# On Maximizing the Probability of Achieving Deadlines in Communication Networks
## 7 Performance Evaluation  
In this section, we evaluate the performance of both proposed algorithms via simulation. The first batch of simulations was run to validate that the ADPAD and AMPAD produced accurate DAP-CDF estimations. The evaluation was performed with the AMPAD because the ADPAD does not have a priori defined routing tables, while the AMPAD determines them. Whether these are optimal or not in the DAP sense is not relevant in this case. The simulations recreated 32 h of network time, of which the last 8 h were used for measuring the actual deadline achievement ratio (DAR) of the data packets. The DAR is the fraction of data packets created in the network that arrive at the sink within their respective deadlines. During the simulation, certain packets were lost for reasons such as channel access failure or reaching the maximum number of transmission attempts. We also classified such occurrences as instances of missed deadlines. Figure 3 compares the measured DAR values with the DAP predicted by the DAP-CDFs that were reached by the AMPAD at the end of the simulations. In all cases, the initial TTD was 35 ms. The DAPs versus DARs of all 3600 nodes of all 60 simulation runs of the square topologies are plotted in the figure. The DAP is overestimated above the diagonal dashed line; below the line, it is underestimated. The dashed horizontal and vertical lines represent the respective average values. The mean square error of DAP prediction versus the actual DAR was \(5.089\cdot 10^{-4}\). This confirms that the algorithm converged to the correct DAP-CDFs. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Described in Section** \\ \hline Path loss exponent & 2.4 & Section 6.1 \\ \hline Reference distance & 1 m & Section 6.1 \\ \hline Path loss at reference distance & \(-\)55 dB & Section 6.1 \\ \hline Rice fading K factor & 4 & Section 6.1 \\ \hline Signal-to-noise ratio threshold & 5 dB & Section 6.2 \\ \hline Transmit power & 0 dBm & Section 6.2 \\ \hline Random contention interval & 5 ms & Section 6.3 \\ \hline Maximum number of & 2 & Section 6.3 \\ transmission attempts & & \\ \hline Link delay probing interval & 120 s & Section 6.4 \\ \hline CDF broadcast interval & 5 s & Section 6.4 \\ \hline Data traffic load & 1 packet per 80 s per node & Section 6.6 \\ \hline Initial TTD & 35 ms & Section 6.6 \\ \hline Link-PLR threshold & 0.125 & Section 6.7 \\ \hline Network size & 60 nodes & Section 6.8 \\ \hline Network area &
\begin{tabular}{c} 30,000 m\({}^{2}\) (square \\ configuration) \\ \end{tabular} & Section 6.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters along with their respective default values and references to their introduction. Next, we are interested in understanding the role of the link quality in the performance of the algorithms. The motivation for studying this aspect is as follows. Links with a longer physical distance tend to have a higher outage probability. On the other hand, long links move packets potentially faster toward the sink because fewer hops are needed. When the initial TTD is small, we expect better DAR performance when links with a higher packet loss are allowed because that enables using fewer hops to the sink by following longer and less reliable links. When a longer initial TTD is specified, then using links with lower packet loss is beneficial because that fosters the use of shorter, more reliable links when more hops to the sink are tolerable. We are interested in understanding how well the AMPAD deals with this trade-off in comparison with AD. For this, we used the loss rates of packets at the data link layer seen by the network layer (link-PLR) for ruling out links with poor performance in AD while keeping all links available to the AMPAD. The following thresholds for the maximum allowable link-PLR for AD were tested: 0.0625, 0.125, 0.5, and 1. A link-PLR-threshold of one does not impose any constraints on the neighbors that can be chosen for routing.