The Mathematics of Aircraft Boarding

The suggested system by this guy is very similar to the method employed by Southwest Airlines.

Grouping is mostly by check-in time, and groups are let in, in order, but seats are chosen at random by people. This means that as soon as someone sees a "good" seat, they get down, and people can keep moving. This has its own issues, but in my experience flying on many different airlines, leads to the smoothest and fastest boarding I've experienced.