'The Elevator ' by Matt Leibel

He rented a unit in the world's tallest building; it was a billion floors high. The elevator ride to his apartment took an entire life. On the way, he read books, fell in love, got married, had children, found his vocation. After he died, just 3 floors short of his new home, the landlord re-rented the place—handing the keys to a new young tenant in the lobby, and pointing her to the block of elevators down the hall.