Airplay stuttering when loading some webpages

[DenBeke]

Airplay sometimes stutters when I'm loading a webpage or some other simple network activity.
When loading a webpage (like Facebook or a simple Google search) it stutters on the actual fetching of the page itself (i.e. when the screen is still blank). When it actually starts loading the content of the page, the stuttering is gone.
It also sometimes happens when Wunderlist is syncing.

My Mac (running El Capitan) is connect to my router via Wifi. I'm streaming audio to my Raspberry Pi which is connect with an ethernet cable to the router.

It seems like OS X has some network issues, and blocks somewhere causing Airplay to stutter.
(I can't remember when it started to happen, but it has worked flawlessly in the past. And it doesn't happen with other devices like my iPhone)

Anyone who has the same problem? Or knows how to tackle/debug this?

 

[ScoobyMcDoo]

You might take a look at your router settings. Some routers allow you to prioritize some nodes and/or types of traffic.

 

[DenBeke]

You might take a look at your router settings. Some routers allow you to prioritize some nodes and/or types of traffic.

I can't do such a things on the router of my ISP.
And I don't think that'll help, because when the stuttering is happening my Mac only sends a few kilobytes of traffic to my router. Which it should be able to handle without any problem. To me it looks more like software problems on Apple's side...