  Network virtualization is a key enabler for 5G systems to support the
expected use cases of vertical markets. In this context, we study the joint
optimal deployment of Virtual Network Functions (VNFs) and allocation of
computational resources in a hybrid cloud infrastructure by taking the
requirements of the 5G services and the characteristics of the cloud
architecture into consideration. The resulting mixed-integer problem is
reformulated as an integer linear problem, which can be solved by using a
standard solver. Our results underline the advantages of a hybrid
infrastructure over a standard centralized radio access network consisting only
of a central cloud, and show that the proposed mechanism to deploy VNF chains
leads to high resource utilization efficiency and large gains in terms of the
number of supported VNF chains. To deal with the computational complexity of
optimizing a large number of clouds and VNF chains, we propose a simple
low-complexity heuristic that attempts to find a feasible VNF deployment
solution with a limited number of functional splits. Numerical results indicate
that the performance of the proposed heuristic is close to the optimal one when
the edge clouds are well dimensioned with respect to the computational
requirements of the 5G services.
