  Network function virtualization is a promising technology to simultaneously
support multiple services with diverse characteristics and requirements in the
5G and beyond networks. In particular, each service consists of a predetermined
sequence of functions, called service function chain (SFC), running on a cloud
environment. To make different service slices work properly in harmony, it is
crucial to appropriately select the cloud nodes to deploy the functions in the
SFC and flexibly route the flow of the services such that these functions are
processed in the order defined in the corresponding SFC, the end-to-end (E2E)
latency constraints of all services are guaranteed, and all cloud and
communication resource budget constraints are respected. In this paper, we
first propose a new mixed binary linear program (MBLP) formulation of the above
network slicing problem that optimizes the system energy efficiency while
jointly considers the E2E latency requirement, resource budget, flow routing,
and functional instantiation. Then, we develop another MBLP formulation and
show that the two formulations are equivalent in the sense that they share the
same optimal solution. However, since the numbers of variables and constraints
in the second problem formulation are significantly smaller than those in the
first one, solving the second problem formulation is more computationally
efficient especially when the dimension of the corresponding network is large.
Numerical results demonstrate the advantage of the proposed formulations
compared with the existing ones.
