# Expanded Combinatorial Designs as Tool to Model Network Slicing in 5G

## TL;DR

This paper introduces a mathematical framework using combinatorial designs to model and optimize network slicing in 5G, providing algorithms and simulations to improve slice management.

## Contribution

It develops a novel combinatorial design-based model for 5G network slicing, including stability analysis and optimization algorithms for resource utilization.

## Key findings

- Proved a stability lemma for network slice configurations.
- Developed an algorithm to maximize utilization ratio.
- Validated models through simulations and experiments.

## Abstract

The network slice management function (NSMF) in 5G has a task to configure the network slice instances and to combine network slice subnet instances from the new-generation radio access network and the core network into an end-to-end network slice instance. In this paper, we propose a mathematical model for network slicing based on combinatorial designs such as Latin squares and rectangles and their conjugate forms. We extend those designs with attributes that offer different levels of abstraction. For one set of attributes we prove a stability Lemma for the necessary conditions to reach a stationary ergodic stage. We also introduce a definition of utilization ratio function and offer an algorithm for its maximization. Moreover, we provide algorithms that simulate the work of NSMF with randomized or optimized strategies, and we report the results of our implementation, experiments and simulations for one set of attributes.