## 4 Improved Adaptive Backoff Algorithm (I-ABA)
### Markov-Based Mathematical Model for I-ABA
Furthermore, for convenience, and since different works assess how efficient their techniques are in utilizing the wireless channel using different (but comparable) metrics, channel efficiency is used in this table to refer to channel utilization, channel idle time, channel collision time, throughput, or goodput; that is, any work that supports one or more of these metrics is assumed to have evaluated channel efficiency (of course, against network size). All works, including I-ABA, assume a single-hop star topology (with the exception of [16], as explained shortly). Finally, power or energy consumption refers to whether there has been any power or energy analysis (including consumption and wastage due to collisions) conducted in the work. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & & & & & & & & & & & & & & \\ \hline
[14] & 50 nodes & & x & x & ✓ & ✓ & ✓ & x & x & ✓ & Aims at optimizing CW \\ \hline
[15] & 5 nodes & ✓ & x & NA & NA & NA & NA & NA & NA & Scalability is not considered \\ \hline
[16] & 14 nodes & & x & x & ✓ & x & ✓ & ✓ & x & ✓ & Scalability is considered in a multi-hop scenario, WBAN is studied for a single-hop star topology with up to 14 nodes \\ \hline
[17] & 5-30 nodes & & x & x & x & x & ✓ & ✓ & x & ✓ & PAN coordinator controls backoff behavior of nodes based on the number of failed transmissions \\ \hline
[18] & 12 nodes & & x & x & ✓ & ✓ & ✓ & ✓ & x & ✓ & Scalability is not considered beyond 12 nodes \\ \hline
[19] & 2–40 nodes & ✓ & x & x & x & ✓ & x & x & ✓ & Boost in performance focuses on efficient GTS allocation; Scalability is not considered \\ \hline
[20] & 5 nodes & & x & x & ✓ & x & ✓ & x & x & ✓ & Scalability is not considered \\ \hline
[21] & 14 nodes & & x & x & ✓ & ✓ & ✓ & ✓ & x & ✓ & Scalability is not considered \\ \hline
[22] & 6 nodes & ✓ & x & NA & NA & NA & NA & NA & NA & Scalability is not considered \\ \hline
[23] & 1–20 nodes & ✓ & x & NA & NA & NA & NA & NA & ✓ & Scalability is not considered \\ \hline I-ABA & 340 nodes & & x & ✓ & ✓ & ✓ & ✓ & ✓ & ✓ & ✓ & Scalability is a main goal \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison between I-ABA and related works. Based on Table 5, we can see that our work is distinguished by designing a new technique that focuses on scalability. I-ABA is the only technique in this table that supports single-hop WBANs that are composed of hundreds of nodes. Furthermore, the table shows that our performance evaluation is comprehensive and covers an important set of performance metrics; none of the surveyed works covers all of the listed metrics. The only exception is reference [16], which studies networks composed of 100 nodes. However, the evaluated topology is multi-hop, and the targeted application is non-medical; the same reference uses a single-hop WBAN of 14 nodes to evaluate the performance. For references [14; 17; 19], which evaluate the performance with network sizes 50, 30, and 40 nodes, respectively, it is not clear how the performance will behave when the network size reaches hundreds of nodes, as is the case with I-ABA. Furthermore, reference [17] relies on the PAN coordinator in its operation, which poses a single point of failure, and reference [19] targets the efficient allocation of GTS while GTS is not used in I-ABA. It is also worth noting that I-ABA requires no parameter tuning for 802.15.4 MAC, while several works rely on that [15; 19; 22; 23]; that is, I-ABA requires no changes to the default parameters of 802.15.4 MAC and imposes minimal changes to its mechanism (as evident when comparing Figures 1 and 4). Finally, it is worth mentioning that the proposal in [14] follows the same approach as in both ABA and I-ABA in terms of optimizing the size of the contention window (CW) based on the conditions over the wireless medium that lead to collisions. However, as stated earlier, the work in [14] does not consider large-scale WBANs.