###### Abstract  
The Time-Sensitive Networking (TSN) Task Group has standardised different mechanisms to provide Ethernet with hard real-time guarantees and reliability in layer 2 of the network architecture. Specifically, TSN proposes using space redundancy to increase the reliability of Ethernet networks, but using space redundancy to tolerate temporary faults is not a cost-effective solution. For this reason, we propose to use time redundancy to tolerate temporary faults in the links of TSN-based networks. Specifically, in previous works we proposed the Proactive Transmission of Replicated Frames (PTRF) mechanism to tolerate temporary faults in the links. Now, in this work we present a series of models of TSN and PTRF developed using PRISM, a probabilistic model checker that can be used to evaluate the reliability of systems. After that, we carry out a parametric sensitivity analysis of the reliability achievable by TSN and PTRF and we show that we can increase the reliability of TSN-based networks using PTRF to tolerate temporary faults in the links of TSN networks. This is the first work that presents a quantitative analysis of the reliability of TSN networks. reliability analysis; time redundancy; Proactive Transmission of Replicated Frames; Time-Sensitive Networking +
Footnote †: journal: _Sensors_  
0000-0001-5000-0000-0000-0000-0000-0000-0000-0000-0000-0000-0000-0000-0000-00000-00000-0000-00000-00000-0000-00000-00000-00000-00000-  
In order to increase the reliability achievable by Ethernet networks, the TSN TG has completed the standardisation of two fault tolerance mechanisms. The first mechanism enables the use of space redundancy [6; 7], i.e., it allows for an end-system to send each frame through several communication paths in parallel. The second mechanism implements error containment, which allows detecting incorrect frames and reducing the negative impact that they may have on the network [8]. Nevertheless, the TSN TG has not proposed any time redundancy mechanisms in layer 2 of the network architecture to tolerate temporary faults in the links. Even though temporary faults can be tolerated using space redundancy, it is not always the most adequate solution nor the classical approach for tolerating temporary faults. Since space redundancy requires the addition of hardware to the network, using it to tolerate temporary faults may not be cost-effective and it increases the size, weight, cabling routing, installation effort and energy consumption of the network subsystem. Therefore, in previous works we proposed to use time redundancy to tolerate temporary faults in the links, as we think it is a more suitable solution, specifically for systems with cost, size, weight, or energy restrictions. Specifically, we have designed the Proactive Transmission of Replicated Frames (PTRF) mechanism to provide time redundancy to TSN-based networks. PTRF consists in transmitting several copies (replicas) of each frame in a preventive manner, to increase the chances of each frame reaching its destination. We have designed three different approaches to PTRF: We presented the first two, namely A and B, in [9]; whereas we proposed the third one, \(C\), in [10]. Furthermore, we published a detailed description of all the PTRF mechanisms in [11]. Despite the interest in providing TSN networks with fault-tolerance mechanisms, to the best of the authors' knowledge, there are no previous works that quantify the reliability that these mechanisms can yield. In fact, most of the works that treat space redundancy in TSN focus on evaluating the impact on the performance, bandwidth or schedulability of the network. Furthermore, even the works that do focus on dependability aspects do not provide a quantitative measure for the reliability. Instead, they analyse it in a qualitative manner or focus on specific gains in the fault tolerance capabilities, e.g., counting the number of simultaneous faults that can be tolerated.