Have you ever been driving on an interstate highway when traffic
slows to a crawl? You inch along for many minutes while waiting to see
the accident which must have caused the jam. At the same time you also
curse the "rubberneckers" who are causing the whole problem. But then all
the cars ahead of you take off at high speed. The jam is over, but no
accident, no police cars, nothing. WHAT THE HECK WAS THAT?!! A traffic
jam with no cause? In the
rear-view mirror you see all the poor saps behind you still stuck in the
jam. But why? If all those people could just speed up at the same time,
the whole traffic jam would evaporate. Why don't they ever do that? What
caused the mysterious slowdown in the first place?
After experiencing many of these "invisible accidents", I came up with
the following explanation. To best understand this, imagine that you look
down on traffic from an aerial view point. Pretend you're in a Traffic
Reporter's helicopter looking downwards.
figure 1. Cars lining up behind an accident
Above in fig. 1 I've drawn a one-lane road, an accident, and a row
of cars stuck behind the wreck. Other cars are approaching from the left
and stopping too. Suppose that the "wrecked" car (the red one above) has
simply become temporarily stuck. Maybe it spun out on ice. What will
happen when the red car moves and unplugs the flow?
figure 2. A wave of 'condensed' traffic creeps backwards
Refer to fig. 2 above. In the top row (fig. 2A) the flow is suddenly
unplugged. But not all the cars can move, since most cars are stuck
behind drivers who are stopped. Figure 2B shows the traffic a few moments
later, and figure 2C shows it a few moments after that. Notice the orange
car in 2A, and see how it eventually becomes unjammed in 2D and begins
moving. At the same time the red car in 2A approaches the jam and is
A MOVING WAVE OF "JAM"
After the wreck is removed, there seems to be no reason for the traffic
jam to persist. Yet it does. The reason for this is sensible: if I am
stuck behind a car that is stopped, then I have to stop too, and so does
the car behind me. All the cars in the jam are in this situation. Even
though the wreck is gone, they remain locked at standstill because if they
want to move, they ALL have to move at once. They never do, because each
driver is waiting for the car ahead to move. If I am in the traffic jam,
I'm not going to move forward because I have no room to do so. I'd bump
the car ahead of me. We all think like this, so none of us can move.
When the car in front of me leaves, I still cannot accelerate
instantly, so I will remain stopped for a moment. I must delay leaving
for a moment. If I started up instantly, I'd stay too close to the car
ahead of me, and that would not be safe. Each departing car must delay in
the same way, and this causes the jam to "evaporate" starting from the
forward downstream end. It evaporates in a wave which begins at the
forward end of the jam, (near the wreck). The wave eats into the jam from
right to left, yet new cars are piling onto the back end of the jam.
Starting at figure 2A, the cars depart from the jam in sequence. In 2B
the wave of "evaporation" has moved away from the wreck site, and in 2C
and 2D it is far from the wreck. But notice an interesting thing: even
though the CARS THEMSELVES are moving from left to right, the "wave of
evaporation" moves in the opposite direction. It moves leftwards as it
eats into the traffic jam.
There is a second important thing to notice. While some cars are still
jammed, more cars are piling up behind them at the trailing end of the
jam. Even after the wreck is removed, more cars are still "condensing"
onto the back of the jam. The traffic jam is like a solid object whose
front end is evaporating and whose back end is growing like a crystal.
Cars move left to right, yet look at the the group of stopped cars. The
stoppage is creeping slowly upstream, in the opposite direction to the
moving cars. The accident is gone, but a "moving wave" of stopped cars
remains behind. It's not a traffic jam, it's a shock wave which
propagates through the "automotive material". It's a traffic-clot in the
blood vessel. It's a travelling wave of traffic-condensation.
NOT CAUSED BY ACCIDENTS
These sorts of travelling waves are common during heavy traffic
conditions. An accident isn't needed to create them, sometimes they are
caused by near-misses, by people cutting each other off, by merging
lanes at a construction site, or simply by extra cars entering from an
on-ramp. In traffic engineering lingo, they can be caused by "incidents"
the highway. A single "rubbernecker" could cause one by momentarily
stopping to look at something interesting. Whenever you slow way down in
order to merge across a lane to get to your upcoming exit, YOU could
Also see my Frequently
asked questions page, and
Sometimes the traffic waves have have no real cause at all. They
appear because tiny random motions can trigger large results. They are
like sand ripples and sand dunes, and they just build up for no clear
reason. They are like ocean waves caused by the steady breeze, or like
the waves which move along a flapping flag. They just "emerge"
spontaneously from the writheing lines of traffic. In the science of
Nonlinear Dynamics this is called an EMERGENT PHENOMENON."
How long will the "traffic wave" last after the accident is cleared?
Its lifetime depends upon the amount of traffic, and on the number of cars
trapped in the jam, but sometimes these things can persist for many hours.
When traffic is slight, the jam might shrink rapidly to nothing.
But if traffic remains heavy, then there's no reason for the travelling
wave to ever dissipate at all. Also, if the conditions are just right (if
the "condensation" happens faster than the "evaporation",) then even a
tiny wave could grow large and larger. Sort of like dropping a tiny seed
crystal into a supersaturated solution. When traffic is heavy and
unstable, slight braking by any driver can cause the traffic
to freeze into a gigantic
crystal. Like Kurt Vonnegut's end of the world story
CAT'S CRADLE it's the "Ice Nine" of the highways.
So, next time you are commuting and you approach a stoppage, don't
think of it as a stupid f@#$% traffic jam. Think of it as a pressure wave
which has approached your car and engulfed it. Think of it as a simple
living thing which is composed of cars rather than molecules. Stay
hopeful that the Crystalline Amoeba poops your car out soon. Take an
aerial viewpoint, and visualize the wave which is moving backwards as you
NEXT, PAGE 2: TRAFFIC
EXPERIMENTS and a possible cure for certain types of traffic congestion
Note that traffic physicists have a different name for traffic waves:
the pinch effect.