The two kinds of traffic jams

A famous example of the traditional type of jam: end of Chinese week-long national holiday, drone footage by Sohu TV

A pure phantom traffic jam
Also, see the great Mythbusters episode on several traffic myths.

Bruce Greenshields the pioneer: flow = density * velocity

PhD work in 30s
Discovered two linear regimes for traffic

Lighthill & Whitham's two-part paper of 1955

The first paper was on "flood movement in long rivers"

The second paper was a landmark paper, giving rise to the macroscopic flow density and shock formation from physical theories like those of compressible gases, instead of just tracking each vehicle individually.

See here for an introduction to and review of the continuum traffic flow models

The all-important q-k curve

(On chalkboard)

MIT Mathematics: Traffic Modeling

Research group homepage (and there are many more research groups working on mathematics & modeling of traffic flow)

Jamitons and Jamitinos: a hybrid traffic jam example
Comments on the inviscid model
    - No dissipation of shock unless conditions change dramatically enough
    - Some viscosity (i.e. preventative, overly-careful drivers) can also help

The end of phantom traffic jams? 

Legality of public road testing of driverless cars as of February 23, 2016

Take-home message from's Bill Beaty

Summary video

Bonus topic: on & off ramps

For on/off ramps (and just curvy roads, too) it can be much easier to anticipate the curvature by watching the inner line of paint, and not the outer one: