# An Analytical Model for 5G Network Resource Sharing with Flexible SLA-Oriented Slice Isolation

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## Abstract

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## 1. Introduction

- to efficiently transmit data with completely different characteristics and Quality of Service (QoS) requirements over the same physical network infrastructure, and
- to provide seamless support for diverse business models and market scenarios, for example, Mobile Virtual Network Operators (MVNO), which do not possess their own network infrastructure yet seek autonomy in administration and admission control.

- efficient resource usage,
- fair, non-discriminating resource allocation among users, and
- flexible isolation of slices from one another.

## 2. Basic Assumptions

## 3. Network Slicing with Performance Isolation

#### 3.1. Resource Allocation

#### 3.2. Admission Control and Resource Preemption

Algorithm 1: Resource preemption upon an arrival into slice s in state n |

## 4. A CTMC Model

#### 4.1. Model Assumptions

#### 4.2. Stationary State Distribution

Algorithm 2: Construction of the preemption rate matrix H |

#### 4.3. Performance Measures

## 5. Numerical Results

Algorithm 3: Numerical solution of (3)–(5) using the Gradient Projection Method |

## 6. Discussion

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The blocking probabilities vs. the booked capacity shares ${\gamma}_{s}=\gamma $, $s\in \mathcal{S}$ (solid lines—slicing, dashed lines—complete partitioning (CP)). The blocking probabilities under CP for slices 1 and 3 are not plotted due to high values and equal, respectively, 7.5 % and 16.9 %. Note that the complete sharing (CS) values coincide with that under slicing for $\gamma =1$ and are not shown explicitly.

**Figure 2.**The average user data rates vs. the booked capacity shares ${\gamma}_{s}=\gamma $, $s\in \mathcal{S}$ (solid lines—slicing, dashed lines—CP). Note that the CS values coincide with that under slicing for $\gamma =1$ and are not shown explicitly.

**Figure 3.**The average session duration vs. the booked capacity shares ${\gamma}_{s}=\gamma $, $s\in \mathcal{S}$ (solid lines—slicing, dashed lines—CP). Note that the CS values coincide with that under slicing for $\gamma =1$ and are not shown explicitly.

**Figure 4.**The blocking probabilities vs. ${\gamma}_{3}$; ${\gamma}_{2}=\frac{\alpha -{\gamma}_{3}}{3}$, ${\gamma}_{1}=2{\gamma}_{2}$ (solid lines—$\alpha =1$, dashed lines—$\alpha =1.1$).

**Figure 5.**The average data rates ${\overline{x}}_{s}$ vs. ${\gamma}_{3}$; ${\gamma}_{2}=\frac{\alpha -{\gamma}_{3}}{3}$, ${\gamma}_{1}=2{\gamma}_{2}$ (solid lines—$\alpha =1$, dashed lines—$\alpha =1.1$).

**Figure 6.**The average session duration ${T}_{s}$ vs. ${\gamma}_{3}$; ${\gamma}_{2}=\frac{\alpha -{\gamma}_{3}}{3}$, ${\gamma}_{1}=2{\gamma}_{2}$ (solid lines—$\alpha =1$, dashed lines—$\alpha =1.1$).

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**MDPI and ACS Style**

Yarkina, N.; Gaidamaka, Y.; Correia, L.M.; Samouylov, K.
An Analytical Model for 5G Network Resource Sharing with Flexible SLA-Oriented Slice Isolation. *Mathematics* **2020**, *8*, 1177.
https://doi.org/10.3390/math8071177

**AMA Style**

Yarkina N, Gaidamaka Y, Correia LM, Samouylov K.
An Analytical Model for 5G Network Resource Sharing with Flexible SLA-Oriented Slice Isolation. *Mathematics*. 2020; 8(7):1177.
https://doi.org/10.3390/math8071177

**Chicago/Turabian Style**

Yarkina, Natalia, Yuliya Gaidamaka, Luis M. Correia, and Konstantin Samouylov.
2020. "An Analytical Model for 5G Network Resource Sharing with Flexible SLA-Oriented Slice Isolation" *Mathematics* 8, no. 7: 1177.
https://doi.org/10.3390/math8071177