This paper addresses an important aspect of mobile core network virtualization: The combined optimization of the virtual mobile core network topology (graph) and its embedding onto a physical substrate network. Basically this comprises the placement of mobile core virtual network functions (VNFs) onto the nodes of the physical substrate network, the determination of the interconnections towards the radio access network (RAN) and the Internet as well as the traffic routing between the VNFs. This problem differs from the traditional virtual network embedding (VNE) problem as the virtual network topology is not known in advance and several additional constraints apply, e.g. not every node of the physical substrate network might be able to host every VNF. We assume that the topology, link capacities and node resources of the physical substrate network are predefined and that a node comprises both packet forwarding and datacenter/server functionality.

The node capabilities are defined by the processing, storage and switching (throughput) resources as well as the ability to host specific mobile core VNFs, i.e. the SGW, PGW, MME and HSS virtual functions. For the traffic routing, explicit single path routing is assumed. We propose a novel integer linear programming formulation which combines the optimization of the virtual network topology with VNE optimization. Optimization target is to minimize the cost of occupied link and node resources. Our formulation relies on the joint embedding of individual core network service chains where a core network service chain denotes the sequence of mobile core VNFs a user or control plane traffic flow traverses. We evaluate our model by means of two physical network topology examples taken from SNDlib [1]. It is shown that our approach outperforms traditional VNE optimization approaches in terms of optimality and computation time.