## 7 Results
### Number of Replicas  
It is expected that the number of replicas transmitted for each frame impacts the reliability achievable by the communications subsystem. Nonetheless, we need to note that the level of time redundancy can negatively impact other aspects of the system, such as the end-to-end delay, jitter and bandwidth consumption, as we show in [11]. Therefore, choosing a level of temporal redundancy that provides the network with the intended reliability, while ensuring an adequate quality of service is of utmost importance. Figure 13 shows how the number of replicas transmitted impacts the reliability achievable by TSN, approach A and approach B when the BER of the network is \(1\times 10^{-10}\). Note that the number of replicas in TSN is always one, as it does not count with any time redundancy mechanism. If we focus on Figure 13a what we first see is that the reliability is improved by almost 15% when using time redundancy in this scenario. However, if we focus on the first three columns, when replication is not used, we can see that the reliability actually drops when using approaches A and B to transmit non-replicated frames. This is because PTRF-enabled devices have a higher temporary failure rate (\(1.5\times 10^{-4}\)) than standard TSN devices (\(1\times 10^{-4}\)). Thus, when no redundancy is used, the probability of losing frames due to temporary faults affecting the bridges or end-devices is higher in PTRF than in TSN. Furthermore, this is more noticeable in approach B than in approach A, as the number of PTRF-enabled devices is higher in the former. In fact, if we focus on Figure 13b we can see that the increased failure rate of PTRF-enabled devices limits the reliability benefits provided by B when compared to A. This is because PTRF is designed to tolerate link faults only and, thus, it cannot tolerate most faults that occur in end-systems or bridges. Therefore, in networks where the BER is low, approach A is a more adequate solution than approach B to tolerate temporary faults. In any case, we see that the reliability is always above 99.99% for both approaches. On the other hand, Figure 14 depicts the reliability achievable by approach A and approach B when transmitting a different number of replicas in a network with a BER of \(1\times 10^{-6}\). Please note that we do not include \(k=1\) in this plot as the reliability achievable by the three solutions in the absence of redundancy is around \(5.76\times 10^{-12}\). As we can see, the reliability increases significantly with the number of replicas transmitted. As indicated in the section devoted to analyse the frame size, we also see that transmitting only two  
Figure 13: Reliability achievable when varying the number of replicas in a network with a BER of \(1\times 10^{-10}\). TSN is represented in grey, approach A in orange and approach B in green. The \(x\) axis represents the number of replicas, while the \(y\) axis represents the reliability. (**a**) Reliability achievable by TSN, approach A and approach B when varying the number of replicas. In TSN the number of replicas is always 1. (**b**) Zoom in the reliability achievable by approach A and approach B when varying the number of replicas. replicas is no longer enough to achieve high reliability, especially in approach A, where the reliability is only 26.31%, compared to the 82.36% of approach B. Furthermore, we can see that the comparison of the reliability benefits provided by A versus B is the opposite of what we have just described when considering a low BER of \(1\times 10^{-10}\). Specifically, we can see that when the BER is high approach B provides higher reliability than approach A, even with a low number of replicas. This is because when the BER is high, its contribution to the unreliability is higher than the contribution of the failure rate of devices, i.e., it is more likely that a frame is affected by a fault in the link than in a device.