Autogrowth and Initial Size with T-Log
I think you can calculate each 15 min time slot before doing transaction backup, because after transaction backup, the previous transaction logs will be rewriteable, and that will be the maximum of the transaction log file size.

DBCC Shrinkfile sometimes could not work well because there are some transaction not write down to database already (transaction will be wrote to log file first and    then write to database), you can wait a while and DBCC again.