How to set-up an on-demand streaming music server

What I'm looking to accomplish seems to be a bit out of the ordinary. In fact after searching Google for over an hour, I haven't found anything that will work for what we want to do.

What we want to do is a bit of a hybrid between live and archived audio streaming. I'll do my best to explain it as clearly as possible.

We want to create a website that will play a bands music. We want the site to function similarly to how an internet radio station would. And by that I mean when a visitor loads the site, a predetermined playlist will already be playing.

Where the tricky part comes in is rather than streaming these audio files from a local PC using something like SAM 2, we want the files to already be stored on our web hosts server.

The songs won't actually be being streamed live, but it will act like it is.

Does that make sense?

Does anyone have any ideas on how to accomplish this? Any ideas/software would be greatly appriciated.

Of course it is possible. Just install a streaming server software like free Icecast and offer your visitors on-demand music streams.