## 4 Numerical Results
### Performance of LDCP-MILP Model  
We begin with evaluating the complexity of the LDCP-MILP model and the quality of obtained solutions. To this end, we solve different instances of the LDCP problem that vary in size. In particular, different network topologies, number of demands (\(|\mathcal{D}|\)), and PP capacities (expressed using PP capacity multiplier \(C\)) are considered. We remind that each RU involves two associated demands in the network, namely an uplink and a downlink demand; hence, the number of RUs in each scenario is \(|\mathcal{D}|/2\). A 3 h computation limit is assumed in the CPLEX solver. The metrics that we report are the objective function value (\(z^{MILP}\)), computation time (\(T^{MILP}\)), and MILP optimality gap \(\Delta^{MILP}\). The optimality gap is a relative difference between \(z^{MILP}\) and the solution lower bound (\(z^{LB}\)) found in CPLEX within the computation period. Additionally, we report the obtained values of the number of active PPs (\"_Active PPs_\") and the overall latency of flows (\"_Latency_\").  
In Table 4, we can see that the results obtained by solving the LDCP-MILP model are either optimal (i.e., \(\Delta^{MILP}=0\%\)) or close to optimal for the majority of scenarios tested. In the cases for which near-optimal results were obtained (i.e., \(\Delta^{MILP}\leq 0.06\%\)), the number of active PPs is optimal (compare the most significant numbers in \(z^{LB}\) and \(z^{MILP}\)), and there is some difference in terms of latency between solution lower bounds (\(z^{LB}\)) and best objective value (\(z^{MILP}\)). We remind that the number of active PPs is the main optimization objective in the optimization problem considered. For the cases with larger optimality gaps (\(\Delta^{MILP}=3.94\%\) and \(\Delta^{MILP}=9.17\%\)), we can deduce that the number of active PPs is also optimal. In particular, by subtracting the value of latency from \(z^{LB}\) and dividing the obtained number by the weighting coefficient (\(A=10^{5}\)), we obtain a number--namely 9.6 for \(\Delta^{MILP}=3.94\%\) and 4.53 for \(\Delta^{MILP}=9.17\%\)--that, rounded up, equals to the obtained value of active PPs. Note that in this analysis, rounding up is performed because the number of active PPs should be an integer number and not lower than the value resulting from the lower bound. Eventually, in the case for which \(\Delta^{MILP}=11.12\%\), the obtained number of active PPs is either optimal or it differs by not more than one from the optimal value (compare the values of \(z^{LB}\) and \(z^{MILP}\) divided by weighting coefficient \(A\)).  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Network Link** & **Link Length (km)** & **Link Capacity (Gbit/s)** \\ \hline Switch–RU & \([0.2\dots 0.5]\) & 25 \\ Switch–PP & \([0.2\dots 0.5]\) & 400 \\ Switch–DC & \([10\dots 15]\) & 400 \\ Switch–switch & \([1\dots 3]\) & 100 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Assumed values of link lengths and capacities.  
In Table 4, we can also see that the complexity of solving the LDCP-MILP model decreases with increasing the available PP capacity (\(C\)). Finally, we report that when solving larger problem instances, we have encountered the problem of out-of-memory during processing of the branch-and-bound tree in CPLEX. Therefore, for solving larger problem instances, heuristic methods might be used, and we plan to develop such optimization methods in our future work.  
After verifying that the quality of LDCP-MILP solutions is high, in the remainder of this work, we analyze the NGFI network using the LDCP-MILP model.