I agree that with information about traffic and signal condition we can save lot of frustration and fuel. the solution is simple enough but it will require major investment from government/public as they will need to build data centers that could provide updated information to millions of smartdevices every fraction of second.
To me, the benefit of a connected car is to have better information gathering. Most drivers would like to know the traffic condition in order to look for alternative route. An apps can already do that. WAZE or simply Google Map can achieve the goal. The idea of knowing how far you are from the light and when the light is going to turn is a very interesting concept. I guess a lot of drivers are already practicing slowing down once they are approaching red light. Thanks to hybrid driving lesson. ;)
To me, a connected car shall do more than saving fuel, primarily safety and collision warning. It shall never create more distraction to the drivers.
... lets the driver know how fast he should drive to get the next light when it turns green.
Interesting concept. Along my commute where daily drivers have learned the synchronized traffic light patterns many will reduce their speed in an effort to coast to a stop at the next red light without braking (using the vehicle's natural friction to save brake pads or wasting the fuel it took to get up to speed), or keep the speed slower than the posted limit so as to arrive just after the light has turned green and traffic in front has cleared the intersection.
I like to see my gas mileage indicator display above 30 miles per gallon at the end of the 10 mile 20 minute trip (Chevy Cobalt).
Those who do not follow a daily route would benefit from a connected system as described. Even those drivers who know the route would benefit.