## 4 Improved Adaptive Backoff Algorithm (I-ABA)
### Markov-Based Mathematical Model for I-ABA
Programming bugs could potentially lead to incorrect results. To mitigate this situation, we conducted thorough code reviews, unit testing, and cross-validation between the Java and C implementations to minimize the risk imposed by errors on our results. For model accuracy, it is apparent that inaccurate models fail to mimic real-world scenarios and, as such, lead to invalid and potentially misleading results. To deal with this, we ensured that the simulation parameters (e.g., network size, node behavior, collision detection, etc.) closely match those used in real-world WBAN deployments. We validated our model against known results from established backoff algorithms like BEB and ABA. For simplified simulation assumptions, there is always the risk of oversimplifying the simulation or experimental environment to the extent that it no longer reflects a practical situation (for example, the use of a uniform node distribution or deterministic patterns). To mitigate this, we used randomized inputs and varied simulation parameters across multiple runs. This randomness helps mimic the unpredictability of real-world environments. We also identify the applicability to real networks and environmental factors as potential external threats to our simulations. These threats are legitimate and can be better mitigated through actual deployment and experimentation on real sensor nodes, which is beyond the scope of this study and is left for future investigation. Our simulations compare the performance of I-ABA to ABA, standard BEB, and the optimal channel utilization performance that was determined based on experiments. Figures 14-21 show the simulation results. Figure 16: Channel idle time against the size of the network. Figure 17: Channel Collision Time against the size of the Network. Figure 15: Channel utilization against the size of the network. Figure 19: Reliability against the size of the network. Figure 20: Average energy consumption against the size of the network. Figure 18: Transmission delay against the size of the network. In Figure 14, we consider the probability of collision over the wireless medium as the size of the network increases. The figure clearly shows that as the network size increases and becomes as high as 350 nodes, the standard BEB performs poorly, leading to high collision probabilities. However, compared to the standard BEB and ABA, I-ABA can maintain a slow increase in the probability of collision as the size of the network increases. As the size reaches 340 nodes, the collision probability is around 40%, while it is 49% and 95.2% for ABA and the standard BEB, respectively. I-ABA is also able to remained closer to the optimal protocol compared to ABA. At 340 nodes, the probability of collision is 28.2% with the optimal protocol. In Figure 15, we depict the performance in terms of channel utilization. It is evident again that the standard BEB channel utilization deteriorates with the increase in network size. At 340 nodes, BEB hits a channel utilization of 13.3%, which is extremely poor. For I-ABA and ABA, the channel utilization is 61.1% and 57.6%, respectively. Again, I-ABA is closer to the optimal protocol that achieves a channel utilization of 63.7% at a network size of 340 nodes. The performance in terms of channel idle time is illustrated in Figure 16. As shown, the standard BEB is far from the optimal case that maintains the channel idle time percentage at around 24.5%. BEB decreases the channel idle time percentage to 12.8% as the network size reaches 340 nodes. I-ABA, however, supports a channel idle time of 19.8% at a network size of 340 nodes. ABA, on the other hand, hits a channel idle time of 17.8%. These results show again that I-ABA is still closer to the optimal case compared to ABA and BEB. In Figure 17, we examine channel collision time, a parameter that should be lowered as it indicates how long the wireless medium was busy with useless activity. The figure shows the rapid increase in channel collision time with BEB. It reaches a percentage as high as 74% at 350 nodes.