Like Dan quickly explains it, the scheduling tools are the same as a teacher. The additional layer, which I call the "queue", is where the users can publicize their availability. That way, a student can go to the "queue" and see who is available. Maybe a rating system is used to keep the naughty ones out.
Edit: Thanks Ash and Albert for your inputs.
Mentioning Tinder was only a joke.
I was thinking that a first-come, first-serve queue would allow people to be more available with their time, especially busy people. Technically, it shouldn't be that different from a teacher profile who offers an instant class.