>> Family/VIP, who can reach me 24/7/365.
Also: a message like "Hi family, I'm asleep/busy, but if you really need me, press 1 to ring me anyway" would be wonderful. They wouldn't worry about calling at a bad time, and you wouldn't get awakened for something trivial.
In general, "what would a good human assistant do?" is a good question for computer systems. A secretary wouldn't wake you unless it was important.