Not really a Perl solution, but..

Your poor streaming performance is likely due to your upstream being totally swamped by torrent uploads. Packets get queued in your modem and TCP ACK takes forever to get through, significantly reducing downstream throughput. Try capping your uploads in Azureus.

You'll want to look into Traffic shaping for a more general solution. Typically this runs on your router, but as you have a hardware SOHO box this may not be a tenable solution. If you're running Linux, you can set up local traffic shaping. There are some good docs (although a bit dated) on the Linux Advanced Routing & Traffic Control page.