## 5 Performance Evaluation and Analysis  
The performance of the proposed BMA-RSA algorithm is evaluated using distance-adaptive modulation format selection on _USNET_ topology (24 nodes and 43 links) and _NSFNET_ topology (14 nodes and 21 links), as shown in Figure 3a,b. The distance and spectrum occupation for various bit rates are shown in Table 2. We used JAVA to set up a simulation platform to solve the situation. The simulation requires a total of 8 THz spectra for each link, which is evenly divided in each direction. A total of 500,000 connection requests following Poisson arrival and exponential departure were generated in each simulation run, and the bitrate demands of the connection requests are chosen uniformly among {40, 100, 200, 400} Gbps. For each traffic load scenario, 20 simulation experiments were conducted for different serials of connection requests. Both the mean and confidence interval at the 95% were evaluated and plotted as \"I\" in the result graphs. Spectrum continuity and contiguity are taken into consideration. During the process of node upgrade, we assumed that no new services were accommodated for in the network. Therefore, when the network node is selected to be upgraded, we changed the node attributes from the fixed-grid node to the flex-grid node. In our simulation, we generated a large number of services according to the traditional model, and analyzed the traffic information of each node statistically as the basis for analyzing and computing the upgrade probability of nodes. Since traffic may influence the migration strategies, two traffic models, in which traffic either uniformly or non-uniformly distributed among all the nodes are considered in practical fixed/flex-grid optical networks. In the non-uniform case, traffic is distributed according to the population of the city at the corresponding node and is positively correlated with the population [25]. In the uniform case, traffic is evenly distributed at all nodes. For the traffic models, the upgrading of 8 nodes and 16 nodes is considered, respectively. For each request, in order to verify the performance of the _brown-field migration aware routing and spectrum assignment_ algorithm, we use traditional _K-shortest-path routing and spectrum assignment (K-SP-RSA)_ algorithm with first fit spectrum assignment (\(k=1,2,3\)) as a comparison. In this section, we focused on the terms of bandwidth blocking ratio, which represents the rejected request bandwidth over the total bandwidth, and connection interrupted ratio, which is defined by the number of services interrupted due to node upgrade over the total number of deployed service connection, the result is statistically averaged after multiple simulations. The simulations run on a computer with 1.8 GHz Intel Core i7-8565U CPU. The IntelliJ IDEA 2020 is installed in this computer to implement the proposed algorithm. Figure 3: Simulation topology. (**a**) USNET topology (24 nodes and 43 links) (**b**) NSFNET topology (14 nodes and 21 links). Comparison of the proposed _BMA-RSA_ algorithm and _SP-RSA_ algorithm, by upgrading 8 nodes in _USNET_ topology and upgrading 5 nodes in _NSFNET_ topology under a uniform and non-uniform traffic model in terms of BBR, are shown in Figure 4. We set \(\alpha=1\), \(\beta=2\) and \(\alpha=1\), \(\beta=0\) for their topologies, respectively. We can see that the trend of the bandwidth blocking ratio versus traffic load in _USNET_ topology and _NSFNET_ topology is similar. It is obvious that the BBR increases with the increase of the traffic load in both algorithms in two topologies. Meanwhile, as the number of paths (i.e., the value of k) selected increases, the bandwidth blocking ratio of both algorithms decreases. The reason is that a larger number of short paths mean more options for data transmission, which will more effectively resist service interruption. Meanwhile, we find that the BBR under the _NSFNET_ topology is generally higher than that under the _USNET_ topology.