Let's talk about the incredible punch Tom Schelling's seemingly simple models carry in an extremely light package. One of my favorite of his models is the highway gawker model. It starts with a curiosity he likely picked up in the local news. 
What we've got here, one is inclined to conclude, is failure to communicate. More precisely, the failure to negotiate over a shared resource called the buffer: the strip of empty roadway between two cars.
If we are negotiating over a shared resource with negative externalities and catastrophic consequences, textbook economics tells us we should simply build fences and establish property rights. But how do you fence in a constantly shifting piece of empty roadway?
Maybe we can create a kitty for someone willing to jump out of the car in order to remove the endangering obstacle. This could solve the problem known as dilution of responsibility.
How much do you think has to be in the kitty, and how do you collect it from passing motorists?
How much do you think has to be in the kitty, and how do you collect it from passing motorists?
The answer is hidden in the word "buffer", which is an inventory term. Once the buffer goes down to zero, the inventory explodes, and you get a pile-up of problems. Indeed we are in a world of Forrester shocks, and the application of Forrester shocks to traffic flow.
In transportation science, these Forrester shocks are known as ghost traffic jams, jams out of nowhere, or traffic shockwaves: an invisible dynamic trigger causing a huge pile-up. Traffic flow modelers obsess over them.
In traffic flow we are looking at vehicle spacing or follower models (if we're not looking at lane changes, exits, or intersections): a dynamic queueing model.
One of my favorite models is the psychophysical follower model. Indeed, it might be my favorite model ever.
One of my favorite models is the psychophysical follower model. Indeed, it might be my favorite model ever.
Originally developed in 1974 at the University of Karlsruhe (my alma mater), Wiedemann's psychophysical model is one of the earliest human-machine interaction models — now we call it "UI". And yes, even in the convergent case, it introduces circumnutation (those swirls).
In light of the massive spending on autonomous driving this is now a thriving research topic, using many of the methods in the intersection of stats and ML I've described before. Nagel-Schreckenberg is another nice one, using cellular automata.
Four of the harder classes I took in college were Markov processes, linear & nonlinear dynamic systems, Bayesian belief networks, and stochastic interaction in lattices.
Tom Schelling managed to capture the essence of all four.
Tom Schelling managed to capture the essence of all four.
