Cloud computing and Network Function Virtualization (NFV) represent together a promising solution for wireless network operators to improve business agility and cope with the continuing growth in data traffic. Furthermore, the use of edge clouds in association with a centralized cloud, referred to as the edge-central cloud, notably improves user experience while ensuring scalability and load balancing. In such carrier cloud environment, efficient management mechanisms for the Virtualized Network Functions (VNFs) are of crucial importance. In this paper, we introduce VNF placement and provisioning optimization strategies over an edge- central carrier cloud infrastructure taking into account Quality of Service (QoS) requirements (i.e., response time, latency constraints and real-time requirements) and using queuing and QoS models. Our main design goals are to optimize resource utilization, to prevent cloudlet overload, and to avoid violation of Service Level Agreement (SLA) requirements. Through extensive simulations, we show how a trade-off can be achieved between these conflicting objectives.