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Cisco - How to limit bandwidth on web server

Below is a simple diagram of my network.  As you can see I have a DMZ that comes off the ASA, and I have a web server coming off the DMZ switch.  This web server in the coming weeks will have  video tours that people can click on and watch.  I'm concerned about bandwidth usage on my internet circuit when people start watching these video.  How can I limit the amount of internet bandwidth this web server can consume?  I've done some traffic shaping in scenarios where I control both ends, like for example limiting bandwidth over a site to site VPN, but in this case I don't control users from the internet who will be we watching videos from this web server.  Everybody seems to have video on their web servers these days, what are people doing to ensure all their bandwidth isn't consumed?  Network diagram
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Most Valuable Expert 2015
You want QoS.

Here is an excellent article:


In summary, you will create:
   1) A class map
   2) A policy map to which  you'll appy the class map and define the traffic shaping
   3) Apply the policy to the interface