They are a combination of timers and sensors. And yes, we know all about this. Your assumption is correct. Doing this allows traffic to move with greater throughput overall. If it wasn't done, heavier trafficked thoroughfares would have long periods where they were the only priority.

Err... I modeled traffic.

The possible solution would be roundabouts and yield signs, but that would be expensive, require redesign, and we humans pretty much suck at roundabouts.