Off-topic: Does anybody know why you have to wait for a pedestrian crossing light to turn green at all?
If it's usually green for car traffic all the time, and only turns green for pedestrians on request, why not change immediately when somebody pushes the button?
The basic idea regarding vehicle and pedestrian movements is that the system can be entirely pretimed (interval control) or divided up into phases (phase control). The typical idea of operation is that any compatible phases should be able to run concurrently so long as there is time available. During Pedestrian Walk and Clearance time however these phases cannot be forced off or timed out. (Otherwise people could get hit by cars) This limits the amount of time the button can be pressed during a green light and still change the pedestrian signal.
Some do. Lights do all sorts of different things, ranging from turning immediately (as long as they did not just turn) to fully ignoring your input and just letting you feel better by pounding the button, and all sorts of things in between.
If it's usually green for car traffic all the time, and only turns green for pedestrians on request, why not change immediately when somebody pushes the button?