Check in at the port begins around 10:30. Boarding numbers are assigned based on your PAT. Actual boarding begins around 11:15-11:30 with Concierge and Platinum
Castaway Club members, followed by the announcement of boarding numbers. The next number is generally announced every 5-10 minutes, depending on how quickly the line is moving.
Once the number being announced for boarding catches up with the number being issued at check in Open Boarding is called. Anyone holding any boarding number may board. This typically happens around 12:30-12:45.
Pretty much everyone (not arriving from WDW resorts) is onboard by 1:00 at the latest.