# On the Design of a Network Digital Twin for the Radio Access Network in 5G and Beyond
## 5 Conclusions  
This paper has discussed on the design and applicability of a Network Digital Twin (NDT) for the Radio Access Network (RAN) subsystem. Aligned with the terminology on NDT introduced by IETF, the paper has proposed the architecture of a RAN NDT that is composed of different components for the gathering of data from the real RAN, for the representation of the different entities and functionalities of the RAN, for exporting relevant metrics and for the management of the RAN NDT. Based on the proposed RAN NDT architecture, the specific RAN NDT use case of training Reinforcement Learning (RL) algorithms for the RAN is described and different functionalities aligned with the O-RAN Alliance ML workflow are proposed to support the training on the RAN NDT.  
Moreover, the paper has described an illustrative example of an implemented RAN NDT for the training of a specific RL solution for capacity sharing, namely, the DQN-MARL capacity sharing solution, which allows the dynamic distribution of capacity in scenarios with multiple gNBs among multiple tenants. Results to illustrate the performance evaluation of the training of the solution have been provided for a specific configuration of the RAN NDT. Results show that the training of the solution is successfully performed, which proves the suitability of the implemented RAN NDT as a platform to conduct the training. Also, the learnt policies after training achieve high performance, satisfying the traffic demands of both tenants with low levels of overprovisioning and high service-level agreement satisfaction.  
Conceptualization, I.V., O.S. and J.P.-R.; Data curation, I.V. and J.P.-R.; Funding acquisition, O.S. and J.P.-R.; Investigation, I.V., O.S. and J.P.-R.; Methodology, I.V., O.S. and J.P.-R.; Project administration, O.S.; Resources, J.P.-R.; Software, I.V. and J.P.-R.; Supervision, O.S. and J.P.-R.; Validation, I.V., O.S. and J.P.-R.; Visualization, I.V. and J.P.-R.; Writing--original draft, I.V.; Writing--review & editing, I.V., O.S. and J.P.-R. All authors have read and agreed to the published version of the manuscript.  
This research has been partly funded by the Spanish Ministries of Science and Innovation (ARTIST project, ref. PID2020-115104 RB-I00, MCIN/AEI/10.13039/501100011033) and Economic Affairs and Digital Transformation and the European Union-NextGenerationEU (OPTIMAIX_NDT project, ref. TSI-063000-2021-35). The work is also partly funded by the European Union Smart Networks and Services (SNS) under Horizon-JU-SNS-2022 program (projects VERGE -grant #101096034- and BeGREEN - grant #101097083). The work of [PERSON] has also been funded by the European Union-NextGenerationEU, Spanish Ministry of Universities and the Plan for Recovery, Transformation and Resilience, through the call for Margarita Salas Grants of the Universitat Politecnica de Catalunya (ref. 2022 UPC-MSC-94079).  
Not applicable.  
The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline  & **Parameter** & **Tenant 1** & **Tenant 2** \\ \hline Average reward & 0.78 & 0.84 \\ Average SLA satisfaction & 0.88 & 0.90 \\  & gNB 1 & 0.83 & 0.88 \\ Assigned & gNB 2 & 0.77 & 0.82 \\ capacity & gNB 3 & 0.78 & 0.80 \\ utilization & gNB 4 & 0.77 & 0.83 \\  & gNB 5 & 0.78 & 0.80 \\ \hline \hline \end{tabular}
\end{table}
Table 4: KPI metrics obtained from _KPI metrics model_.