If they are doing PRI to PRI, I assume they are using the DIAL PLAN, otherwise they could just use T1 CSU ACE. If they are using the DIAL PLAN, I assume they are either changing the SWITCH TYPE (Switch Protocol) or routing by number dialed - or again, the CSU ACE would be a more cost efficient solution.
The first thing to look at is to verify all the PRI circuits are running "clean." You can look under the MODULES and then look at the PERFORMANCE statistics to see if any of the interfaces are accumulating errors. If they are "clean" then you will probably have to monitor the PRI messages through the ATLAS and look for the calls that are getting the fast busy and try to find out, A) if the calls are making to the ATLAS, B) if they are being sent to the Avaya PBX, and C) what the Avaya is sending back. To do this you'll need a Syslog Server program and you'll need to configure the ATLAS to send its logging to the Syslog Server. In the ATLAS you'll need to configure under SYSTEM CONFIG, and EVENT LOGGING the ISDN L2 FORMATTED events to INFO. This will give you all the ISDN messages for all the interfaces (I'm afraid there is not a way to isolate it to a specific interface).
You can look at the following document: Using the Adtran Utility Syslog with the Atlas, and while the "Adtran Utilities" are no longer supported, any Syslog program will work, and configuring the ATLAS is the same.
Hope this helps,