Timed lights; Timed Driver app

One of those useful things that we don’t pay much attention to are streets that have timed lights. Timed lights work such that if you are going the speed limit or a few miles an hour below, lights just keep turning green for you.
What I want to know is why we can’t turn that idea on its head and create timed drivers. I’m thinking of traffic lights that can broadcast their status as to what currently has the green. Then there is an app that takes that information along with my preset route plan -> plugged in before I leave, and tells me what speed I need to go at any given time to make my lights. The app should also broadcast back to the light my information as to the plan. Implicit in this is the assumption that there are some kind of savings (time, gas, psychic) to be constantly moving as opposed to start/stop. If enough folks are using the system, then you’d expect to make the lights smarter to plan for traffic that is expected to be at the light shortly. One problem I can see immediately is if what I need to do at the upcoming light is in conflict with what someone else needs to do. For example, the guy next to me needs to make a left coming up but I want to go straight. We both can’t necessarily go through the intersection at the same time depending on the needs of the other drivers. As a quick thought, it seems like it might alter the tromp on the gas then brake at the next light pattern that is common. After all, why rush to get to a light you are going to have to sit at when you know in advance you will have to sit? It seems like there is quite a bit more complicated problem here to resolve everyone but on the other hand it doesn’t seem impossible and if the app is telling you what to do then presumably there is flexibility in how to solve the problem. Is this like the traveling salesman problem? Does this get you partway toward the ideal where self driving cars can eliminate congestion by all behaving so that everyone comes out for the better? What percentage of drivers do you need as participants to get herd effects?

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