## 2 Related Work  
At the moment of writing this article, we have published four works related to the PTRF mechanism. In [9] we present a first overview of the mechanism, we propose two of the approaches and we compare them using a preliminary probability analysis to calculate the number of replicas required by each approach to reach the same reliability. We base our analysis on the Bit Error Rate (BER) of the links and we assume that the occurrence of bit errors follows a Poisson distribution. Even though this first analysis allows us to see which one of the two approaches can provide the highest reliability using a specific number of replicas, it does not allow to quantify the reliability that each approach can yield under different operation conditions. In [12] we present a proposal to integrate PTRF with the IEEE Std 802.1 CB standard for Frame Replication and Elimination for Reliability (FRER) that supports space redundancy in TSN [6; 7], while in [10] we present the third approach of the PTRF mechanism, we build a simulation model for each approach and we use exhaustive fault injection to compare them in terms of the number of fault scenarios that each can tolerate. Furthermore, we present a mathematical analysis to calculate the expected fault scenarios that each approach can tolerate. Finally, in [11] we present a detailed description of the PTRF mechanism, its operation and its implementation in a real TSN bridge. We also present a quantitative evaluation of PTRF, where we measure its impact on the end-to-end delay, jitter and bandwidth consumption; as well as a comparison with a standard TSN network. We must note that in the particular case of data networks, retransmissions are normally based on ARQ techniques [13], which rely on ACK/NACK messages and/or timeouts to trigger the retransmission of lost frames. However ACKs are not well-suited for RT highly reliable industrial networks. First, due to the random nature of temporary faults, ARQ solutions are non-deterministic in terms of end-to-end delay and bandwidth consumption. Second, the end-to-end delay of a frame significantly increases when, and only when, retransmissions are required, which leads to a high jitter in the communications. Third, ARQ solutions introduce additional scenarios involving faults, which are harder to tolerate [14] as temporary faults can also affect ACK/NACKs. Finally, when the network conveys TT traffic, the schedule must cope with the worst-case scenario involving temporary faults. Since ACK/NACKs have to be scheduled in addition to frame retransmissions, ARQ solutions further worsen the utilisation efficiency of the bandwidth. So far we have only talked about space redundancy, proactive transmission of replicas and backward error recovery to achieve fault tolerance. Nonetheless, we must note that there are other fault tolerance techniques, such as error correction codes. Error correction codes have been extensively used in wireless networks with really high noise, but they are rarely used in wired ones [15]. This is because when the noise is as low as in wired networks, the time required to produce the correction codes and to decode and rebuild frames is considerably higher than the time required for simple retransmissions. Furthermore, in some cases correction codes transmit frames in groups to improve channel efficiency. Nevertheless, the size of the group significantly impacts the time response. This is because frames cannot be transmitted immediately after their creation, but they need to be buffered and transmitted when the whole group is ready. Another common technique to improve the efficiency of correction codes consists in transmitting ACK messages, which, as we have already discussed, introduces a high jitter in the communication. For these reasons, error correction codes are not a suitable solution to tolerate faults in wired networks with hard real-time requirements. We can find in the literature other works related to the study of TSN and its fault tolerance mechanisms.