The virtual identity concept has been introduced to protect the users privacy towards service providers as well as towards access network providers on a service session basis. So far the concept has been only considered from the security and privacy perspective. However, performance analysis is necessary as well to gain insights into the additional costs and their scaling behavior with respect to signaling load and state management. In this paper we propose an analytical model to evaluate the cost introduced by virtual identities. The model allows to quantify the additional signaling overhead and the additional states created by distributing service sessions of users across several virtual identities. We exemplify the use of the model for an authentication, authorization and accounting (AAA) infrastructure based on EAP-TLS and derive figures on the required signaling bandwidth and state overhead to support the virtual identity concept in various service usage scenarios.