# Planning of Optical Connections in 5G Packet-Optical xHaul Access Network
## 5 Numerical Results  
In this section, we apply the ILP optimization model presented in Section 4 in network analysis. The evaluation is performed in two network topologies of different size: a 17-node city network (WRO17) and a 38-node mesh network (MESH38), shown in Figure 3. Topology WRO17 was developed based on a subset of real antenna locations (marked by triangles in Figure 3) in the center of city Wroclaw in Poland, where remote sites (marked by circles) are placed in proximity of antennas and connected using links driven along streets. The lengths of links in WRO17 reflect real physical lengths of depicted connections. In reference topology MESH38, which was used in C-RAN studies in Reference [20], we consider that link lengths are uniformly distributed between 1 and 3 kilometers. In both topologies, the hub site is denoted by a hexagonal. The routes of candidate transmission paths between remote nodes and the hub site have been generated using a \(k\)-shortest path algorithm. The paths of the length exceeding the maximum allowable path length (i.e., 10 km as discussed in Section 3.2) were excluded from the generated sets of candidate paths. In Table 4, we present some link and path-related statistics corresponding to the topologies. As mentioned in Section 4, each remote site requests a certain number of wavelengths to be carried towards the hub site. The number of wavelengths requested by a remote site is generated randomly with a uniform distribution between \(N^{min}\) and \(N^{max}\). Traffic load, denoted as \(\rho\), is defined as the average number of requested wavelengths per remote site, namely \(\rho=(N^{min}+N^{max})/2\). We evaluate different traffic scenarios, where \(N^{min}\geq 1\) and \(N^{max}\leq 4\). In particular, we have \(\rho=1.0\) for \(N^{min}=N^{max}=1\); \(\rho=1.5\) for \(N^{min}=1,N^{max}=2\); \(\rho=2.0\) for \(N^{min}=1,N^{max}=3\), etc. In each traffic scenario, the results are obtained and averaged over 10 randomly generated demand sets. We assume the transmission model and system parameters discussed in Section 3.1. In particular, we evaluate the impact of MUX loss \(A_{\text{MUX}}\) on network performance, where \(A_{\text{MUX}}\in\{1.8,1.62,1.44\}\) dB. As a reference scenario, denoted as no-OADMs, we consider the network in which OADMs are not used and dedicated transmission paths are estab \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Network**} & \multirow{2}{*}{**Remote Sites**} & \multirow{2}{*}{**Links**} & \multicolumn{2}{c}{**Link length [km]**} & \multicolumn{2}{c}{**SP length [km]**} & \multicolumn{2}{c}{**SP hops**} \\ \cline{3-10}  & & & **Mean** & **Max** & **Mean** & **Max** & **Mean** & **Max** \\ \hline WRO17 & 17 & 25 & 0.54 & 1.55 & 2.03 & 3.01 & 3.7 & 6 \\ MESH38 & 38 & 64 & 2.12 & 2.92 & 4.38 & 8.42 & 2.5 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Characteristics of analyzed networks; SP denotes the shortest path. Figure 3: WRO17 and MESH38 network topologies showing fiber connectivity between remote sites (circles) and hub site (hexagon); the triangles in WRO-17 represent real antenna locations. lished between every remote node and the hub. In particular, we have 17 and 38 such transmission paths in WRO17 and MESH38, respectively. The numerical experiments are performed on a 3.7 GHz 32-core Ryzen Threadripper-class machine with 64 GB RAM. To solve the ILP model, we use CPLEX v.12.9 solver [32]. All the results are optimal and computation times of CPLEX do not exceed 80 s in the most demanding scenario. In Figure 4, we illustrate optimal transmission paths found in network WRO17 for two selected traffic scenarios with loads \(\rho=1.0\) and \(\rho=2.0\), assuming MUX attenuation \(A_{\text{MUX}}=1.8\) dB and \(k=3\) candidate routing paths (no impact on results were observed for \(k>3\) in WRO17). The paths, as well as the remote nodes making use of the paths, are marked with different colors.