## 3 System Model and QoT Estimation
### Physical-Layer Impairments Estimation  
In C+L-EONs, the deployment and maintenance of Raman amplification across all links bring significant challenges. Therefore, for long-haul transmission, the optical signals in both C and L bands are amplified solely by EDFA. Given the distinct characteristics of these bands, it was necessary to configure different parameters for EDFA in each band. Additionally, we employed the generalized GN model, as described in [21], to accurately assess the \(OSNR\). This model comprehensively considers various factors, including ISRS, ASE noise, SPM, and XPM. Consequently, the \(OSNR\) of a given request, designated as \(r\), can be accurately determined by Equation (6). \[OSNR_{r}=\frac{P_{r}}{\sigma_{\text{ASE}}^{2}(f_{r})+\sigma_{\text{NLI}}^{2}(f_{ r})}, \tag{6}\]  
The transmit power of request \(r\) is denoted as \(P_{r}\). The ASE noise variance is represented as \(\sigma_{\text{ASE}}^{2}(f_{r})\), which can be determined through Equation (7). Furthermore, the NLI variance is designated as \(\sigma_{\text{NLI}}^{2}(f_{r})\) and can be calculated by Equation (8). These parameters play a crucial role in accurately assessing the performance of the system. \[\sigma_{\text{ASE}}^{2}(f_{r})=2n_{sp}\text{h}f_{r}B_{r}(\alpha L-1), \tag{7}\]  
\[\sigma_{\text{NLI}}^{2}(f_{r})=\sigma_{\text{SPM}}^{2}(f_{r})+\sigma_{\text{ XPM}}^{2}(f_{r}), \tag{8}\]  
The spontaneous emission noise on EDFA is denoted as \(n_{sp}\), while h signifies [PERSON]'s constant, and \(\alpha\) denotes the attenuation coefficient of the fiber. The SPM and XPM variances are designated as \(\sigma_{\text{SPM}}^{2}(f_{r})\) and \(\sigma_{\text{XPM}}^{2}(f_{r})\), respectively, and they can be computed by Equations (9) and (10). \[ \begin{array}{l}\sigma_{\text{SPM}}^{2}(f_{r})=\frac{4}{27}N\frac{P_{r}^{3} }{B_{r}^{2}}\frac{\gamma_{r}^{2}\tau}{\phi_{r}\alpha^{2}}e^{2C\overline{k}_{ rff}(L),f_{r}}\\ \left[\frac{(2\alpha-C,f_{r})^{2}-a^{2}}{\alpha}\arcsinh(\frac{\phi_{r}B_{r}^ {2}}{\alpha\pi})+\right.\\ \frac{4\alpha^{2}-(2\alpha-C,f_{r})^{2}}{2\alpha}\arcsinh(\frac{\phi_{r}B_{r} ^{2}}{\alpha\pi})\right]\end{array} , \tag{9}\]  
Figure 1: The example of calculating the weight of the route. (**a**) The network topology with 4 nodes and 5 links. (**b**) The occupancy of the spectrum resource in the network. (**c**) The alternative routes and corresponding parameters. \[ \begin{split}&\sigma_{\text{XPM}}^{2}(f_{r})=\frac{32}{81}P_{r}N\sum \limits_{k=1}^{N_{s,l}}\frac{P_{k}^{2}}{B_{k}}\frac{\gamma_{r,k}^{2}}{\phi_{r,k} a^{2}}\varepsilon^{2C,\overline{k}L_{eff}(L)/f_{k}}\\ &[\frac{(2\alpha-C_{r}f_{k})^{2}-\alpha^{2}}{\alpha}\text{arctan }(\frac{\phi_{r,k}B_{r}}{\alpha})+\\ &\frac{4\alpha^{2}-(2\alpha-C_{r}f_{k})^{2}}{2\alpha}\text{ arctan}(\frac{\phi_{r,k}B_{r}}{2\alpha})]\end{split} , \tag{10}\]  
In Equations (9) and (10), the variable \(N\) represents the total number of spans within the system. \(P_{r}\) denotes the transmit power associated with request \(r\). \(\gamma_{r,r}\) denotes the nonlinear coefficient on the fiber. Furthermore, \(C_{r}\) signifies the linear regression slope pertaining to the normalized Raman gain spectrum. \(N_{s,l}\) denotes the count of requests present in link \(l\), excluding request \(r\). The request transmit power within link \(l\) is represented by \(P_{k}\). The required bandwidth of request is denoted as \(B_{k}\). \(f_{k}\) represents the request center frequency. The effective length \(L_{eff}(L)\), nonlinear coefficient \(\gamma_{r,k}\), phase rotation \(\phi_{r}\), and cross-phase modulation \(\phi_{r,k}\) can be calculated by Equations (11)-(14), respectively. \[L_{eff}(L)=\frac{1-e^{-\alpha L}}{\alpha}, \tag{11}\]  
\[\gamma_{r,k}=\frac{2\pi}{\lambda_{r}}\frac{2n_{2}}{A_{eff}(\lambda_{r})+A_{ eff}(\lambda_{k})}, \tag{12}\]  
\[\phi_{r}=\frac{2}{3}\pi^{2}(\beta_{2}+2\pi\beta_{3}f_{r}), \tag{13}\]  
\[\phi_{r,k}=2\pi^{2}(f_{k}-f_{r})[\beta_{2}+\pi\beta_{3}(f_{k}+f_{r})], \tag{14}\]  
where \(\lambda_{r}\) represents the wavelength associated with request \(r\).