# On Maximizing the Probability of Achieving Deadlines in Communication Networks
## 7 Performance Evaluation
In this case, the next hop selection was based only on the average times, regardless of packet loss. The AMPAD and AD were simulated with the described square network realizations, with the various link-PLR thresholds for AD and varying initial TTDs. The performance metric of interest is the achieved DAR, which was averaged over all nodes and all simulated networks. The results are plotted in Figure 4. As expected, the DAR benefited from larger initial TTDs in all cases. The AMPAD consistently achieved the highest DAR performance for all initial TTDs. Interestingly, the DAR did not tend toward one in all cases, even with a large initial TTD. This is because the DLL discards frames that fail to reach the next hop neighbor within the given maximum number of allowed transmission attempts. This cause of packet loss is substantial for AD with thresholds that allow more unreliable links to be used. It drops as links with high link-PLR are filtered out through the thresholding method described. The curves for AD reflect the trade-off between the link length and hop count as the initial TTD varied. The ideal link-PLR threshold depended on the initial TTD; high link-PLR thresholds were better for low initial TTDs, and low link-PLR thresholds were preferred for high initial TTDs. The effect of lowering the link-PLR threshold for keeping better quality links had a limit because it reduced network connectivity, eventually creating isolated nodes or network islands whose traffic could never reach the sink, thus deteriorating the DAR further. Similar behavior was observed in the case of the other metrics, HOP and ETX, when different link-PLR thresholds were applied (not shown). It is to be noted that the AMPAD is free from this trading off by thresholding the link quality. It picks the optimal links automatically. Figure 3: Fraction of packets that arrived at the sink in time (DAR) vs. estimated deadline achievement probability (DAP) obtained by evaluating the DAP-CDF returned by AMPAD. Next, we assessed the performance of the various routing algorithms for different initial TTD values with a link-PLR threshold of 0.125 for all approaches (except the AMPAD). The results are shown in Figure 5, which presents the average DAR statistics from 60 simulation runs with the square topology with 60 nodes each. The variance in DAR values producing those averages (markers) was generally wide, including nodes close to the sink with DAR values close to one and nodes far away from the sink with DAR values close to zero. The AMPAD had the highest DAR among all considered initial TTD values, consistently outperforming all other approaches. On the other hand, HOP consistently exhibited the poorest performance out of all the algorithms simulated, while ETX and AD performed slightly better and similarly between them. Next, we considered a line topology of 60 nodes distributed evenly over a distance of 295 m, with the sink located at one end of the line. Based on empirical observations, we opted for a consistent initial TTD of 35 ms throughout all simulation runs. This specific initial TTD choice was deliberate to present a challenging scenario for the protocols, allowing for a thorough analysis of their behaviors across all nodes in the network. It is intuitive that the DAR dropped with an increasing distance to the sink because data packets originating from nodes located further away from the sink would follow longer paths (more hops). Figure 6 depicts this relationship between the distance to the sink and DAR, while Figure 7 presents the average hop count as a function of the distance for packets that successfully reached the sink within their deadline. Intuitively, for nodes at a  
Figure 4: DAR vs. initial TTD for different link-PLR thresholds of AD. AMPAD always achieved the highest DAR. Figure 5: DAR vs. initial TTD for AMPAD vs. AD, ETX, and HOP, with a link-PLR threshold of 0.125. The AMPAD always achieved the highest DAR. high distance from the sink, priority should be given to fast paths rather than reliable ones.