Limit user access to external Website due to high bandwidth utilization using LTM and iRules

I have a situation in which there are several users who are streaming video causing high bandwidth utilization and impacting other users on our environment. There is no authentication required to view the website so I do not know how I would gather user id's and restrict by that and because many users are on non persistent VDI's these users desktops change everyday limiting group policy. Also, due to company security requirements all IE security settings are applied to the computer object versus the user object, I cannot apply policy per user and loopback processing doesn't matter then because user settings are disregarded by IE. I know this may seem confusing though I have looked at group policy, there is no forward proxy to prevent users by security group and there is no authentication so anyone with a computer and IE can browse to this external website. Does anyone have experience or know how to deny access for a all but a few users (by userid) with LTM only and no authentication anywhere in the traffic? Even if there is no authentication, is a user ID included any packets in which no user authentication is required? Thanks in advance.