Broadcast traffic light data, and let cars use it
Self-driving cars are still some ways in the future, but there are some things they will want that human drivers can also make use of.
I think it would be nice if the urban data networks were to broadcast the upcoming schedule for traffic light changes in systems with synchronized traffic lights. Information like "The light at location X will go green westbound at 3:42:15.3, amber at 3:42.45.6 and red at 3:42.47.8" and so on. Data for all directions and for turn arrow lights etc. This could be broadcast on data networks, or actually even in modulations of the light from the LEDs in the traffic lights themselves (though you could not see that around turns and over hills.)
Now a simple device that could go in the car could be a heads-up-display (perhaps even just an audio tone) that tells you whether you are in the "zone" for a green light. As you move through the flow, if you started getting so fast that you would get to the intersection too early for it to be green, it could show you in the too-fast zone with a blinking light or a tone that rises in pitch the faster you are. A green light (no tone) would appear when you were in the zone.
It would arrange for you to arrive at the light after it had been green for a second or two, to avoid the risk of hitting cars running the red light in the other direction. Sometimes when I drive down a street with timed lights I will find myself trusting the timing a bit too much, so I am blowing through the moment the light is green, which actually is a bit risky because of red light runners. (Perhaps the city puts in a longer all-red gap on such lights to deal with this?)
More controversial is the other direction, a tone telling you that you will need to speed up to catch this green before it goes amber. This might encourage people to drive recklessly fast and might be a harder product to legally sell. Though perhaps it could tell you that if you sped up to the limit you would make the light but stop telling you after no legal speed can make it. Of course, people would learn to figure it out.
We figure that out already of course. Many walk/don't walk signs now have red light countdown timers, and how many of us have not sped up upon seeing the counter getting low? Perhaps this isn't that dangerous. Just squeaking through a light rarely helps, of course, because the way the timing works you usually are even more likely to miss the next one, and you have to go even faster to make it -- to the point that even a daredevil won't try.
This simple device could be just the start of it. Knowledge of this data for the city (combined with a good GPS map system of course) could advise you of good alternate routes where you will get better traffic light timing. It could advise you to turn if you're first at a red light (which it will know thanks to GPS) if your destination is off to the right anwyay. Of course it could do better combined with real traffic data and information on construction, gridlock etc.
This is not a cruise control, you would still control the gas. However, if you pressed too hard on the gas your alert would start making the tone, and you would soon learn it is quite unproductive to keep pressing. (You could make this a cruise control but you need to be able to speed up some times to avoid things and change lanes.) People tend more often to speed up and then have to break for a short while waiting for the green, which doesn't get you there any faster, and is a jerky ride.
The system I describe could be a nice add-on for car GPS systems.