If I was Alice's employer and valued her (and other employees) being able to do deep work, I'd have a policy whereby employees could schedule do-not-disturb time (large blocks of it, depending on their needs) where they could shut their doors and turn off IM. Have a red light on the outside of the door, like a film production booth. Book end the day. First 1-2 hours are disturb time. Middle of the day is DND time. Last part of the day is disturb time.

All scheduled meetings have to happen in disturb time.

Now, that doesn't really work for a customer-facing role, at least not without the cooperation of your customers, but having managed a customer-facing team before, I'll say I encouraged my people to schedule office-hour time with their customers to try to channel the interactions in a more predictable period of time.