How to make a mathematical model?

Question

Mathematics

Let's suppose that traffic lights were combined into a peer-to-peer network and they were given the command to reduce the time of a red or green signal when there are no pedestrians / cars. Traffic lights "communicate" with each other and can make decisions collectively.
The idea came to create a model of the city with its crossroads, cars, pedestrians, to see and understand what would come of it. What technologies are needed for this? How to make a mathematical model if visualization is not so important?

Answer 1

Modeling of traffic flows can be imitation (hydrodynamic) and automatic. In the first case, the road network is considered as a network of pipes with fluid and flow, in the second case, as a state machine (a close example is Conway's "Life").
As a start in mathematical modeling, I recommend the following authors:
Pirumov U. G. (no, not science fiction) "Numerical Methods"
Bakhvalov, Zhidkov, Kobelkov "Numerical Methods"
Samarsky, Mikhailov "Mathematical Modeling"
Ferziger, JH and Peric, M., Computational Methods for Fluid Dynamics, 2nd ed., Springer-Verlag (2001). ISBN 978-3-540-42074-3.