 0.66 & 2.27 & 1.03 & 4.08 & 1.43 & 6.10 & 1.84 & 8.18 \\
**900** & 0.65 & 2.20 & 1.02 & 4.04 & 1.44 & 6.06 & 1.85 & 8.16 \\
**1000** & 0.65 & 2.18 & 1.03 & 4.95 & 1.45 & 6.88 & 1.87 & 8.01 \\
**1100** & 0.65 & 2.16 & 1.03 & 4.88 & 1.45 & 6.74 & 1.88 & 8.96 \\
**1200** & 0.66 & 2.15 & 1.05 & 4.86 & 1.44 & 6.83 & 1.91 & 8.85 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Case B (\(MAC_{nBackoff}^{max}=10\)): Average and maximum e2 eD varying the number of EDs and the \(U_{backoff}\) parameter. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Number**} & \multicolumn{2}{c}{**5 ms**} & \multicolumn{4}{c}{**10 ms**} & \multicolumn{4}{c}{**15 ms**} & \multicolumn{4}{c}{**20 ms**} \\  & **Avg e2 eD (s)** & **Max e2 eD** & **Avg e2 eD (s)** & **Max e2 eD** & **Avg e2 eD (s)** & **Max e2 eD** (s)** & **Max e2 eD** (s)** \\ \hline
**100** & 0  
Comparing the three Figures 5-7 it can be seen that in all the three cases A, B and C, the higher the number of EDs the lower the MDelivR. In fact, the graphs in the Figures 5-7 show similar trends. The difference lays in the highest MDelivR value achievable, as Case B and Case C, where the maximum number of backoffs is set to 10 and 15, respectively, obtain higher MDelivR values than Case A. In all the considered cases, the effect of the backoff unit duration on the ability to provide acceptable MDelivR values to a large number of EDs is more evident for a number of EDs between 100 and 400. In fact, when the number of EDs exceeds 400 the impact of the backoff unit duration becomes less significant for any maximum number of backoffs. The difference between the obtained MDelivR values is limited, as it is always lower than 7% for each configuration with a given number of EDs. Conversely, the impact on the e2 eD is more significant.