## 5 Simulation Results and Analysis
### Performance of Bandwidth Blocking Probability and Resource Utilization  
In this section, we evaluate the performance of our proposed algorithm in terms of BBP and RU. These metrics can calculated as given in Equations (19) and (20) [34]:  
\[BBP=\frac{B_{\text{block}}}{B_{\text{total}}}, \tag{19}\]  
\[RU=\frac{\mu\cdot N_{\text{FS,occupied}}}{N_{\text{FS,total}}\cdot t_{\text{ network}}}, \tag{20}\]  
In the above formula, \(\mu\) denotes the holding time for all requests, which follows a negative exponential distribution. \(N_{\text{FS,occupied}}\) refers to the quantity of frequency slots currently in use by successfully established lightpaths, and \(N_{\text{FS,total}}\) signifies the total available FSs within the network; \(t_{\text{network}}\) represents the network runtime. Figure 3 compares the BBP between the proposed algorithm and the benchmark algorithms. The traffic load increases in both the NSFNET network and COST239 network, and the BBP also rises. This trend is attributable to the fact that a higher traffic load translates into a greater number of incoming requests per unit time, subsequently depleting the available FSs within the network. Consequently, a significant proportion of requests are either blocked or rejected, ultimately leading to a degradation in network performance. In comparison to benchmark algorithms, the proposed algorithm exhibits a lower BBP. Specifically, in the NSFNET network topology, under a traffic load of 600 Erlang, the BBP of the proposed algorithm is reduced by approximately 47.7% compared to the KSP(L)-MSP(C)-EFM algorithm. This is because the KSP(L)-MSP(C)-EFM algorithm employs the KSP routing strategy for the primary path selection, which, compared to the minimum  
Figure 2: The network topologies: (**a**) NSFNET network and (**b**) COST239 network. congestion-based routing method, tends to facilitate an excessive concentration of single-link services. This significantly elevates the BBP. The primary path selection in the LC(L)-DP(C)-EFM algorithm employs the minimum congestion-based routing strategy, leading to a lower BBP compared to the KSP(L)-MSP(C)-EFM algorithm. However, its backup path selection involves DPP, requiring one-to-one backup resources for the primary path, thereby increasing network resource consumption. As a result, its BBP is higher than that of the LC(L)-MSP(C)-EFM and LC(C)-MSP(L)-EFM algorithms, which employ SBPP. The comparison between the LC(L)-MSP(C)-EFM algorithm and the LC(C)-MSP(L)-EFM algorithm demonstrates that assigning the primary path to the L band and the backup path to the C band is superior to the reverse allocation of the primary path to the C band and the backup path to the L band. The proposed algorithm not only integrates both the minimum congestion and maximum sharing path selection methods but also refines the fragmentation measurement process. In comparison to entropy-based fragmentation measurement methods, the proposed algorithm enables a more precise quantification of path fragmentation, thereby facilitating the selection of optimal paths for services. Consequently, the chosen algorithm exhibits the lowest bandwidth blocking rate. Similarly, in the COST239 network, at a traffic load of 4200 Erlang, the BBP is reduced by approximately 22.1% compared to the LC(L)-DP(C)-EFM algorithm. This is due to the fact that the backup path of the LC(L)-DP(C)-EFM algorithm employs the DPP routing method. In contrast to the SBPP routing method, the DPP routing method consumes a greater amount of spectrum resources, significantly increasing the blocking rate. The KSP(L)-MSP(C)-EFM algorithm employs the KSP routing method for its primary path. In comparison to the minimum congestion routing method, the KSP routing method is prone to the phenomenon of an excessive number of single-link services, significantly escalating the BBP. Therefore, its level of BBP is inferior to algorithms employing the minimum congestion routing method.