Network Slicing with Flexible VNF Order: A Branch-and-Bound Approach

TL;DR

An innovative optimization framework to tackle the challenges of jointly optimizing slice admission control and embedding with flexible VNF ordering is proposed and a near-optimal branch-and-bound (BnB) algorithm is introduced, combined with the A* search algorithm, to generate embedding solutions efficiently.

Abstract

Network slicing is a critical feature in 5G and beyond communication systems, enabling the creation of multiple virtual networks (i.e., slices) on a shared physical network infrastructure. This involves efficiently mapping each slice component, including virtual network functions (VNFs) and their interconnections (virtual links), onto the physical network. This paper considers slice embedding problem in which the order of VNFs can be adjusted, providing increased flexibility for service deployment on the infrastructure. This also complicates embedding, as the best order has to be selected. We propose an innovative optimization framework to tackle the challenges of jointly optimizing slice admission control and embedding with flexible VNF ordering. Additionally, we introduce a near-optimal branch-and-bound (BnB) algorithm, combined with the A* search algorithm, to generate embedding solutions efficiently. Extensive simulations on both small and large-scale scenarios demonstrate that flexible VNF ordering significantly increases the number of deployable slices within the network infrastructure, thereby improving resource utilization and meeting diverse demands across varied network topologies.

Figures (12)

• Figure 1: An example of a slice with flexible VNF ordering is one dedicated to a video streaming service, consisting of five VNFs: an intrusion detection and prevention system (IDPS), video optimization controller (VOC), traffic monitoring (TM), gateway (GW), and distributed unit (DU). In this case, the TM and VOC functions can be swapped with each other, resulting in two possible slice configurations.
• Figure 2: Illustration of the considered problem: The three steps: ($1$) slice admission control, ($2$) VNF order selection and ($3$) network slice embedding are jointly optimized. This illustration considers one single slice $s$.
• Figure 3: Illustration of constraint \ref{['FO:C6c']} when (a) $\mathcal{N}_{s}^{\prime} = \{v, v'\}$, (b) $\mathcal{N}_{s}^{\prime} = \{v', v"\}$, and (c) $\mathcal{N}_{s}^{\prime} = \{v, v"\}$.
• Figure 4: Illustration of the branching process in $\mathtt{BnB^*}$. Starting from the root node, where the status of the available physical resources is represented by the physical graph $\mathcal{G}$. At each depth $p$ of the BnB tree, $\mathtt{BnB^*}$ selects the candidate physical node to map the $p$-th VNF ($v_{p}$) of the considered slice. Each candidate $i_{m}$ for the mapping ($i_{m} \mapsto v_{p}$) adds a new branch to the BnB tree. The mapping choice is registered in the vector $\boldsymbol{\mathrm{x}}^{(pm)}$. The status of the physical graph after the mapping is then updated as $\mathcal{G}^{(pm)}$.
• Figure 5: Four layers of the fat-tree topology: Each node provides a fixed amount of compute and storage resources, measured in the number of vCPUs and GBs respectively. Links have a fixed amount of available bandwidth, measured in Gbps.

Theorems & Definitions (1)

• Lemma 1