Network Function Virtualization (NFV) allows datacenters to consolidate network appliance functions onto commodity servers and devices. Currently telecommunication carriers are re-architecting their central offices as NFV datacenters that, along with SDN, help network service providers to speed deployment and reduce cost. However, it is still unclear how a carrier network shall organize its NFV datacenter resources into a coherent service architecture to support global network functional demands. This work proposes a hierarchical NFV/SDN-integrated architecture in which datacenters are organized into a multi-tree overlay network to collaboratively process user traffic flows. The proposed architecture steers traffic to a nearby datacenter to optimize user-perceived service response time. Our experimental results reveal that the 3-tier architecture is favored over others as it strikes a good balance between centralized processing and edge computing, and the resource allocation should be decided based on traffic's source-destination attributes. Our results indicate that when most traffic flows within the same edge datacenter, the strategy whereby resources are concentrated at the carrier's bottom-tier datacenters is preferred, but when most traffic flows across a carrier network or across different carrier networks, a uniform distribution over the datacenters or over the tiers, respectively, stands out from others.