The problem we are trying to optimize is: How can we move the most cars (maximize distance) in the least amount of time. i.e. dX/dT. Which looks like a differential equation.
One small but important nit-- you're not trying to move the most cars, but the most people.
It is a shame that the Dept. of Motor Vehicles doesn't know shit about standing waves nor teaches people how to help optimize keeping vehicles moving in the traffic flow. One of these days every car will be able to pass it's current speed both forward and backwards to its neighbor's car so that people 5, 10, 20 mins down the road can know about future traffic conditions. i.e. Peer-to-Peer Car Knowledge.
In LA they most certainly do. They can't make drivers drive better, but they instrument the hell out of the roads and there are a number of ways for drivers to get detailed real time information. The whole region's freeway system is instrumented and you can get near real time updates of freeway speeds at sigalert.com as well as most of the popular mapping apps. It even gives the dispatch reports from incidents so you know which lanes are blocked. I glance at sigalert and replan my route in an instant due to a collision 15 miles away. The city of LA also just completed integration of city street sensors and lights system wide, and it does work. You can get street speed data on google maps, and there are also crowdsourced apps like waze (which I don't use since it put me on a dead stopped 405) or trapster, that integrate realtime data from drivers on the road.