## 4 Numerical Results
### Analysis of Network Performance  
In this section, we evaluate performance of the NGFI network in different network scenarios. The main performance metrics that we focus on are the number of active PP nodes and flows latencies. The evaluation is performed in the RING-10 network topology in which different numbers of RUs (\(R\in\{20,30,40\}\)) are considered. Moreover, the lengths of network links are scaled using parameter \(M\). Namely, for link multiplier \(M=1\), the lengths of links are shown in Table 3, and the links are twice long for \(M=2\). Eventually, we scale PP capacities by considering different vales of \(C\), where \(C\) is between 1 and 2.5. In Figure 4, the number of active PPs as well as the average latency of the total RU-DU-CU-DC flow is shown in different RING-10 scenarios. The network with longer links requires a higher number of active PPs than the network with basic links. This is related to larger propagation delays in the former scenario, what turns into the need for closer placement of DUs in the network with respect to the RU sites in order to meet latency requirements. Moreover, we can observe that increasing the PP capacity (parameter \(C\)) allows to activate a smaller number of PP nodes in which the DU and CU entities are placed. Note that in each network there is some value of \(C\)--for instance, \(C=1.5\) for the network with basic links and 40 RUs--above which the number of active PPs is not decreased anymore. This value can be considered as the best one since it minimizes both the number of active PP nodes and the required PP processing capacity, where both factors contribute to the network deployment cost. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multicolumn{2}{c}{**Scenario**} & \multicolumn{5}{c}{**Optimization Results**} \\ \hline
**Network** & \(|\mathcal{D}|\) & \(C\) & \(z^{LB}\) & \(z^{MILP}\) & \(\Delta^{MILP}\) & \(T^{MILP}\) (s) & Active PPs & Latency [\(\mu\)s] \\ \hline RING-10 & 80 & 1 & 715,485 & 715,668 & 0.03\% & 10,800 & 7 & 15,668 \\  & & 2 & 418,224 & 418,224 & 0.00\% & 935 & 4 & 18,224 \\  & & 3 & 418,224 & 418,224 & 0.00\% & 446 & 4 & 18,224 \\ \hline DRING-16 & 64 & 1 & 973,213 & 1,013,174 & 3.94\% & 10,800 & 10 & 13,174 \\  & & 2 & 513,737 & 514,023 & 0.06\% & 10,800 & 5 & 14,023 \\  & & 3 & 513,514 & 513,514 & 0.00\% & 961 & 5 & 13,514 \\ \cline{2-8}  & 80 & 1 & 1,016,681 & 1,017,050 & 0.04\% & 10,800 & 10 & 17,050 \\  & & 2 & 521,205 & 521,443 & 0.05\% & 10,800 & 5 & 21,443 \\  & & 3 & & & _out-of-memory_ & & & \\ \hline MESH-20 & 40 & 1 & 805,959 & 805,959 & 0.00\% & 696 & 8 & 5959 \\  & & 2 & 406,450 & 406,450 & 0.00\% & 295 & 4 & 6450 \\  & & 3 & 405,822 & 405,822 & 0.00\% & 91 & 4 & 5822 \\ \cline{2-8}  & 60 & 1 & 809,233 & 910,424 & 11.12\% & 10,800 & 9 & 10,424 \\  & & 2 & 463,297 & 510,047 & 9.17\% & 10,800 & 5 & 10,047 \\  & & 3 & 412,050 & 412,050 & 0.00\% & 348 & 4 & 12,In Figure 4, we can also see that the average latencies of the RU-DU-CU-DC flow are maintained on quite a similar level, which does not change significantly with \(R\) and \(C\). This can be explained as following. On one hand, increasing the number of RUs in the network should increase the overall network latency. However, this effect is compensated by a larger number of active PPs and higher PP capacities (see Equation (29)) available in the scenarios with a larger number of RUs. In particular, it allows to place the DUs and CUs in less distant PP nodes and, by these means, to decrease flow latencies. To analyze this relationship in detail, in Figure 5 we present the percentage of demands for which the DU and CU processing is performed in the same PP nodes. As we can see, if a higher PP node capacity is available, which may be due to both higher number of RUs and larger \(C\), then more demands have their DU and CU entities placed in the same PP node. Consequently, the MH flows are not present in the network, and they do not contribute to the overall network latency.