I made the original post in case I had noticed an intermittent slow response problem with this server. In hindsight I should not have reported this as if it had actually been a problem someone else with more networking knowledge than me would have noticed and reported it.
As for why I was running a trace route for the first time I was testing our internet connection to see if there were local internet backbone routers with latency issues which could explain the high network latency in this Steam Remote Play Together streaming log message:
Slow framerate: game 21.73, capture 0.31, convert 0.01, encode 5.06, network 52.02, decode 1.58, display 4.54 (network)
I was streaming a local multiplayer game to two friends who didn't own it sending 4mbps 720p video streams to each and receiving their inputs in return. We all have cable connections to our routers though one of my friends has a power socket adapter connection to his router. This friend lives 10 miles away and the other 11 miles.
Given that you've told me its normal for internet backbone routers to some times take 57ms to respond to trace route ping requests they can normally respond to in 6ms, I suppose they may sometimes have to significantly delay passing on game stream video frame packets resulting in the 52ms network latency I saw mentioned in that slow frame rate log message.
