live.twitch.tv is US West: San Francisio.
The old “global load balancing service” was live-3c.justin.tv. I’m not sure how it was implemented but it never worked very well so eventually it was quietly removed. This was from back in the day when FMLE was still the streaming application of choice (and you had to manually enter the RTMP server in the application), XSplit was still getting started and no one know what an OBS was.