How do traffic waves travel downstream (traveling in the same direction as the flow of traffic)?

i.e. How can the flow of traffic in a particular location be affected by the flow of traffic behind that location?

I think I understand how traffic waves can travel upstream (against the flow of traffic). It can happen in many ways, e.g. A car in front applies the brakes, so the car behind also brakes, then the one behind that etc. This information can travel faster than the flow of traffic, so this wave of braking travels upstream down the motorway, sometimes for miles.

However, I cannot workout how a traffic wave could travel downstream. Can somebody please provide me with an explanation as to how this could happen?

  • $\begingroup$ There's no citation at wikipedia for downstream propagation, and I don't recall ever seeing such an event, unless you count the slow spread of cars past the blockage as they speed up and increase their relative separations. That's really not a wave, just a dispersion effect. $\endgroup$ – Carl Witthoft Nov 13 '14 at 14:32

In highway traffic dynamics there's a well-known common event called the "Boomerang effect." It occurs at merge zones, when an event causes a backwards-propagating wave which then halts, then the wave returns forward with traffic and encounters the merge zone again.

Search on this: freeway unstable "boomerang effect"

If a traffic wave involves halted cars, the wave must travel upstream. But if cars aren't slowing all the way to zero-velocity, then the upstream wave propagation can be very slow, and can even halt in place ...or drift forward.

See animation of non-moving wave

For a wave moving upstream, the flow rate within the densest part of the wave must be lower than in the sparse parts. E.g. a typical stop-wave or traffic shock, where the flow rate for the halted cars is zero.

But for a wave halted in place, a standing wave, the flow rate in the dense part of the wave must be exactly equal to the flow rate in the sparse sections. That way the transition between the sparse and dense segments need not move at all.

For a wave moving forward, the flow rate in the dense part must be higher than the flow within the sparse parts. The simplest case is a short dense segment on the freeway, but where all cars have the same velocity, and the dense part moves with the flow. (Since speeds are equal, the dense part has higher flow rate than the sparse parts.)


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