The Physics Behind Traffic Jamsby William Beaty
I live in Seattle and my two daily commutes last about 45 minutes. (That's when I'm lucky; sometimes it's more like two hours each.) This has given me an immense amount of time for watching the interesting patterns in the cars. Boredom led me to fantasize about the traffic being like a flowing liquid, with cars acting as giant water molecules. Over many months I slowly realized that this was not just a fantasy. Why had I never noticed all the "traffic fluid dynamics" out there? Once my brain became sensitized to it, I started seeing quite a variety of interesting things occurring. Eventually I started using my car to poke at the flowing traffic. Observation eventually leads to experimentation, no? There are amazing things you can do as an "amateur traffic dynamicist." But first, some basic phenomena.
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.
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) has simply become temporarily stuck. Maybe it spun out on ice. What will happen when the red car moves and unplugs the flow?
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.
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 watch 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 traveling wave of traffic-condensation.
NOT CAUSED BY ACCIDENTS
These sorts of traveling 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" on 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 create one.
Sometimes they have no cause at all. They are like sand ripples and sand dunes, and they just appear 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 writhing 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 traffic jam might shrink rapidly to nothing. But if traffic remains heavy, then there's no reason for the traveling 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, a single 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 made 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 move forwards.
Merging-lane Traffic Jams, A Simple Cure
<<<<< ON THE LEFT: NORMAL DRIVERS WHO PACK THEMSELVES TIGHTLY TOGETHER WHENEVER THE TRAFFIC COMES TO A STOP. NOBODY CAN MERGE EXCEPT AT THE END OF THE JAM. NOTE THEIR LOW SPEED.
ON THE RIGHT >>>>> DRIVERS WITH UNUSUAL BEHAVIOR: THEY ENCOURAGE OTHERS TO MERGE AHEAD OF THEM, AND THEY TEND TO MAINTAIN LARGE SPACES AHEAD, EVEN IF TRAFFIC SLOWS TO A CRAWL. MERGING IS EASY. SEE HOW MUCH FASTER THEY GO?
Traffic jams often occur on highways wherever two lanes must merge into one. Lanes of cars cannot merge if there are no large gaps between cars. Therefore, drivers who create large gaps between cars will ease this type of traffic jam.
To ease this type of jam:
- Maintain a large space ahead of your car.
- Encourage one, two even three cars to merge ahead of you.
- If traffic slows to a complete stop, KEEP TWO CAR-LENGTHS OF SPACE OPEN AHEAD OF YOU.
- Never "punish" merging drivers by closing your gap.
- Other suggestions
Amazingly enough, it is not necessary that EVERYONE do this. If only a few drivers will maintain large gaps during heavy traffic, then merging traffic is not forbidden, and the situation in the left-hand diagram can be prevented.
Yes you're right, you cannot eliminate every problem by simply making a big gap in front of your car. When there are too many cars on the road, traffic slows down. But if we use these special driving habits, the smaller jams can be erased, and stop-and-go traffic can be smoothed out. Since many traffic jams are caused by merging lanes, many traffic jams can be improved by the actions of just one driver.
TRAFFIC "EXPERIMENTS" AND A CURE FOR WAVES & JAMS
My first 'experiment'
Once upon a time, years ago, I was driving through a number of stop/go traffic waves on I-520 at rush hour in Seattle. I decided to try something. On a day when I immediately started hitting the usual "waves" of stopped traffic, I decided to drive slow. Rather than repeatedly rushing ahead with everyone else, only to come to a halt, I decided to try to drive at the average speed of the traffic. I let a huge gap open up ahead of me, and timed things so I was arriving at the next "stop-wave" just as the last red brake lights were turning off ahead of me. It certainly felt weird to have that huge empty space ahead of me, but I knew I was driving no slower than anyone else. Sometimes I hit it just right and never had to touch the brakes at all, but sometimes I was too fast or slow. There were many "waves" that evening, and this gave me many opportunities to improve my skill as I drove along.
I kept this up for maybe half an hour while approaching the city. Finally I happened to glance at my rearview mirror. There was an interesting sight.
It was dusk, the headlights were on, and I was going down a long hill to the bridges. I had a view of miles of highway behind me. In the other lane I could see maybe five of the traffic stop-waves. But in the lane behind me, for miles, TOTALLY UNIFORM DISTRIBUTION. I hadn't realized it, but by driving at the average speed, my car had been "eating" traffic waves. Everyone ahead of me was caught in the stop/go cycle, while everyone behind me was forced to go at a nice smooth 35MPH or so. My single tiny car had erased miles and miles of stop-and-go traffic. Just one single "lubricant atom" had a profound effect on the turbulent particle flow within the "tube."
It's always a good idea to drive without changing speed and without competing with other drivers for bits of headway. But I'd always assumed that the reasons were philosophical rather than practical (i.e. try to be a calm, nice person.) But my above experience shows differently. A single solitary driver, if they stop "competing" and instead adopt some unusual driving habits, can actually wipe away some of the frustrating traffic patterns on a highway. That "nice" noncompetitive driver can erase traffic waves. I suspect that the opposite is also true: normal competitive behavior CREATES the traffic waves.
Suppose we push constantly ahead, change lanes to grab a bit of headway, and always eliminate our forward space in order to prevent other drivers from "cutting us off". If tiny traffic waves appear, we will rush ahead and then brake hard, leaving larger waves behind us. Repeated action causes the waves to grow. Ironic that the angry people who drive as fast as possible might unwittingly participate in "amplifying" the very waves that they hate so much.
I rarely commute on 520 where the good traffic waves appear. I started to miss having opportunities to cancel them. However, I soon realized that the same process could be used to affect small traffic jams too. Traffic waves are simply a series of small traffic jams with even spacing. Each little jam is destroyed when a large empty space approaches it from behind. If no new cars are feeding into the jam from behind, yet cars are leaving from the front, then the jam is eroding away. If the jam is small enough, or if the empty space is large enough, then the jam can be annihilated entirely by a single car, as I had done with traffic waves.
Now I remember something from years farther back. When leaving one of those "rubbernecker slowdowns", I always tried to accelerate like mad. I figured that if everyone did this, then the slowdown would evaporate. Yet this did little good, because the car ahead of me would not accelerate. I could not force the cars ahead of me to stomp on the gas, so I could do nothing to aid the "evaporation" of the traffic stoppage. Aha! I can control the people behind me by slowing down, but I cannot control the people in front of me by speeding up. Therefore, I can destroy a small traffic stoppage by slowing down long before I approach it, but I can do nothing to aid the "evaporation" at the other end of the jam. Accelerating out of the jam does nothing unless EVERYONE would do the same, and there is no way to change everyone's behavior. But just one single car, if it decelerates while approaching, can change the behavior of everyone behind it. It can bite a chunk out of the region of stopped traffic. If that driver gradually builds up some empty space before encountering the slowdown, the slowdown can be "eaten" just as the traffic waves were "eaten."
On my evening commute on I-5 southbound from Everett there is always a right-lane traffic jam at one of the Lynnwood off-ramps. Close-packed cars must crawl along at 2mph for a very long time. Therefore I intentionally approached that jam in the right lane, and started letting a REALLY huge empty space open up ahead of me. By the time I hit the jam, there was maybe 1000ft of empty road ahead of me. Sure enough, my big empty space stopped traffic from feeding it from behind, while the front of the jam kept dissolving as usual. By the time I arrived, the jam was about half the size it had been. Amazing. This wasn't any little traffic wave, yet just a single driver was able to take a huge bite out of it.
Obviously my actions did more than just reduce the size of the jam. In order to create the empty space, I was temporarily driving about 10 mph below the speed of the heavy traffic. I did this for several minutes, and therefore I was causing a slight slowdown behind me. After I arrived at the jam, the jam was smaller. When all was said and done, part of the traffic jam had been removed. However, it was changed into a mild slowdown, and it was spread backwards upstream over several miles of traffic. Rather than driving at 50mph only to crawl along through a traffic jam for several minutes, everybody was now driving at 40mph for a few minutes before the jam, but then having a much smaller traffic jam to endure. The nasty, frustrating part of the 2-mph jam was changed into a large "fuzzy" area of reduced speed. If I had done it correctly, I could have erased the whole jam, transforming it into many minutes of slightly-slow driving for everyone behind me. (If I could have started 30mi upstream of the jam, maybe I would have only needed to drive 3mph slower than traffic.)
Here's a general principle I take from the above. (I guess it's obvious in hindsight!) ANTITRAFFIC DESTROYS TRAFFIC. Empty spaces can eat a traffic jam. While I was slightly slowing down to allow a space to gradually open up before me, I was creating a pulse of "antitraffic". When my antitraffic-pulse finally collided with the dense "traffic" of the jam, the two annihilated each other like a positron meeting an electron. It's nonlinear soliton physics. The soliton waves destroy each other, leaving only a slight smudge behind.
My next thought: if I took several friends along on my experiment, we could have spaced our cars out over many miles. Each of us could have allowed a big blob of anti-traffic to appear, and then the successive impacts of the antitraffic could have completely erased the traffic jam at the Lynnwood exit. When traffic is sparse, we cannot keep a large space ahead of us, since it's easy for cars to pass a slightly-slow driver. But a number of separate drivers could bring smaller spaces along with them, and any traffic jam would succumb to the barrage of "antitraffic."
Another lesson I learned: plan ahead. Plan WAY ahead. When stuck in traffic jams, I discovered that I cannot to affect them by "peeling out" after I'd made my way through the jam. I hoped to make the far end of the jam dissolve faster. It never worked because I couldn't get rid of the slow guy ahead of me. But if I'd planned way ahead and brought an empty space with me into the jam, I could use that space to manipulate the jam. Once I get myself packed in with everyone else, I can do nothing. In order to have an effect, I must behave differently BEFORE the jam, not while trapped inside it.
While doing all of the above, I once caught myself behaving normally and creating a huge traffic wave. What a hypocrite! Bad habits die hard.
Traffic was heavy and I was in the left lane. I had to merge across several lanes in order to get to my exit. I merged right once, but the next lane was packed solid (but moving, not jammed.) Nobody would let me in. I drove like this for a long while, then started driving fairly slow in order to drift backwards along the lane. I found a slot and got in, but now I had to merge right once more. Many minutes had passed, and my exit was coming up. The right lane was packed solid, NOBODY WAS LETTING ME IN. I drove slower and slower, and in a panic I finally forced my way into a small gap, making the guy behind me jam on brakes. After awhile I realized that I had just created a huge traffic wave with my behavior. Just like any rubbernecker I had suddenly slowed way down. But I had an excuse, I had to get to my exit! To make matters worse, I had nearly come to a stop, and brought two lanes of traffic to a near halt too. I probably left a long-term traffic wave at that spot on the highway. But it wasn't my fault! Yeah, suuuure.
In stewing about this I realized that EVERYONE has this same problem: an inability to merge in dense traffic. Others were probably doing the same thing that I did, and this would make the "wave" worse and worse. The simple cure is to give up, not merge, and miss the exit. I shouldn't have forced the issue, I should have let my exit go past. But there is a bigger issue here. People SHOULD be able to merge. Why was traffic packed so tightly? One obvious reason: to punish the idiots who will jump into any little space. I had always done the same myself. I never allow a space to appear ahead of me or some other driver will immediately fill it in their quest to get a couple of feet of headway. But this sort of driving would also prevent any necessary merges at off ramps (and at on ramps too, of course.) By eliminating the space ahead of me, I become part of the impenetrable wall which creates the "waves" and screws up the traffic at highway ramps.
So, if I keep a few car-lengths of space ahead of me, not only can I use it to help vaporize waves and jams, but it also eliminates one of the major causes of waves and jams. It eliminates the "solid wall" of traffic at merge areas, and lets people merge without slowing down and creating traffic waves. Take a look at this animation. Ideally a merge area will act like gear teeth. But if everyone is defending themselves against opportunistic drivers by eliminating all gaps in traffic, then the valid merges cannot take place either. A traffic jam is created. Sometimes the jam is the fault of people like me who panic at missing their exit and come to a complete stop. Sometimes the jam is the fault of the huge blinking arrow which blocks one entire lane of traffic during construction. But the traffic jam is ALWAYS the fault of those who refuse to let anyone merge ahead of them. "Just merge behind me." No, that doesn't work, since everyone in the whole lane is saying the same thing!
Delusions of Grandeur
Seattle suffers from many separate rush-hour traffic jams. Why stop with the Lynnwood I-5 jam? With enough people (maybe with cellphones and GPS units), we could intentionally smooth out ALL the traffic jams on all the main Seattle highways!
This is all fantasy at this point. It's probably illegal for several people to "conspire" to mess with traffic patterns (would we be arrested under a drag-racing law?) And while it is possible for a single driver to have huge effects on traffic patterns, some things can't be done by a few people. For example, suppose I want to eat the I-5 traffic jam south of the city. I would have to go all the way to Tacoma, then drive north. But if I tried driving slightly slow, a space would not open up ahead of me because nothing stops other drivers from passing me. In my experiments, I could make "antitraffic" spaces only because traffic was very heavy, and because only a very few people had the ambition to leave their lane and move into the empty space.
Rolling barriers made of State Troopers
OK, so here's how to dissolve a major interstate traffic jam. Start many miles upstream from the jam. Put a row of State Trooper vehicles across the road and have them drive towards the jam. They drive perhaps at 55 or 50 rather than 70 as everyone else had been driving. Nobody can get by them, and so all the traffic behind the State Troopers is moving at 55 or so. In front of them a vast space opens up. After many minutes, the traffic which had been feeding into the traffic jam simply stops arriving. The jam trickles away. Just as the last of it is gone, the row of State troopers arrives, and the jam has been transformed into miles and miles of slightly slow traffic upstream from the old location of the jam.
The situation is not so simple if extra traffic is entering from numerous on-ramps. The "rolling barrier" can't affect these extra inputs, and if the major portion of the traffic is from on-ramps, then the "rolling barrier" idea would be worthless. Ah, but what about "rubbernecker slowdowns"? A rolling barrier could let the slowdown evaporate, and change it into a wide area of slightly-slow traffic a few miles upstream from the accident. Would the slowdown re-form? Would rubberneckers hit the brakes and re-create the "traffic standing wave"? I don’t know. Sometimes "rubbernecker slowdowns" persist for hours after the accident has been cleared. This suggests that the slowdown is self-perpetuating. If so, then "erasing" the slowdown might be worthwhile, because once it's erased, it will only re-form very slowly (or not at all). If the slowdown normally persists for several hours, yet it only takes half of an hour to erase it, why not erase it? True, the slowdown is not "gone," since it has become a wide area of slightly slow traffic. However, over many months of slowdown-erasure, this could prevent lots of fender-benders and road-rage incidents, and eliminate thousands of man-years of anger and frustration.
Also, the average speed and traffic throughput on the highway MIGHT actually improve if region of stopped traffic could be removed. "Removing" the jam just spreads it out and does not immediately alter the average speed. But the resulting improvements in speed might be more than you'd expect. After all, things are not "linear" in traffic flow, since those who sit at 0 mph for many minutes in a jam cannot compensate by driving at twice the speed limit afterwards. And once a jam is gone, the remaining region of slightly-slowed traffic might disperse fairly rapidly, whereas a traffic jam/stoppage is a different animal and can self-perpetuate once it has formed. And there's another thing that happens when we spread out a "jam"...
MAKING A REAL DIFFERENCE
During a year of practicing the "wave-smoothing" driving habits, I kept looking for places where I could make a big difference in traffic flow. Yes, I could always use an empty space to move a piece of the traffic jam to another location. With a big empty space, I could even spread the cars apart as I moved them, the way I did it with the jammed sections in the "traffic wave." Finally I saw that there was one common situation where I could do some real good.
If you drive in heavy highway traffic, you've probably seen a traffic wave develop at a construction site where one lane is blocked. You crawl and crawl at 3 mph until you get to the bottleneck, then you take your turn merging as the two lanes slooooowly come together. Then you race off at 60 mph! The merging lanes formed a terrible bottleneck. A "traffic wave" develops at (and behind) the merge zone. After the bottleneck, it's clear sailing.
WHY must a bottleneck develop at a merge zone? Well, because everyone must take turns. Wrong! Under low-traffic conditions, everyone still takes turns, yet everyone merges at high speed. A bottleneck never appears. Traffic jams develop at a merge zone whenever the cars get so close together that there are no gaps between them. Without gaps, nobody can merge, and so the traffic comes to a near halt. But whenever traffic comes to a near halt, people always pack themselves together. Huh. This is screwy. At the place where the lanes merge together, close-packed cars cause the bottleneck, but the bottleneck is the cause of the close-packed cars. But, but... do traffic jams CAUSE THEMSELVES? After thinking about this even more, I realized that the answer is yes. It goes like this:
- Traffic is going slow
- Everyone packs together and closes up the gaps
- Fast merging becomes impossible
- Incoming cars create a huge back-up
- Cars must slooooowly take turns merging
- This makes traffic go slow
- Go back to the top of the loop.
This is absolutely fascinating, since this self-caused situation has a counterpart:
- Traffic flows along rapidly
- Nobody closes the gaps (they follow the 2-second rule?)
- Merging is easy
- Streams of traffic flow together like a zipper
- This allows traffic to go fast
- Go back to the top of the loop.
At a merge zone, fast traffic causes traffic to be fast, while slow traffic causes a jam. Weird! The difference between these two situations is enormous, yet EITHER ONE can arise on the exact same highway under the exact same amount of traffic. In the first one the speed might be 2 mph, while in the second one it could be 40 mph. And here's the important part: because the situations create themselves once they are established, they can sometimes switch from one to the other. Or somebody can switch them intentionally.
Suppose the traffic at a merge zone was flowing fast as in number 2 above. Suppose I wanted to wreck everything. I could slow way down and make all the cars pack together behind me. This would keep the other lane from merging into the close-packed lane. Cars in the merge-lane would pile up too. Then I drive off laughing evilly, because I have just caused a MASSIVE LONG-TERM TRAFFIC JAM!
Or, I could do the opposite. Suppose everything is jammed up at the merge zone. Suppose I accumulate a huge space ahead of me and bring it into the jam. When the huge space gets there, the other lane can suddenly change lanes, spread out, and start flowing fast. Next, I speed up and merge with it, and so do the cars behind me. The "zipper-like" flow has begun. The switch has flipped. I have just ERASED a long-term bottleneck. As they say in Seattle, pretty cool, eh?