# On Maximizing the Probability of Achieving Deadlines in Communication Networks
## 7 Performance Evaluation
Conversely, at shorter distances, deadlines can be achieved by following slower but more reliable links and paths. This trade-off was observed for the AMPAD (Figure 7) but not for the benchmark protocols, whose hop counts increased approximately proportionally to the distance to the sink. With the AMPAD, nodes in close proximity to the sink (below 150 m) tended to utilize paths with higher hop counts compared with the benchmark protocols, resulting in improved reliability. Conversely, nodes located further away from the sink (above 170 m) tended to utilize paths with lower hop counts compared with the benchmark protocols, leading to reduced latency. This explains the superior DAR performance of the AMPAD shown in Figure 6 for short and long distances. In Figure 8, we show the performance of the different approaches in terms of the DAR under various constant traffic loads in the square networks with 60 nodes and an initial  
Figure 6: DAR vs. distance to sink. AMPAD outperformed all other approaches for distances higher than 170 m.  
Figure 7: Average hop count vs. distance to sink. AMPAD chose comparably more hops when close to the sink but fewer hops at higher distances. TTD of 35 ms. Traffic ranged from 0.75 to 96 packets per second and was generated at the application layer. The AMPAD consistently outperformed the other approaches, with a DAR difference of up to 0.15 under high traffic conditions. The superior performance of the AMPAD was partly a result of how the AMPAD discards packets; it does so before the deadlines have passed and as soon as the deadline achievement probability reaches zero, while the other approaches discard packets only after their deadlines have passed. Consequently, traffic load was alleviated sooner under the AMPAD, especially near the sink, where traffic load was the highest. As a result, the AMPAD was able to maintain a more robust performance under high-traffic scenarios compared with the other approaches. Figure 9 presents the performance of the different approaches over 8 h of simulation time under varying traffic load. The traffic load was set initially to 0.75 packets per second for the first 6 h (left of line B) and then increased to 48 packets per second for the remaining 2 h. At 4 h (line A), all overhead traffic at the NET (link probing and broadcasting of CDFs, etc. ), as well as updating of the routing tables, was stopped for the remaining simulation time. The DAP slightly improved at this time because of the freed up network bandwidth. At 6 h (line B), the figure depicts a decline in performance because of the traffic burst. The protocols continued to rely on previously established routing tables set up from DAP-CDFs and metrics that corresponded to the initial load conditions. When comparing the performance during the last 2 h of network time in Figure 9 (48 packets per second to the right of line B) with Figure 8 at that traffic load (line C), it stands out that the AD, ETX, and HOP performed better in the burst case (achieving DAR values above 0.4 compared with values below it). This was due to the additional bandwidth for lack of monitoring overhead. In contrast, the AMPAD achieved similar performance in both experiment sets. This indicates that the added bandwidth was lost for the suboptimal routing tables. Nevertheless, the AMPAD still outperformed all other approaches. The frequency of retransmission attempts and packet loss rates at the DLL were strongly influenced by small-scale fading in the wireless propagation medium. In Figure 10, we investigated the performance of the AMPAD under various values of the Ricean fading \(K\) factor and compared it to the benchmark protocols for an initial TTD of 35 ms.  
Figure 8: DAR under different traffic loads. Under high traffic, AMPAD performed significantly better than ETX, AD, and HOP. We observed that all cases performed worse at smaller values of \(K\), confirming that networks with stronger small-scale fading in their links present more challenging routing environments for time-sensitive traffic.