# On the Design of a Network Digital Twin for the Radio Access Network in 5G and Beyond
## 4 Results
### Performance Evaluation  
The assessment of the performance of the training of the DQN-MARL capacity sharing solution on the implemented RAN NDT is provided in this section. To conduct the training, the _environment specification_ functionality in Figure 2 has provided the model configuration values in Table 1 to the _models activation & configuration_ functionality of the implemented RAN NDT. The scenario consists of two tenants, denoted as Tenant 1 and Tenant 2, that share the capacity of 5 gNBs. Moreover, the _environment specification_ functionality sets the emulation parameters in the _emulating running control_ functionality of the implemented RAN NDT according to the values included Table 2 in terms of the user density in the RANarea for the two considered tenants, the percentage of users of each type (i.e., stationary, pedestrian or vehicle) at morning, afternoon and night and the traffic generation parameters. The parameters considered for Tenant 1 correspond to a business profile, which has more density of users during the morning, while those considered for Tenant 2 correspond to a residential profile, which is more intense during the afternoon. The RAN NDT execution for the training is performed by repeatedly generating different random realizations of traffic generation and mobility following the parameters in Table 2. The emulation in the RAN is performed in time steps of 1 s duration, while the monitoring of the different models is performed by averaging the different traffic-related metrics every 3 min. The considered configuration for the DQN-MARL capacity sharing solution is given by the parameters of Table 3. For details on the meaning of each parameter, the reader is referred to [19]. Based on this, the training is performed through the interaction of the RL agents in the DQN-MARL capacity sharing solution with the RAN NDT according to an \(\epsilon\)-Greedy policy. Moreover, the RAN NDT is configured to provide an evaluation of the trained policy every 5000 steps of training, where a step is one interaction of the RL agents with the RAN NDT instance. This evaluation consists in the application of the trained policy until that moment without considering random actions (i.e., a greedy policy) to a specific realization of the morning-afternoon-night pattern of Table 2 that is shown in Figure 4. The subplots from (a)-(e) depict the evolution of the offered load (i.e., required bit rate) per tenant and the aggregated offered load of both tenants in gNBs 1 to 5, respectively, both normalized to the average gNB capacity. In all the gNBs and according to the emulation configuration in Table 2, the offered load of Tenant 1 is larger during the morning (\(t=0\) min until \(t=480\) min in Figure 4), while it is reduced approximately by 40% during the afternoon (\(t=480\) min until \(t=960\) min in Figure 4) and it is very low during the night (\(t=960\) min until \(t=1440\) min in Figure 4). Instead, the offered load of Tenant 2 remains low during the morning and night, but experiences similar offered load levels to Tenant 1 during the afternoon. Focusing on the aggregated offered loads in each gNB, gNB 1 experiences overload sometimes during the afternoon (i.e., the aggregated offered load is larger than 1), while gNBs 2-5 always have enough capacity to fulfil the offered loads of both tenants. This is because gNB 1 is located in a park (see Figure 3) with higher affluence than the rest of the gNBs. Moreover, subplot (f) in Figure 4 shows the aggregated offered load in the system (i.e., among all the gNBs) per tenant, jointly with the aggregated offered load of both tenants in the system, both normalized to the total system capacity. Note that the aggregated offered loads in the system are generally below the \(SAGBR_{k}\) of both tenants (i.e., 50% of system capacity for Tenant 1 and 30% of system capacity for Tenant 2), only exceeding it sporadically in the case of Tenant 2 during the afternoon.