## 4 Algorithm Analysis
## 6 Evaluation

This study employs the MCD-BP algorithm in experiments with both real and simulated topologies. The real topology comprises 12 distinct topology diagrams, each depicting varying scales of network structures. Conversely, the simulated topology consists of 11 real topologies [32], generated using the Brite topology tool ([[https://www.cs.bu.edu/brite/download.html](https://www.cs.bu.edu/brite/download.html)]([https://www.cs.bu.edu/brite/download.html](https://www.cs.bu.edu/brite/download.html))). The model settings for this generator include Waxman as the configuration, along-side alpha values of 0.15 and beta values of 0.2. This generator produced five topologies with a degree of 4 and node counts of 20, 40, 60, 80, and 100. It also created six topologies with node counts of 200 and degrees of 2, 4, 6, 8, 10, and 12. The following Table 2 present the performance outcomes of the scheme across these diverse topologies. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Topology Name** & **Number of Routers** & **Number of Links** \\ \hline Abilene & 11 & 14 \\ Agis & 16 & 21 \\ Ans & 17 & 24 \\ Arpanet19719 & 18 & 22 \\ Arpanet19723 & 24 & 27 \\ Arpanet19728 & 29 & 32 \\ AttMpls & 25 & 56 \\ Belnet2004 & 18 & 34 \\ Cernet & 14 & 16 \\ NJLATA & 11 & 23 \\ USLD & 28 & 45 \\ VtlWavenet2008 & 88 & 92 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Topology information. The following table shows the detailed data of the real topology. ### Failure Protection Rate

The Failure Protection Rate (FPR) quantifies the likelihood that data can be successfully transmitted to the destination node in the event of a network failure. This metric serves as an index of the reliability of the routing protection scheme. Let \(N_{protected}\) denote the quantity of nodes that can be transmitted via the backup path in the event of network failure. Let \(N_{total}\) refer to the total count of nodes, excluding the destination node. The fault protection rate ranges from 0 to 1, where a value closer to 1 indicates superior fault protection capabilities. The FPR formula is expressed as follows:

\[FPR=\frac{N_{protected}}{N_{total}} \tag{12}\]

The subsequent figure illustrates the FPR as encapsulated by the MCD-BP algorithm, compared with other algorithms across various topologies. Figures 3 and 4 illustrate that the proposed MCD-BP method outperforms other algorithms in terms of FPR in real topologies. Specifically, Figure 3 shows that in real topology Abilene, the MCD-BP algorithm achieves a superior FPR of 1, significantly exceeding the rates of other algorithms. The FPR for the MARA, U-turn, LFC, and NPC algorithms are 0.88, 0.75, 0.49, and 0.48, respectively. The data presented clearly illustrate the substantial impact of the MCD-BP algorithm on fault recovery. This effect is markedly pronounced in the real topology A19728, where the MCD-BP algorithm demonstrates a FPR of 1. This rate noticeably surpasses those of the MARA algorithm (0.84), the U-turn algorithm (0.23), the LFC algorithm (0.069), and the NPC algorithm (0.069). Figure 4 present experimental data from the real topology V2008, demonstrating that the FPR of LFC, NPC, and U-turn are markedly lower than that of the MCD-BP algorithm. Specifically, the FPR of LFC and NPC, both 0.01926, are significantly below the rate achieved by the MCD-BP algorithm. The subsequent figure illustrates the FPR of various algorithms on a simulated topology. Through Figure 5, it is apparent that the proposed MCD-BP algorithm consistently exhibits a superior FPR within the simulated topology in comparison to its counterparts, maintaining stability. While the MARA algorithm's performance in the figure bears some resemblance to that of the MCD-BP algorithm, it surpasses MCD-BP slightly from the 60-4 virtual topology onwards. The LFC, NPC, and U-turn algorithms exhibit a decreasing trend in FPR as the node degree in the topology incrementally rises, as observed in the 40-4 and 60-4 topologies.