Network Function Virtualization (NFV) is a promising solution for telecom operators and service providers to improve business agility, fast deployment of new services and cope with the increasing service demand. In the mobile networks, NFV enables virtualization of the core network functions as well as radio access network functions, effectively reducing deployment and operational costs of mobile networks. However, to benefit from the advantages of NFV, proper models that represent mobile networks and satisfy the QoS requirements need to be developed. To this end, in this project, we develop models and algorithms for mobile core virtualized network functions placement and service provisioning. The overall goal is to develop models and algorithms and evaluate the performance pertaining to the standard QoS requirements of the 5th generation mobile core network.