# Statistical Multiplexing and Traffic Shaping Games for Network Slicing

## TL;DR

This paper analyzes a dynamic resource sharing policy for network slicing in wireless networks, demonstrating its performance benefits, dimensioning strategies, and game-theoretic user management, supported by simulations.

## Contribution

It introduces and characterizes the Share Constrained Proportionally Fair (SCPF) policy, providing performance analysis, robust dimensioning solutions, and a traffic shaping game framework.

## Key findings

- SCPF outperforms static slicing, especially with imbalanced or orthogonal loads.
- A feasible share allocation exists under certain load and performance conditions.
- High load equilibrium and gains are explicitly characterized.

## Abstract

Next generation wireless architectures are expected to enable slices of shared wireless infrastructure which are customized to specific mobile operators/services. Given infrastructure costs and the stochastic nature of mobile services' spatial loads, it is highly desirable to achieve efficient statistical multiplexing amongst such slices. We study a simple dynamic resource sharing policy which allocates a 'share' of a pool of (distributed) resources to each slice-Share Constrained Proportionally Fair (SCPF). We give a characterization of SCPF's performance gains over static slicing and general processor sharing. We show that higher gains are obtained when a slice's spatial load is more 'imbalanced' than, and/or 'orthogonal' to, the aggregate network load, and that the overall gain across slices is positive. We then address the associated dimensioning problem. Under SCPF, traditional network dimensioning translates to a coupled share dimensioning problem, which characterizes the existence of a feasible share allocation given slices' expected loads and performance requirements. We provide a solution to robust share dimensioning for SCPF-based network slicing. Slices may wish to unilaterally manage their users' performance via admission control which maximizes their carried loads subject to performance requirements. We show this can be modeled as a 'traffic shaping' game with an achievable Nash equilibrium. Under high loads, the equilibrium is explicitly characterized, as are the gains in the carried load under SCPF vs. static slicing. Detailed simulations of a wireless infrastructure supporting multiple slices with heterogeneous mobile loads show the fidelity of our models and range of validity of our high load equilibrium analysis.