Invisible accidents

Have you ever been driving on an interstate highway when traffic suddenly 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 swallowed up.





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