# Introduction to the Traffic Light Scheduling Problem

I would like to understand the basics of how traffic light scheduling works. Looking through research papers the topics typically revolve around actual highway systems in urban areas, but also includes managing information routing in wireless networks, and a few other areas. They also seem to be modeled similar to how machine learning is modelled, using feature vectors and optimization functions rather than using discrete concrete objects. This approach is a bit hard to comprehend as a newcomer, which leads me to look for a graph theory based approach.

I am wondering what the basic graph theoretical mathematical model looks like for a traffic system composed of discrete entities such as traffic light and entity, and how they go about modeling the optimization of the flow of traffic, not necessarily specific to cars or wireless networks, but to agents or entities in general.

It seems that it would start off like this:

Given an entity $\phi$ and a traffic light $\psi$, and intersection $\gamma$, the entities are essentially messages being passed around through intersections, which are being governed by traffic lights. This could be seen as a graph $G = (V, E)$ where intersections are the nodes $V$ and the edges are the roads $E$. The roads are directed.

Given that, I am left wondering how to possibly define the problem of the flow of entities through the roads/intersections, governed by the traffic lights, and how the traffic lights are turned on and off. At first glance it seems like an unsolvable problem. I understand basic graph theory but haven't seen anything on this complexity of entities flowing through the graph with these sort of constraints. Would like to know what the general model is of it so I can learn where to go from here.

The specific example I am interested in is making sure each intersection has an equal amount of entities pass through it.

• Interesting topic! I have zero background in this, but since intersection "busyness" varies a great deal, I would guess that the goal is more like minimising the expected waiting time at any intersection, under an empirically estimated model describing how many people are trying to get from A to B by road, for all A and B. – j_random_hacker Apr 25 '18 at 19:13
• maybe somewhat related: cs.stackexchange.com/questions/50932/… But perhaps you want to add the tag "reference-request". – Albert Hendriks Apr 25 '18 at 21:30