Many of the facts that I'm giving about the story, I'm not 100% confident in, so if you think of something matching this roughly feel free to suggest
- I think it's a short story, rather than a longer piece
- I think it's by a very famous sci-fi author, back when I was a child (like 25 years ago) my favorites were Clifford Simak, Robert Sheckley, Roger Zelazny, Robert Heinlein, Philip Dick, Isaac Asimov and the like.
- The story is about a teleportation station, with a single human inhabitant
- This inhabitant was a "randomly" chosen human, and once chosen he became responsible for hard moral choices
- He acts as a sort of immigration officer granting and denying others their wish to teleport
- He has a "term", and when it ends another poor soul will have to fulfill these duties, there were many before him and there will be many after him.