# Planning of Optical Connections in 5G Packet-Optical xHaul Access Network
## 5 Numerical Results
For instance, one of the paths in the left-side figure begins in node 8 and goes through intermediate nodes 3 and 0, where some wavelengths are introduced into the path by means of OADMs, and finally terminates in the hub site attached to node 2. We can see that six optical paths are sufficient to carry traffic load \(\rho=1.0\), whereas two more paths (eight paths in total) are required to support scenario \(\rho=2.0\). This difference is a result of a higher number of wavelengths requested at certain sites in the latter scenario which cannot be served due to a limited capacity of the WDM transmission system (4 wavelengths). Note that there are also some differences in the placement of OADMs (i.e., the assignment of remote nodes to the paths) in both scenarios. For instance, node 12 is either an intermediate node of the orange path in scenario \(\rho=1.0\) or an end node of the light blue path in scenario \(\rho=2.0\). In Figure 5, we present averaged results of the number of transmission paths (left chart) and overall length of transmission paths (right chart) in a function of traffic load (\(\rho\)) in WRO17, assuming MUX loss \(A_{\text{MUX}}=1.8\) dB and \(k=3\) candidate paths. Additionally, in both figures, we show a relative difference (gain) in the obtained results when compared to the noOADM reference scenario. We can see that 6 transmission paths are sufficient to serve all traffic in the network when each remote node generates a 1-wavelength demand (i.e., \(\rho=1.0\)). This is achieved by aggregation of wavelengths (using OADMs) from different remote sites onto WDM optical transmission paths. In this case, the reduction of the number of required transmission paths (i.e., relative gain) versus the scenario without OADMs reaches about 65%. Increasing the traffic load, the number of transmission paths increases (and the relative gain decreases) up to the moment when all remote nodes need dedicated transmission paths. It happens when 3.5 wavelengths, on average, are requested by each remote node (\(\rho=3.5\)), and there is no use of OADMs due to saturation of the WDM system, which capacity is 4 wavelengths. The overall length of optical transmission paths (shown in the right chart) follows a similar trend. In particular, the length of dedicated fiber connections required in the noOADM scenario is about 34.5 km, which can be reduced by up to 60% (to about 14 km) in a network with a low load (\(\rho=1.0\)). We report that similar results were obtained for other considered values of \(A_{\text{MUX}}\). Figure 4: Optimal solutions obtained in WRO17 for traffic load \(\rho=1.0\) (**left**) and \(\rho=2.0\) (**right**). In Figure 6, we analyze the impact of the number of candidate routing paths \(k\) on obtained results in network MESH38. We focus on the number of optical transmission paths (left chart) in a function of \(k\) and traffic load, \(\rho\in\{1.0,1.5,2.0\}\), for different values of MUX loss (\(A_{\text{MUX}}\)). Moreover, in the right chart, we show a relative difference in results when compared to a single (shortest) path scenario (\(k=1\)). In each scenario, we can see that provisioning of a higher number of candidate routes (\(k>1\)) allows for reducing the number of optical transmission paths required in the network when compared to the shortest-path case. The gain in performance increases with \(k\) and ranges between \(16\%\) and \(32\%\), depending on traffic and MUX scenario, for \(k\geq 5\). We can also see that the results stabilize for \(k\geq 5\) and that the improvement for \(k=7\) is either none or irrelevant (as for \(\rho=2.0\)). Finally, higher differences in obtained results are observed for lower MUX loss values at lower traffic loads. It can be explained by higher transmission distances and numbers of allowable OADMs (as shown in Table 2) in low MUX loss scenarios, which translates into a higher chance to inject single wavelengths into transmission paths at intermediate nodes, especially if several alternative candidate paths are available.