Depending on the amount of videos,, visitors, length of the video and your amount of bandwidth.
A dedicated box should be able to handle it if it is a good one. Then you have bandwidth and port speed. If you port speed is 10mbps then you are sure going to be problems. For video streaming i would suggest a 1 gbps port. Also enough monthly bandwidth as videos can burn away a lot of bandwidth.
If you like to use another option than you diedicated box, we can help you with setting your video streaming up one of our cloud server with SSD disk and 1 gbps port, 2tb or more bandwidth.
Contact me and i will give you your first month for free and we will do all the setup for you.
http://diploy.net