We were on the 12-27-03 NYE cruise, which was sold out.
Only time we were aware of the crowd was on disembarcation day. They started letting passengers off at 8 am, and it took until 10:15 am to get everyone off. The line was 45 minutes long on the ship to get off. Once in the cruise terminal, it only took about 10 minutes to clear customs and immigration, pickup your bags, check them at the airline counters at the port, and get on the bus to leave.