## 5 Conclusions  
In this paper, motivated by the need for simple mathematical models for RAT network slicing, we proposed and solved the model for mixed reservation- and priority-based traffic coexistence. The proposed framework aims to provide the balance between traffic isolation and efficient use of resources and also includes numerous service strategies as its special cases including full reservation, priority-only strategies, as well as mixed strategy without pre-emption. The system is formulated and solved by utilizing the tools of the queuing theory. We also demonstrated how the input parameters can be related to the wireless channel specifics including antennas and propagation models.  
Our numerical results demonstrate that the proposed mixed reservation- and priority-based strategy allows resource utilization to be improved up to 95% while still providing isolation between traffic types in highly overloaded conditions. Compared to the full reservation strategy, the gains are in the range 10-15% across a wide range of system parameters. The mixed scheme is also better in terms of session drop probabilities for low and moderate offered traffic load of the highest priority sessions. However, elastic eMBB traffic benefits more from the full reservation strategy in terms of both drop and pre-emption probabilities.  
One of the important advantages of the proposed approach is the simplicity of implementation, since for one of the models the steady-state probability distribution can be obtained by solving the system of local balance equations in a product form. However, for the model with pre-emption, the product-form solution is not available, so the steady-state distribution can only be estimated numerically by solving a system of linear equations. In addition, we considered 5G NR, which may operate in a mmWave or sub-6 GHz band. The proposed model is general and does not depend on the type of propagation environment and operational frequency.  
In our future studies, the performance of the proposed algorithm on specific traffic sets and per-slice QoS/QoE (quality of Experience) will be evaluated. Moreover, propagation models that are closer to reality will also be utilized.  
Conceptualization, E.M., Y.G., and K.S.; methodology, D.I., E.M. and Y.G.; software, D.I.; validation, E.M. and Y.G.; formal analysis, E.M. and D.I; investigation, D.I.; resources, E.M. and D.I.; data curation, E.M.; writing--original draft preparation, D.I. and E.M.; writing--review and editing, Y.A., E.M. and Y.G.; visualization, Y.A.; supervision, E.M. and Y.G.; project administration, E.M., Y.G. and K.S.; funding acquisition, E.M. and K.S. All authors have read and agreed to the published version of the manuscript.  
Figure 5: System resource utilization: (**a**) varying \(\rho_{1}\), (**b**) varying \(b_{2}^{\max}\).  
**Funding:** Sections 2-4 were written by [PERSON], [PERSON], and [PERSON] under the support of the Russian Science Foundation, project no. 22-79-10053, [[https://rscf.ru/en/project/22](https://rscf.ru/en/project/22)]([https://rscf.ru/en/project/22](https://rscf.ru/en/project/22)) -79-10053/, accessed 1 September 2022. This paper has been supported by the RUDN University Strategic Academic Leadership Program (recipients [PERSON], [PERSON], Sections 1 and 5).  
**Data Availability Statement:** Not applicable.  
**Conflicts of Interest:** The authors declare no conflict of interest.