I watched a youtube video about a certain interesting property of springs and road networks. It made me think: if we represent a network of roads as a graph where edges are roads described by a throughput and latency, and vertices correspond to road junctions what would an efficient algorithm for determining the equilibrium (such that no car can make a faster route) of traffic look like? And as a bonus question: how would that algorithm change for different types of agents (say we try the find the equilibrium for super rational agents)
The problem you are interested in is called the Traffic equilibrium problem.
The paper "Traffic Equilibrium and Variational Inequalities" by Stella Dafermos formalizes it, shows that there is a unique equilibrium, and gives an algorithm for computing it.
Note that this works for a particular formalization, for example, it assumes "a fixed travel demand [..] for every origin-destination pair". One could want to model more complex things, like time-dependent travel demand, or arbitrarily complex relations between road congestion and throughput/latency. If you have something specific in mind, I'd recommend to ask another question.