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Due to the traditional separation of radio and IP engineering in 3G cellular networks, the subscriber access-request rate from the RAN is usually a known parameter to radio engineers, whereas the corresponding authentication, authorization, and accounting (AAA) traffic rate generated by the network access server (NAS) in response to the RAN requests is unknown. To bridge this design gap, we analyze a typical NAS-AAA system architecture based on the RADIUS protocol, the de-facto protocol for authentication and billing adopted by the telecom industry. We present the first analytical model for the mean and the variance of the AAA signaling rate and verify it by simulations. The model results can help operators to configure their NASes with proper accounting-interim-interval values as a tradeoff between network cost and accounting reliability.