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Network Functions Virtualization (NFV) is incrementally deployed by Internet Service Providers (ISPs) in their carrier networks, by means of Virtual Network Function (VNF) chains, to address customers' demands. The motivation is the increasing manageability, reliability and performance of NFV systems, the gains in energy and space granted by virtualization, at a cost that becomes competitive with respect to legacy physical network function nodes. From a network optimization perspective, the routing of VNF chains across a carrier network implies key novelties making the VNF chain routing problem unique with respect to the state of the art: the bitrate of each demand flow can change along a VNF chain, the VNF processing latency and computing load can be a function of the demands traffic, VNFs can be shared among demands, etc. In this paper, we provide an NFV network model suitable for ISP operations. We …