## 6 Simulation Results and Discussion  
In Figures 6 and 7, we show the normalized w.r.t. the Optimal solution of (17) energy efficiency (in bits/Joule) and computational time (in logarithmic scale), respectively, for all algorithms and different number of UEs. As can be seen, HERO provided a very good tradeoff between energy efficiency and complexity compared to the other approaches, achieving up to 78% of the Optimal value, with up to 742 times lower complexity. All algorithms had a 100% user acceptance ratio in all cases, except for BCSP which achieved 96% for \(N=20\), 93% for \(N=40\), and 91% for \(N=40\). This is due to the fact that in BCSP the CPU utilization of the computing nodes was not taken into account, resulting in less efficient VNF placement, which under higher traffic load could lead to a few UEs being blocked. The inefficiency of BCSP's VNF placement is also shown in Figure 8, where the power break down of all algorithms for different number of UEs per gNB sector area is presented. As shown, inefficient BCSP VNF placement led to a higher number of deployed computational nodes, and thus, higher power consumption. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** & **Parameter** & **Value** \\ \hline \(P_{i\text{\emph{l}}le}^{(sw)}\) & 315 W & \(P_{port}\) & 7 W & Packet length & 1.5 KB \\ \(N_{RF}^{(gNB)}\) & 8 & \(N_{RF}^{(\text{SC})}\) & 4 & \(N_{RF}^{(mmW)}\) & 64 \\ \(\Delta_{a}^{(gNB)}\) & 4.7 & \(\Delta_{a}^{(\text{SC})}\) & 4 & \(\Delta_{e}^{(mmW)}\) & 100 \\ \(P_{a}^{(gNB,i)}\) & 130 W & \(P_{a}^{(\text{SC},i)}\) & 6.8 W & \(P_{e}^{(mmW,i)}\) & 3.9 W \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Simulation Parameters [15; 25; 34]. Compared to Holu and BCSP, HERO achieved up to 60% and 86% higher energy efficiency, respectively, while keeping the complexity low, as shown in Figure 7. This is due to the fact that HERO additionally considered user association as part of the optimization problem leading to higher flexibility at the expense of a little higher complexity. On the other hand, in both Holu and BCSP, the serving BSs were already decided (based on the best SINR criterion) and then the optimal VNF placement and traffic routing from the UE traffic source to its serving BS were performed. This is also demonstrated in Figure 8, where the Optimal and HERO did not deploy the gNB in any case but used SCs as serving BSs (in contrast to Holu and BCSP), hence, leading to much lower power consumption. We also observed that the power consumption of the Optimal and HERO were scaling better than the SoA with increasing load (HERO still achieved 68% of the Optimal energy efficiency value when \(N=40\)). Figure 6: Energy efficiency (bits/Joule) of all algorithms for different numbers of UEs per gNB area. Figure 7: Execution time (s) in logarithmic scale of all algorithms for different numbers of UEs per gNB area. To further prove the improved performance of the proposed solutions (Optimal and HERO), we show in Figure 9, the percentage of active nodes and links for all algorithms for different number of UEs. As can be observed, Holu and BCSP, which did not optimize user association, kept the gNB always active, thus resulting in much higher power consumption, as shown in Figure 8. In addition, in Holu and BCSP, the number of active SCs, increased at a much higher rate with increasing load compared to the proposed approaches, which proves the scalability in terms of energy efficiency of the proposed solutions unlike the SoA. Compared to Holu, HERO activated fewer BH and FB links, and consequently fewer switches at the expense, however, of a higher number of active computational nodes.