## 7 Results
### Bit Error Rate  
Since we are evaluating the impact of temporary faults in the network, the first parameter we want to study is the BER of the links. The BER of the links severely affects the reliability of the communication subsystem, so we have selected a wide range of BER values to carry out our analysis, which go from \(1\times 10^{-12}\) to \(1\times 10^{-4}\). Figures 10 and 11 show the evolution of the reliability achievable by TSN, approach A and approach B when modifying the BER.  
As expected, we see that the reliability is severely affected by the increase in the BER. We can also see that the impact is significantly higher in TSN than in approaches A and B when the BER is the same. This is because TSN does not count with any time redundancy mechanism to tolerate the faults in the links, while approaches A and B do. Furthermore, these results also show that approaches A and B can reach reliability values over 99.9% for BER values up to \(1\times 10^{-8}\) and over 99.8% for a BER of \(1\times 10^{-7}\) when transmitting just two replicas. As the BER increases, we see that the reliability drops dramatically even when using PTRF. This is because two replicas are no longer enough to tolerate the great number of faults that affect the links in those cases.  
If we pay close attention to the results of approach A and B, we see that the increase in the BER has a higher impact in approach A than in approach B. This is because in approach A there is a single set of replicas that traverse the network, so whenever a replica is affected  
Figure 10: Reliability achievable when varying the BER from \(1\times 10^{-12}\) to \(1\times 10^{-4}\). TSN is represented in gray, approach A in orange and approach B in green. The \(x\) axis represents the BER values, while the \(y\) axis represents the reliability.  
by a fault in a link it is lost in the whole path. On the contrary, in approach B bridges create a new set of replicas in each hop, so even if a replica is affected by a fault in a link the following bridge transmits two replicas again. Therefore, we can conclude that in networks with high BER values, approach B is a more adequate solution as it can provide higher reliability values than approach A using the same number of replicas and, thus, the same bandwidth.  
These results confirm the benefits of using time redundancy to tolerate temporary faults and show that in many cases a low level of redundancy can provide benefits. Nonetheless, we can see that two replicas are not enough to reach the reliability levels required in highly critical applications, e.g., 99.999% for throttle-by-wire applications [34].  
Finally, the huge difference in the reliability achievable when moving from a BER of \(1\times 10^{-7}\) to \(1\times 10^{-6}\) can let us envision that the BER value can impact the results obtained when studying how the frame size, the number of replicas and the number of bridges affect reliability. Thus, if we only study the behaviour of PTRF in scenarios with BER of  
Figure 11: Zoom in the reliability achievable by TSN, approach A and approach B for BERs from \(1\times 10^{-8}\) to \(1\times 10^{-4}\). TSN is represented in grey, approach A in orange and approach B in green. The \(x\) axis represents the BER values, while the \(y\) axis represents the reliability.  
\(1\times 10^{-10}\), we could be masking important interactions between parameters. Therefore, we have expanded the case of reference to include a BER value of \(1\times 10^{-6}\), which is high enough to see how PTRF behaves in harsh environments.