# On the Design of a Network Digital Twin for the Radio Access Network in 5G and Beyond
## 4 Results
### Performance Evaluation
\begin{table}
\begin{tabular}{l c c c c} \hline \hline  & **Parameter** & \begin{tabular}{c} **Moming** \\ **(8–16 h)** \\ \end{tabular} & \begin{tabular}{c} **Afternoon** \\ **(16–24 h)** \\ \end{tabular} & \begin{tabular}{c} **Night** \\ **(0–8 h)** \\ \end{tabular} \\ \hline \begin{tabular}{c} User density \\ (users/km\({}^{2}\)) \\ \end{tabular} & Tenant 1 & 3000 & 2000 & 100 \\  & Tenant 2 & 1000 & 4000 & 500 \\ \hline \begin{tabular}{c} User types \\ percentages \\ \end{tabular} & \begin{tabular}{c} Stationary \\ Pedestrian \\ Vehicle \\ \end{tabular} & \begin{tabular}{c} 50\% \\ 40\% \\ Vehicle \\ \end{tabular} & \begin{tabular}{c} 60\% \\ 30\% \\ 10\% \\ \end{tabular} & \begin{tabular}{c} 90\% \\ 5\% \\ 5\% \\ \end{tabular} \\ \hline \begin{tabular}{c} Traffic \\ generation \\ parameters \\ \end{tabular} & \
\begin{tabular}{c} Session generation rate (\(\lambda\)) \\ Average session \\ duration (\(\mu\)) \\ \end{tabular} &
\begin{tabular}{c} 1 session/s \\ 300 s \\ \end{tabular} & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Emulation parameters for training. As an output of the _visualization_ model in the RAN NDT, Figure 5 depicts the evolution of the aggregated average reward of both tenants, denoted as \(R\), as a result of the evaluations conducted periodically during the training. The figure shows that during the first 250\(\cdot 10^{3}\) training steps, \(R\) increases abruptly, experiencing large fluctuations. After this period, \(R\) increases in a slower slope with lower fluctuations until it stabilizes at a value of around 1.6 after approximately 1500\(\cdot 10^{3}\) training steps. These results highlight the usefulness of the implemented RAN NDT to conduct the training of the DQN-MARL capacity sharing solution. Moreover, the _visualization_ model in the RAN NDT also provides Figure 6, which compares the assigned capacity per tenant by the learnt policy after convergence to their respective offered loads in the different gNBs (subplots (a)-(e)) and system level (subplot (f)). In subplots (a)-(e) both the offered loads and assigned capacities are normalized to the gNB capacity. The results in these subplots illustrate that the assigned capacity per cell adapts to the offered load in all gNBs. Moreover, subplot (f) compares the offered loads and assigned capacities to both tenants in aggregated terms over all gNBs, both normalized to the system capacity. From this subplot, the fact that the learnt policies allow satisfying the \(SAGBR_{k}\) requirement can be observed as the aggregated offered loads per tenant, which are lower  
Figure 4: Offered loads per tenant and aggregated for (a) gNB 1, (b) gNB 2, (c) gNB 3, (d) gNB 4, (e) gNB 5 and (f) at system level. \begin{table}
\begin{tabular}{l c} \hline \hline  & **Parameter** \\ \hline Initial collect steps & 80,000 \\ Maximum number of time steps for training & 1.5\(\cdot 10^{6}\) \\ Experience Replay Buffer length (\(l\)) & \(10^{7}\) \\ Mini-batch size (\(l\)) & 256 \\ Learning rate (\(\tau\)) & 0.0001 \\ Discount factor(\(\gamma\)) & 0.9 \\ \(\varepsilon\) value (\(\epsilon\)-Greedy) & 0.1 \\  & Input layer: 17 nodes \\ DNN configuration & 1 full connected layer: 100 nodes \\  & Output layer: 243 nodes \\ Reward weights (\(\varphi_{1}\), \(\varphi_{2}\)) & (0.5. 0.4) \\ Action step (\(\Delta\)) & 0.03 \\ Time step (\(\Delta t\)) & 30 s \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Configuration of the hyperparameters of the DQN-MARL capacity sharing solution. than their respective \(SAGBR_{k}\), are satisfied. Hence, the learnt policies on the implemented RAN NDT allow adapting the assigned capacity to the offered loads while satisfying the SLA of both tenants.