This is just a problem that I am curious about investigating.
Lets say we have a standard traffic intersection. The intersection has 4 lanes and each lane either lets cars enter or exit. The lanes each have a specific inflow distribution for example [20, 30, 10, 40] would mean the 20% of the vehicles enter the intersection from lane 1, 30% from lane 2, 10% from lane 3, and 40% from lane 4. Furthermore the traffic light will only let vehicles from one lane pass through the intersection at a time (always 3 red lights and 1 green light). Assume that the vehicle size, vehicles speeds, time delay between vehicles in a queue, resting distance between vehicles, and distance between the traffic light to all lane markers are all constant and equal. What are some possible algorithms to maximize the number of vehicles that pass through the intersection. These algorithms need to be implemented to the green light phase of the traffic intersection.
So far the work that I have done is come up with formula to let a queue of $n$ cars pass assuming constant acceleration. It is as following:
$t=n\tau+\sqrt{\frac{2d+2(n-1)x_0}{a}}$
I am not sure how to use this to create an optimal algorithm.
What I want is just for people to share their ideas and maybe other algorithms for the green light time to optimize the number of vehicles that pass through the intersection.