City traffic is a study in abstract algebra

We have our tree trunks, the intersection choke points which much be queue stablilized. We have individual vectors executing the commutative property in optimally congested streets. Commute in both senses of the term, exchanging places is concurrent with forward motion. No flow not quantization. Quantization isa by vehicel standard sizes, it is a small set.  These are the 'items per basket' but they are preset, the bpit boiss is a deterministic street light.

Instead of a pi boss we have queueing rules, called traffic law. A simple and standard et of rules determining when and where we can commute with other cars. The hologram axis, the linear road with density measured in vehicles, is learned; forcing the intersection queues to self manage without a competitive pit boss.  Abstract tree still applies, we induce a secondary line of symmetry by quantizing a choke point for stable flow.

Ratios then work.

50 MPH means something, it means you can expect a quarter mile of exit lane, you are tuned to the intersection queue lengths. Boundaries conditions, another characteristic of quantum systems exist, called stop signs, red light and parking spots. They must exist because we have a conserved flow system. So we get our ito's calculus, traffic is treated to good enough approximation as a fluid flow.

It is an abstract algebra because your DMV manual is a finite set of rules for commutativity that makes fractional ratios tend toward better approximations in dynamic, bounded situations. Distance behind a truck defines a rule for passing a truck, and so on. Each rule tends to make speed changes minimal, and keep the bounds.

Gaussian arrivals imply minimal interference between agents. But exclusions, like collissions imply the interference is higher than the Gaussian minimum. There are exchanges of finite sets. In all the formulations we use, those exclusions imply flow, an entropy maximizing process. There is a translation between exclusions and fluid flow, Poisson process. And the proper quantization levels find the maximizing commutative property for the given flow.