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

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.