AAA is a concept and an actual software implementation of AAA is in the RADIUS protocol.
Remote Authentication Dial In User Service (RADIUS) is a networking
protocol that provides centralized Authentication, Authorization, and
Accounting (AAA) management for computers to connect and use a network
service. RADIUS was developed by Livingston Enterprises, Inc., in 1991
as an access server authentication and accounting protocol and later
brought into the Internet Engineering Task Force (IETF) standards
FreeRADIUS is the most widely deployed RADIUS server in the world. It is the basis for multiple commercial offerings. It supplies the AAA needs of many Fortune-500 companies and Tier 1 ISPs. It is also widely used in the academic community, including eduroam. The server is fast, feature-rich, modular, and scalable.
TekRADIUS runs on Windows and offers a GUI. The basic features are offered for free; additional versions can be purchased. The TekRADIUS Enterprise version ($149) adds support for EAP-TLS, dynamic self-signed certificate creation for PEAP sessions, NTLM authentication for MS-CHAP authentication methods and regular expression based attribute matching. Then the TekRADIUS SP version ($449) gives you VoIP billing in addition to the enterprise features.
ZeroShell is a router OS, but it is open source and completely free. It also includes a built-in RADIUS server among the usual router functionalities: NAT firewall, VPN, and so on. ZeroShell is offered as a live CD, so it doesn't have to be installed and requires only a small drive to save the configuration.
Here is how to configure and run a RADIUS server on Linux.