It's called an induction, and I had one not-quite-emergency one (my doctor said, "Tonight!" but let me go home for a few hours first) and two that were scheduled but pre-empted by actual labor. (One by only about 12 hours.)
They can be scheduled anytime, I think. However, non-urgent procedures will be scheduled preferentially during daylight hours at most hospitals. I'd expect anytime between about 7/8 am and 4/5 pm would be a likely slot.
When an induction is scheduled, that means that's when you're supposed to show up, bet admitted, and hooked up to the monitors and pitocin and all that fun stuff.
But it's not like if you're late they start without you . . .
Inductions are generally scheduled only if there is (potential) danger to the mother or baby. Going past two weeks overdue (one week, with some practitioners), or low fluid, or certain other complications.
It is considered highly unethical to schedule an unnecessary induction, simply for convenience's sake. There are certain risks that rise with induction. Well worth the risk if the induction is needed; not so much if it's not.
That said, there are doctors who will schedule inductions (and/or c-sections) to suit their schedule or that of the patient.
