On the Interplay Between Network Function Mapping and Scheduling in VNF-Based Networks: A Column Generation Approach

Middleboxes (i.e., firewall, cache, proxy, etc.) are hardware appliances designed to enforce security and performance policies. Being an integral part of today's cloud and enterprise networks, these middleboxes are expensive, hard to manage and to maintain. Network function virtualization has emerged as a promising technology that replaces these hardware appliances by software ones known as virtual network functions (VNFs). Unlike hardware middleboxes, VNFs can be instantiated and deployed on virtual machines running on commodity servers which ensures their flexibility, manageability, cost-efficiency, and reduce their time-to-market. However, efficiently processing services through an ordered chain of VNFs, called service function chaining (SFC), is not trivial. It requires solving three inter-related sub-problems; the network functions (NFs) mapping sub-problem, the traffic routing sub-problem and the service scheduling sub-problem. This paper first highlights the existing interplay between the three sub-problems and then presents a formulation of the SFC scheduling (SFCS) which exploits interactions between NFs mapping onto VNFs, service scheduling and traffic routing. Given the complexity of the SFCS problem, we present a novel primal-dual decomposition using column generation that solves exactly a relaxed version of the problem and can serve as a benchmark approach. We enhance our solution methodology with a diversification technique to help improve the quality of the obtained solutions. We evaluate numerically our method and show that it can attain optimal solutions substantially faster. Finally, we present several engineering insights for improving the network performance.