  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.
