# An Efficient Library for Reliability Block Diagram Evaluation
## 5 Results and Discussion: Evaluation of librbd Performance
### Evaluation of librbd Execution Time
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Topology**} & \multirow{2}{*}{**\# Times**} & \multicolumn{5}{c}{**Execution Time (ms)**} \\  & & **PC1** & **PC2** & **PC3** & **PC4** & **PC5** \\ \hline
1 oo2 & 50,000 & 0.171 & 0.293 & 0.199 & 0.617 & 1.397 \\
1 oo2 & 100,000 & 0.250 & 0.378 & 0.367 & 0.805 & 3.613 \\
1 oo2 & 200,000 & 0.533 & 0.748 & 0.598 & 1.537 & 8.085 \\
2 oo3 & 50,000 & 0.377 & 0.334 & 0.380 & 0.649 & 3.745 \\
2 oo3 & 100,000 & 0.616 & 0.482 & 0.718 & 1.002 & 6.674 \\
2 oo3 & 200,000 & 0.980 & 0.856 & 1.149 & 2.099 & 12.279 \\
3 oo5 & 50,000 & 0.491 & 0.372 & 0.579 & 0.964 & 5.452 \\
3 oo5 & 100,000 & 0.840 & 0.682 & 0.882 & 1.148 & 9.192 \\
3 oo5 & 200,000 & 1.251 & 1.244 & 1.513 & 2.056 & 15.876 \\
5 oo10 & 50,000 & 0.658 & 0.708 & 0.764 & 0.961 & 10.244 \\
5 oo10 & 100,000 & 1.315 & 1.396 & 1.220 & 1.309 & 15.746 \\
5 oo10 & 200,000 & 2.169 & 2.339 & 1.990 & 4.621 & 28.266 \\
8 oo15 & 50,000 & 1.422 & 1.168 & 1.720 & 2.651 & 18.303 \\
8 oo15 & 100,000 & 3.027 & 2.456 & 2.810 & 4.756 & 27.901 \\
8 oo15 & 200,000 & 4.403 & 4.035 & 4.940 & 10.613 & 48.033 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Performance evaluation of \(N/2\)oo\(N\) identical block. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Topology**} & \multirow{2}{*}{**\# Times**} & \multicolumn{5}{c}{**Execution Time (ms)**} \\  & & **PC1** & **PC2** & **PC3** & **PC4** & **PC5** \\ \hline
1 oo15 & 100,000 & 1.280 & 0.765 & 0.929 & 2.305 & 17.021 \\
2 oo15 & 100,000 & 10.944 & 10.057 & 9.167 & 24.552 & 88.657 \\
3 oo15 & 100,000 & 73.165 & 61.577 & 64.344 & 155.191 & 571.809 \\
4 oo15 & 100,000 & 183.721 & 341.797 & 183.270 & 604.827 & 2025.680 \\
5 oo15 & 100,000 & 406.931 & 836.953 & 418.733 & 1297.444 & 4983.553 \\
6 oo15 & 100,000 & 740.532 & 1503.900 & 753.573 & 2314.167 & 9237.214 \\
7 oo15 & 100,000 & 1062.330 & 2126.853 & 1071.369 & 3260.557 & 13.325.713 \\
8 oo15 & 100,000 & 1190.309 & 2386.732 & 1192.385 & 4171.043 & 15,280.717 \\
9 oo15 & 100,000 & 1064.583 & 2134.690 & 1052.093 & 3688.210 & 13,398.969 \\
10 oo15 & 100,000 & 742.056 & 1511.135 & 758.824 & 2466.044 & 9164.543 \\
11 oo15 & 100,000 & 411.900 & 837.570 & 417.853 & 1287.806 & 4967.779 \\
12 oo15 & 100,000 & 183.203 & 341.557 & 189.317 & 590.764 & 2015.668 \\
13 oo15 & 100,000 & 62.120 & 107.026 & 72.951 & 107.102 & 664.601 \\
14 oo15 & 100,000 & 9.432 & 15.416 & 10.368 & 17.220 & 100.526 \\
15 oo15 & 100,000 & 1.440 & 0.933 & 1.041 & 2.163 & 18.609 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Performance evaluation of \(N/2\)oo\(N\) generic block. The experiments with \(N/2\)oo\(N\) blocks are used to evaluate the worst case execution time of \(KooN\) blocks (see Tables 9-10). Using the optimized computation Algorithms 1 and 2 for Koo\(N\) blocks with generic components we verify that the complexity is \(O(N^{2}\cdot T)\) and that the complexity for Koo\(N\) blocks with identical components computed using Algorithm 3 is \(O(N\cdot T)\). The experiments with Koo15 blocks are used to evaluate the impact of the optimized algorithms for Koo\(N\) computation with a fixed number of components (see Tables 11-12). For these experiments, we observe that the execution time is, as expected, symmetrical w.r.t. the worst case \(K=N/2\). The experiments performed on all Koo\(N\) blocks are aligned with the foreseen complexity and hence they validate the correctness of both librbd design and optimization algorithms implemented for the most complex RBD block. Finally, as expected, for bridge block with both generic and identical components, we observe that the computation time is linear w.r.t. the number of time intervals (see Tables 13 and 14). In addition, for this last result, we confirm the correctness of librbd design w.r.t. the optimization of bridge blocks. Finally, it is important to note the execution times on the different PCs. We observe that, for all Intel i7 CPUs, we have obtained comparable results.