# Dynamic Packet Duplication for Industrial URLLC
## 5 Results and Discussion
### Packet Duplication Results  
This subsection presents the results obtained when the ML algorithm was trained and the PD approach is used. In particular, a latency comparison between not using PD (single connection), always duplicating the packet (always PD) and the proposed dynamic PD algorithm is performed. Furthermore, for the PD techniques, a comparison of the resource consumption and latency obtained is performed.  
Figure 6 shows the empirical cumulative distribution function (ECDF) of the latency obtained when PD is not used (single connection), when always duplicating the packet and when activating PD based on the latency prediction using Random Forest, which is the system proposed in this paper. First of all, as it can be seen, the random forest and always PD distributions are similar, and they converge at 1.75 ms. The probability of receiving lower values of latency (below 1 ms) is 70%, 62% and 55% for always PD, random forest and single connection, respectively. There is a remarkable difference on the probability of receiving a latency below 2 ms between both PD methods and by transmitting via single connection. In this case, there is a gap of 20% on the probability.  
The latency below the threshold rate when using PD and not using PD is shown in Table 3, where PD techniques demonstrate that improve the reliability by duplicating the packet incoming for the UE.  
The latency gain distribution when PD is activated by the prediction model is shown in Figure 7. The distribution shows that, when the estimator predicts that latency will be higher than the threshold, in general, there is a latency gain compared to sending over a single link. The latency gain helps to improve the reliability of URLLC communications. The vertical dashed line represents the 75% percentile. In this case, the probability of reducing the latency more than 1 ms is 75%. Otherwise, the probability of not reducing the latency so far, that is, between 0.1 and 0.2 ms, is below 20%.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Technique** & **Latency below Threshold Rate** \\ \hline Single connection & 81.6549\% \\ Always PD & 95.7891\% \\ PD via Random Forest & 95.7541\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Latency below the threshold rate for the different techniques.  
Figure 6: ECDF of the latency received.  
Table 4 shows the results obtained when using a static PD technique, that is, always duplicating the packet transmitted and the results obtained when using PD only when the latency prediction is above the threshold. In particular, the number of packets that have been sent duplicated, the latency below the threshold rate, the average (packet) latency reduction rate and the PD reduction rate.  
Taking into account the number of packets duplicated, it is remarkable that, when using random forest, the number of packets duplicated is lower, specifically, the PD reduction rate is 81.0211%. Both techniques present a similar latency below the threshold rate, with 95.7891% for always PD and 95.7541% when using random forest. That clearly indicates that a dynamic PD is more suitable, guaranteeing the same level of low latency but without wasting extra resources.  
The average (packet) latency reduction rate measures the proportion of times where latency was reduced when duplicating the packet. In the results, the average (packet) latency reduction rate is better when duplicating via random forest than always duplicating, obtaining a latency reduction rate of 86.5506% for the system proposed and 25.0917% for a static duplication. The lower rate when always duplicating is due to sending the packet via two path when conditions are favorable at MN--that is, the latency constraint is fulfilled by MN link.