# Service Chain (SC) Mapping with Multiple SC Instances in a Wide Area Network

## TL;DR

This paper addresses the complex problem of mapping multiple service chain instances in wide area networks to optimize resource use, proposing a novel two-phase solution approach for large-scale networks.

## Contribution

It introduces the first mathematical model and solution method for SC mapping with multiple instances, reducing network resource consumption in WANs.

## Key findings

- A quadratic formulation models the complex SC mapping problem.
- A two-phase column-generation approach efficiently solves large network instances.
- Selecting a small set of SC instances achieves near-optimal bandwidth usage.

## Abstract

Network Function Virtualization (NFV) aims to simplify deployment of network services by running Virtual Network Functions (VNFs) on commercial off-the-shelf servers. Service deployment involves placement of VNFs and in-sequence routing of traffic flows through VNFs comprising a Service Chain (SC). The joint VNF placement and traffic routing is usually referred as SC mapping. In a Wide Area Network (WAN), a situation may arise where several traffic flows, generated by many distributed node pairs, require the same SC, one single instance (or occurrence) of that SC might not be enough. SC mapping with multiple SC instances for the same SC turns out to be a very complex problem, since the sequential traversal of VNFs has to be maintained while accounting for traffic flows in various directions. Our study is the first to deal with SC mapping with multiple SC instances to minimize network resource consumption. Exact mathematical modeling of this problem results in a quadratic formulation. We propose a two-phase column-generation-based model and solution in order to get results over large network topologies within reasonable computational times. Using such an approach, we observe that an appropriate choice of only a small set of SC instances can lead to solution very close to the minimum bandwidth consumption.