Mind explaining your reasoning?
It is set up for remote connections, but its not being used.
So I don't think that could be it.
It's an always on kind of thing. Are you sharing your library with other people? Just because it's not being used, or someone is streaming, just by them browsing your library.
Also, since the Nvidia shield HAS the server on it, and it's pulling media from a NAS, you should probably make sure that it's set not to periodically scan the library. That'll jack up usage also.
Common things like this if it's using cpu cycles.
Maybe there is a media database being updated over WiFi ?
Typically, when I update my firmware and reattach my storage HD with a lot of media to the router, the media server of my router start reading all data and it can take until 10 minutes before it is done. During this updating, the CPU usage is pretty high too (I know you don't use USB connected drives).
You should try to see how the router behaves when nothing is connecting to it beside the device you use to view the GUI.
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