Ghost Jams

You know those strange traffic jams that appear to come out of nowhere, with nothing causing them, and then suddenly end? As Wired reports, a team of M.I.T. mathematicians calls them “phantom jams” or “jamitons,” and has found mathematical equations to describe them, similar to those that describe detonation waves from explosions. Phantom jams, the mathematicians found, can form when a single driver slows down (to take a sip of coffee or talk on the phone) on a road with too many cars on it. They hope the new equations will lead to roads engineered to keep traffic below the density where a jamiton can form. [%comments]

Sean Samis

I did a paper on these in an undergrad class like 20 years ago; don't need any fancy math to figure out what's going on. I called these jams "Sheep Blocks". The legend is that if you get a herd of sheep to start jumping over a short barrier, then pull the barrier out when the herd is half way over it, the later sheep will continue to jump over the same spot even though the barrier is gone.

As your MIT guys figured out, in dense traffic, if a single car slows down, it forces other cars to slow too and if the density is high enough the compressed traffic remains long afterwards.

More interestingly, the "sheep block" itself can migrate up stream if traffic density remains high (analogous to sound).

Jeffrey Trapnell

It is also an interesting trick used in Indy Car and NASCAR racing on a restarts. The lead driver slows just a bit coming out of curve 3 causing the entire pack to slow down. Exiting from curve 4 down the straightaway allows the leader to get an extended jump on the rest of the pack still recovering from the slowing "phantomjam". A good track official will spot the signs and force another yellow lap on the field.

Gotta love IRL and NASCAR to find another way to win!


Out here in California when vehicles are speeding or there is a possible road hazard ahead, the CHP gets in front of the pack and does a "snake dance" to slow down traffic. A single CHP vehicle swings from lane to lane to force everyone to slow down. I guess, the opposite is true when you are driving within the speed limit and everyone around you speed up and you are forced to keep up with the pack otherwise you can get hit. I could observe this happening usually at the beginning and end of long weekends when everyone is trying to head in one direction.


We've always called these slow down's "slinky's", due to their variations in speed.


I'm sure the math is interesting, but the conclusion is somewhat obvious.


I am not sure what they would have found.

I remember reading in Scientific American 40 years ago of equations for the waves or pulses or clusters - choose your term - of vehicles on freeways.

That article was somewhat oriented to the persistence of clusters and their movement down the freeway. I don't think it said much about why jams first form.

It is established that roadways have a maximum flow after which average speed will fall rapidly. That is why metered on-ramps are used, to keep the density below that level at the busiest traffic times.

Joe D

And the solution, to the rational actor showing enlightened self-interest, is to leave sufficient following distance so that rapid deceleration is unnecessary, evening out the speeds of traffic behind him or her. Don't worry about people pulling in front of you; just gently let your following distance increase again.

Freak that traffic-nomics!


The most interesting question that comes out of this phenomenon is how to react as a driver that is at the jam point (e.g., you have been traveling at a consistent speed and have come to a sudden stop. now you are beginning to speed up again) Do you a) decrease the distance between you and the car in front of you as much as possible, decreasing delay of the cars behind you, or b) allow a cushion to develop. State of the art traffic operations technology would attempt to decrease the buffer between cars and thus maximize freeway capacity and speed. This only works when there is (fictional) automation involved, as cars interface with eachother and the road. Until this miraculous technology is perfected, I go with option "B" , so as to guage the appropriate freeway speed and proceed accordingly. That way, lane changes, sudden stops, road hazards, and everyday variety @-holes don't force me to stop, and anyone behind me that is following my lead drives a comfortable, consistent 25 mph instead of 45 and stop like everyone else. It seems that if everyone drove the same speed, then those types of jams would not occur. The key is scaling up the speed together.



I'm with Tracey. I have called it the Slinky effect. Or in
Investment jargon, Gap theory...all gaps get filled. (my belief)

Avi Rappoport

@assumo, I want that technology! Seriously, why are we all controlling metal boxes hurtling along a road and susceptible to the least inattention? 40,000 deaths a year attributed to automobiles. Some kind of freeway car-train seems hugely safer and more efficient.

@lee, the Highway Patrol doesn't have to get in front of people to slow them down. Just being there in any lane reduces the top speed dramatically.

And I'm another one who tries to even out speeds instead of tailgating. Makes dealing with significant traffic jams a little less stressful.


How about rubber-necking an accident in the opposite flow? Maddening!


-1 for the smarts of MIT folks. This is not news. Anyone who observes the phenomena knows what is going on.


Don - it is "obvious" to someone who frequents this board, but you still hear people talking about "getting stuck in traffic for no apparent reason..."

Well, there was a reason and it happened 20 minutes ago 2 miles up the road.

If this new math can help us, then great.

@avi - yeah, 40,000 traffic deaths is ridiculous. we're all driving around at speeds we're not designed for.

@jeffrey - NASCAR is indeed more complicated than most think. Heck, last weeks race saw teams calculating their fuel consumption, and the fact that the two leaders didn't want to risk slowing down made it very interesting. 1 & 2 ran out on the last lap... seams like another potential Freakonomics analysis!


#8: What you're talking about is Adaptive Cruise Control, which is a system that maintains the distance between your car and the car in front, and it exists (although it hasn't been widely available yet). Studies have shown that even if only a small fraction of cars on the road have ACC (say 10% - 20%), traffic jams are greatly reduced or eliminated. This makes intuitive sense: imagine that every 5th car or so acts as a traffic jam "shock absorber", dampening out that chain reaction of tailgaiting cars that over-brake and cause the well-known "slinky effect".

Of course, we can all do the same thing by simply keeping a safe following distance (shout out to #7!). I have often thought of starting a "flash mob" through Facebook, called "Leave-a-Gap Day". I'd choose one typical commuting day and encourage as many people as possible just on that one day to "leave a gap" between their car and the car in front. If enough people do it, traffic jams will magically disappear for that one day. If the news media gets wind of it, then maybe everyone will realize what happened and people will start leaving a gap all the time and traffic jams will be a thing of the past.

Who's with me?



@14 - The key is that only a few in the herd leave the buffer. If there are too many gaps, other, less enlightened drivers speed in to fill them. If the gap is left as a rule, we don't have enough capacity to maintain high speeds. Of course anything is better than gridlock.

Fran Taylor

Sure this seems nothing more than "common sense," but your "common sense" does not have the potential to actually do something about the problem.

Only by analysis can you get these models that can be used to find ways to minimize the problem.

Joe D has the right idea. We don't need to force this on people, but something on the dashboard that uses intelligence to tell you if you are too close to the vehicle in front of you would be very helpful.


Don't these things always seem to end up as a version (in spirit, at least) of the prisoner's dilemma? If we all drove with a moderate buffer, everyone would move along faster however, I can get ahead of everyone else by jumping in that gap (and if I don't someone else surely will).

Given that, I would think it is impossible to appeal to people's "better nature" or rationality.


On a Sunday afternoon during ski season, eastbound I-70 usually jams up in the vicinity of Idaho Springs, Colorado. A mile east of there is a tunnel, after which the jam always breaks loose. I've long been sure the jam is caused by each driver slowing a little approaching the tunnel. I've long wondered if it would help to put up a big sign that said "YOU DO NOT HAVE TO SLOW DOWN TO GO THROUGH THE TUNNEL -- YOU WILL FIT THROUGH JUST FINE."

Jeffrey Trapnell

- Dave: if that be the case, wouldn't people slow to read the sign and then slow again to think if they REALLY would fit through and the flip side, think about what would happen if they didn't fit through and what would it look like if lots of other people didn't fit through... Just remember, it is not against the law to be an idiot.

- Keven: amen on the NASCAR, I have come to believe the driver plays a marginal role to a victory. Ideally, weight to speed ratio being the factor, you would want your car to run out of gas at the finish line and thus your team celebrates with you as they push you into Victory Lane.

Having sailed for many years, it is not the strength of the crew but more the skill of the tactician to read the water, the tattle-tails and the cat's paw and the timing of the crew to know the line taken and how to win races... And never forget, it is not the wind pushing the sail, it is the negative air pressure formed on the back of the sail that cause the boat to move forward with greater speed and cutting.

Racers to the mark!


Sean Samis

#7 said "And the solution, to the rational actor showing enlightened self-interest, is to leave sufficient following distance so that rapid deceleration is unnecessary," (and was seconded #14.)

Problem is that if such a following distance is left (and honored by other drivers) then the carrying-capacity of the road is significantly reduced. During rush hour that would be intolerable. Instead of traffic jams disappearing, they will get MUCH worse.

... as #15 also noticed.

#8 seeks a proper reaction. Unfortunately there's not much you can do. Often traffic flow is simply to high and the delay too long, you will have to stop. Trying to "cushion" the block will only make the block slightly less dense but also proportionately larger. As above, trying to spread out cars to prevent this phenomena only exacerbates blockage on the on-ramps.

#11, a gapper's block is just the same as these sheep blocks (or "slinkies") except we think we know why it happened.

Bottom line: traffic jams are caused by people leaving TOO MUCH room, or driving TOO SLOWLY or both.