Situation was the same last August. We arrived a bit over 2.5 hours prior to departure, took about 5 minutes to check our bags, and were sent into the "Priority Line" to clear passport control. Upon clearing security, we went directly to the gate at a rapid walk and arrived at the time they announced the last call for boarding. Four other people showed up after us (all made the flight).
All passport control lines were the same. Actually, the gate agent said we were going to the shortest and fastest one. No one cleared in less than one hour, many reported being in line in excess of an hour and 45 minutes.
I recommend arriving at least four hours before departure, assuming one is either traveling without checked bags or the gate is open to check them that early.