There are definitely some randomization issues but 15-20 songs isn't nearly enough tracks for the radio to have much of a selection either. The more music you add to the library the more it will play without repeats.
I'd recommend listening to other libraries and radios for a while until your library has hundreads if not thousands of tracks.
All comments reflect the views of the poster and not of last.fm or it's management.
Library not allowing me to play all tracks?