I am experiencing the same issues. When I try to stream video, Watch youtube videos, transfer files via P2P for work, upload or download files via FTP I get service interruption for 1 to 2 minutes. I have read about COX's Traffic Shaping and their used a couple tools to determine that this is in fact what is happening. Using ShaperProbe you can see for your self.
In a move that's basically baiting the FCC and Congress to see if they will act, Cox announced that it's going to experiment with rather aggressive traffic shaping, granting priority to bits that it feels have a great priority. Why Cox gets to describe what gets a priority and what doesn't seems very questionable.
Their employees and company reps will deny deny deny that they are actively throttling and shaping your internet connection.
Since I've been a customer with cox on and off for the last 9 years I have NEVER received the full bandwidth speeds that have been advertised.