The traffic lights in my town aren't automated. They run on 80 second timers. For most of that time, they're red. Thirty seconds green, three seconds yellow, forty-seven seconds red. Someone timed it out that way for optimal traffic flow. When an ambulance comes through, they're surrounded by green lights, like a shaft of sunshine coming down on God's beloved. Then once they're gone all the lights reset back into their normal pattern.
The city is mostly grid shaped, but on a hill. One block is about 1/10th of a mile. Finding out the optimal speed for all green lights is just a matter of finding out how much their timing is offset by and doing a little bit of math. I'm almost tempted to step outside my house and find the nearest two traffic lights to that I can find out what the difference is. What really interests me about this is whether they're setting the lights to lower speeds to within legal limits, or whether they're doing it maximize traffic flow. Maybe both.
It's interesting to note that a staggered light system only has one speed you can consistently travel at keep hitting the greens. There's a thirty second variance in there of course, as you could go through one right after it changes from red and go through the other right before it changes to yellow. In a non-staggered system, where all of the lights in a column are the same color, there would be several speeds you could go to guarantee that you always got the green light. They would, however, be quite slow. An 80 second cycle with one light every block would have you traveling 4.5 miles per hour. You would be able to half that speed any number of times and still be hitting every green light. I think most of us would just gun it and see how many greens we could get through before it turned red on us again.
Also, when I was searching in vain for information about how the lights are programmed, I came across this lovely article about the effects of weather on street car traffic in Duluth, circa 1917. If I had $12 I would buy it.