## 4 Improved Adaptive Backoff Algorithm (I-ABA)
### Markov-Based Mathematical Model for I-ABA
I-ABA and ABA significantly reduce channel collision time to 19% and 24.6%, respectively, at 340 nodes. Consequently, I-ABA is still superior to the other techniques in reducing channel collision time. Figure 18 focuses on the transmission delay. As the size of the network increases, the delay with the standard BEB increases rapidly to reach 11.4 ms at 340 nodes. In the meanwhile, I-ABA achieves a delay of 2.5 ms at the same network size. It is lower than the delay with ABA (2.65 ms) and closer to the optimal protocol (2.4 ms). In Figure 19, the performance in terms of reliability is illustrated. It is interesting to note that I-ABA achieves high reliability at high network sizes. This reliability is as high as 57.8% at a network size of 340 nodes. This reliability is superior to both the standard BEB (3%) and ABA (46.2%) at the same network size. Figure 21: Average energy wasted in collision against the size of the network. In Figure 20, we show the performance in terms of the average energy consumption. The performance of both I-ABA and ABA is quite comparable. However, both techniques manage to reduce energy consumption compared to the standard BEB. At a network size of 340 nodes, BEB consumes average energy of 46 W.s., while I-ABA and ABA consume around 33 W.s. Figure 21 depicts the performance in terms of the average energy wasted in collisions. Again, I-ABA and ABA performance are comparable and much better than the standard BEB. At a network size of 340 nodes, BEB consumes an average energy of 7.47 W.s., while I-ABA and ABA consume 1.17 and 1.56 W.s., respectively. Finally, Figure 22 reflects how fair the techniques under the scope of this paper are. The figure clearly shows that I-ABA, ABA, and the standard BEB can achieve a fairness index close to 1. It indicates that these medium access controls are fair and guarantee an equal opportunity for every node in the network to access the wireless medium. Table 4 summarizes the data that have been collected at a network size of 340 nodes and provides a comparison between I-ABA, ABA, and the standard BEB. Based on the performance evaluation of I-ABA, we now provide a general comparison between I-ABA and the related works that were covered in Section 3. The comparison is provided in Table 5. The comparison criteria are based on the network topology, network size, application area, whether the work relies on 802.15.4 parameter tuning, the applicability to large-scale WBANs (as was defined in Section 1), and performance metrics. Also, the table provides noteworthy comments about each work. While different works use different \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Technique**} \\ \cline{2-4}  & **Standard BEB** & **ABA** & **I-ABA** \\ \hline \multirow{6}{*}{**Performance Metric**} & **Probability of Collision** & 95.2\% & 49\% & 40\% \\ \cline{2-4}  & **Channel Utilization** & 13.3\% & 61.1\% & 57.6\% \\ \cline{2-4}  & **Channel Idle Time** & 12.8\% & 17.8\% & 19.8\% \\ \cline{2-4}  & **Channel Collision Time** & 74\% & 24.6\% & 19\% \\ \cline{2-4}  & **Transmission Delay** & 11.4 ms & 2.65 ms & 2.5 ms \\ \cline{2-4}  & **Reliability** & 3\% & 46.2\% & 57.8\% \\ \cline{2-4}  & **Average Energy Consumption** & 46 W.s. & 33 W.s. & 33 W.s. \\ \cline{2-4}  & **Average Energy Wasted in Collisions** & 7.47 W.s. & 1.56 W.s. & 1.17 W.s. \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance comparison between I-ABA, ABA, and standard BEB at a network size of 340 nodes. Figure 22: Fairness against the size of the network. performance evaluation metrics, the metrics provided in the table are the ones we have evaluated in this paper. These metrics are compared to show how comprehensive and distinguished our evaluation is compared to other works. Also, since this work targets supporting large-scale WBANs, the table examines whether each performance metric has been evaluated against the network size. As a result, the works that lack such evaluation are given the description \"not applicable\" (NA) in the respective table cell.