Network Slicing: Market Mechanism and Competitive Equilibria

TL;DR

The paper addresses spectral scarcity in 5G by modeling network slicing as a three-tier market (NPs, SPs, and users) and proposes a five-step iterative framework featuring a clock auction that converges to a robust $ε$-competitive equilibrium. It advances the theory by handling non-concave sigmoid utilities through regularization and concavification, and by enabling SPs to learn private user parameters via Bayesian inference across market cycles. Key contributions include proving convergence to a unique clearing price, providing a centralized SWM benchmark, and validating the model with numerical experiments that illustrate price discovery, resource allocation, and the impact of learning on performance. The approach provides a scalable, incentive-aligned mechanism for dynamic, end-to-end network slicing with learning-driven improvements in efficiency and fairness across diverse service classes.

Abstract

Towards addressing spectral scarcity and enhancing resource utilization in 5G networks, network slicing is a promising technology to establish end-to-end virtual networks without requiring additional infrastructure investments. By leveraging Software Defined Networks (SDN) and Network Function Virtualization (NFV), we can realize slices completely isolated and dedicated to satisfy the users' diverse Quality of Service (QoS) prerequisites and Service Level Agreements (SLAs). This paper focuses on the technical and economic challenges that emerge from the application of the network slicing architecture to real-world scenarios. We consider a market where multiple Network Providers (NPs) own the physical infrastructure and offer their resources to multiple Service Providers (SPs). Then, the SPs offer those resources as slices to their associated users. We propose a holistic iterative model for the network slicing market along with a clock auction that converges to a robust $ε$-competitive equilibrium. At the end of each cycle of the market, the slices are reconfigured and the SPs aim to learn the private parameters of their users. Numerical results are provided that validate and evaluate the convergence of the clock auction and the capability of the proposed market architecture to express the incentives of the different entities of the system.

Figures (7)

• Figure 1: Concave Envelopes of sigmoid utility functions with $k_{\mathbb{c}(\cdot)} = 100$ and (a) $t^z_{\mathbb{c}(\cdot)} = 0.02$, (b) $t^z_{\mathbb{c}(\cdot)} = 0.2$ and (c) $t^z_{\mathbb{c}(\cdot)} = 2$.
• Figure 2: L2 norm of the excess demand vector throughout the clock auction (a) for $\kappa = 10^{-4}$ and various initialization price vectors $\bm{c}_{init}$, and (b) for $\bm{c}_{init}^T = [0.62, 0.64, 0.58]$ and different values of $\kappa$.
• Figure 3: Illustrating Theorem \ref{['th:convergence']}. Starting from any price vector $\bm{c}_{init}$, the clock auction converges to the market clearing prices $\bm{c^\dagger}$.
• Figure 4: Total amount of resources obtained by every SP $m$ from every NP $k$ in the market, $\bm{x}_{(m,k)}$.
• Figure 5: The solution of the intra-slice resource allocation problem from the perspective of the two different SPs of the market. Specifically, how (a) SP1 distributed the resources of NP1, i.e., $\bm{r}_{1,i}$ for every i in $\mathcal{U}_1$, (b) SP2 distributed the resources of NP1, i.e., $\bm{r}_{1,i}$ for every i in $\mathcal{U}_2$, and (c) SP2 distributed the resources of NP2, i.e., $\bm{r}_{2,i}$ for every i in $\mathcal{U}_2$.

Theorems & Definitions (15)

• Lemma 1
• Lemma 2
• Definition 1: Nonconcavity of a function
• Theorem 1
• Remark 1
• Remark 2
• Definition 2: Competitive equilibrium
• Definition 3: $\epsilon$-Competitive equilibrium
• Lemma 3
• Theorem 2