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Network Function Virtualization is considered one of the key technologies for developing the future mobile networks. In this paper, we propose a theoretical framework to evaluate the performance of an LTE virtualized Mobility Management Entity (vMME) hosted in a data center. This theoretical framework consists of i) a queuing network to model the vMME in a data center, and ii) analytic expressions to estimate the overall mean system delay and the signaling workload to be processed by the vMME. We validate our mathematical model by simulation. One direct use of the proposed model is vMME dimensioning, i.e., to compute the number of vMME processing instances to provide a target system delay given the number of users in the system. Additionally, the paper includes a scalability analysis of the system. In our study, we consider the billing model and a data center setup of Amazon Elastic Compute Cloud service, and estimate experimentally the processing time of MME processing instances for different LTE control procedures. For the considered setup, our results show that a vMME is scalable for signaling workloads up to 37000 LTE control procedures per second for a target mean system delay of 1 ms. The database performance assumed imposes this limit in the system scalability.