Good question ..
.
Sign on a traffic pole:

Been waiting long?
That's because the council thinks someone in a car, half a kilometer away, is more important than you*.
They could make the lights change as soon as you press the button if they wanted, but they don't.
Complain to them 07 3403 4400.
A car moving at 50km/hr will travel almost half a kilometer in 30 seconds.

@RustyFreewheel that is my expectation. I press a button, and the light changes. If it does not, I think it is fair to assume it is broken, and cross the road whenever it feels save for you.