Network Functions Virtualization facilitates the automation of the scaling of softwarized network services (SNSs). However, the realization of such a scenario requires a way to determine the needed amount of resources so that the SNSs performance requisites are met for a given workload. This problem is known as resource dimensioning, and it can be efficiently tackled by performance modeling. In this vein, this paper describes an analytical model based on an open queuing network of G/G/m queues to evaluate the response time of SNSs. We validate our model experimentally for a virtualized Mobility Management Entity (vMME) with a three-tiered architecture running on a testbed that resembles a typical data center virtualization environment. We detail the description of our experimental setup and procedures. We solve our resulting queueing network by using the Queueing Networks Analyzer (QNA), Jackson's networks, and Mean Value Analysis methodologies, and compare them in terms of estimation error. Results show that, for medium and high workloads, the QNA method achieves less than half of error compared to the standard techniques. For low workloads, the three methods produce an error lower than 10 percent. Finally, we show the usefulness of the model for performing the dynamic resource provisioning of the vMME experimentally.