# NMR-MPar: A Fault-Tolerance Approach for Multi-Core and Many-Core Processors
## 5 Discussion  
The MPPA many-core processor running massive parallel applications on POSIX was evaluated through different scenarios of the application: (1) without redundancy; (2) with the NMR-MPar approach without a supervisor; and (3) with the NMR-MPar approach with a supervisor. This section presents a comparison between the results of fault-injection campaigns. Figure 4 illustrates the consequences of injected SEUs. From the results, it is possible to observe that all the erroneous results and timeouts were surpassed by applying the NMR-MPar approach. Concerning the exceptions, the best response is obtained under the scenario with a supervisor. The current study also considers the evaluation of the reliability of a system during its lifetime. Hence, the failure rate function (\(\lambda\)) is assumed to be constant, and the reliability function is characterized by the expression (2). \[R(t)=e^{-\lambda t} \tag{2}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Application** & \(\tau_{Inf\_no\_supervisor}\) & \(\tau_{Inf\_supervisor}\) \\ \hline TSP & 2.45 \% & 0.01 \% \\ MM & 6.04 \% & 0.19 \% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Error-rates for 4 MR-8 Par applications implemented on the MPPA. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Application** & **Silent Faults** & **Erroneous Results** & **Timeouts** & **Exceptions** \\ \hline TSP & 8124 & 0 & 0 & 204 \\ MM & 68,303 & 0 & 0 & 4393 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results of fault-injection campaigns on 4 MR-8 Par applications without a supervisor. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Scenario** & **Core Stuck** & **Segmentation Fault** & **Device Exit** & **Total Exceptions** \\ \hline TSP-no-try & 39 & 165 & 0 & 204 \\ TSP-try & 0 & 0 & 1 & 1 \\ MM-no-try & 402 & 3948 & 43 & 4393 \\ MM-try & 0 & 95 & 46 & 141 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Exceptions produced by fault-injection on the 4 MR-8 Par applications. The failure rate at a given operating environment is calculated from the soft error-rate obtained by fault injection (\(\tau_{Inj}\)) by applying (3). \[\lambda_{CEU}=\tau_{Inj}\times\sigma_{Static}\times\phi \tag{3}\]  
where \(\sigma_{Static}\) is the static cross-section, which is the average number of particles needed to cause a bit-flip in a memory cell. Its value is obtained from radiation experiments. \(\phi\) is the flux of particles at the specific operation environment. Regarding the reliability, it was considered that applications are intended to be used in the avionics domain for commercial airlines, being the neutron flux at 35,000 ft of altitude (\(\phi_{cv}=\)2993.2 n/cm\({}^{2}\)/h) with a system life time of 50,000 h. The \(\sigma_{Static}=\) 12.71\(\times\) 10\({}^{-9}\) cm\({}^{2}\)/device was taken from a previous work [8]. Table 7 summarizes the estimated failure rates per hour computed using (3) at avionics altitude for both applications under three scenarios: without the fault-tolerance approach, NMR-MPar running with the supervisor and implemented with NMR-MPar running without the supervisor device. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Application** & **Without\_FT** & **No\_Supervisor** & **Supervisor** \\ \hline TSP & \(9.93\times 10^{-7}\) & \(9.32\times 10^{-7}\) & \(3.80\times 10^{-9}\) \\ MM & \(5.47\times 10^{-6}\) & \(2.30\times 10^{-6}\) & \(7.23\times 10^{-8}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Failure rates per hour at 35,000 feet for 4 MR-8 PaR applications implemented on the MPPA. Figure 4: Comparison of Single Event Upset consequences per scenario in N-Modular Redundancy and M-Partions applications. The reliability of the MM application under the three mentioned scenarios is shown in Figure 5.  
A similar comparison was done for the TSP application. Figure 6 illustrates the reliability for the three scenarios. From both results, it is possible to confirm the significant reliability improvement by the use of the NMR-MPar approach.