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 called 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; then, a 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
the problem of SC mapping with multiple SC instances to minimize network
resource consumption. We first propose an Integer Linear Program (ILP) to solve
this problem. Since ILP does not scale to large networks, we develop a
column-generation-based ILP (CG-ILP) model. However, we find that exact
mathematical modeling of the problem results in quadratic constraints in our
CG-ILP. The quadratic constraints are made linear but even the scalability of
CG-ILP is limited. Hence, we also propose a two-phase column-generation-based
approach 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 a solution very close to
the minimum bandwidth consumption. Further, this approach also helps us to
analyze the effects of number of VNF replicas and number of NFV nodes on
bandwidth consumption when deploying these minimum number of SC instances.Comment: arXiv admin note: substantial text overlap with arXiv:1704.0671
