A Cure for Waves and Jams
My First "Experiment": Accidentally Erasing Waves!
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 cars, I decided to drive smoothly. Rather than repeatedly rushing ahead with everyone else, only to come to a halt, I decided to try to move 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 brakelights 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. Other times 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 neighboring 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 of the traffic around me, my car had been "eating" the 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 entire miles of "tube."
It's always a good idea to drive without changing speed and without competing with other drivers for bits of headway. 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 huge. Ironic that the angry people who push ahead as fast as possible might unwittingly participate in "amplifying" the very conditions that they hate so much. The solution seems obvious: drivers with a smooth "calm" style will tend to damp out the waves and produce a uniform flow... and the few drivers who intentionally drive at a single constant speed will wipe out the waves entirely.
I rarely commute on 520 where the good traffic waves appear. I started to miss the opportunities to cancel them. However, I soon realized that the same process could be used to affect the smaller 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 a single car can entirely annihilate the jam, as I had done with traffic waves.
Now I remember something from years back. When trapped in one of those "rubbernecker slowdowns", I always tried to accelerate like mad when I escaped at the end. I figured that if everyone did this, then the slowdown would evaporate. Yet this did no good, because the car ahead of me blocked my move. It would not accelerate. I could never force the cars ahead of me to stomp on the gas too, so I could do little to aid the "evaporation" of the traffic stoppage. Aha! I could control the people behind me by slowing down, but I couldn't control the people in front of me by speeding up. Therefore, I can smooth out a small traffic stoppage. I just have to acquire a huge empty space long before I approach it. But if I'm already inside the jam, I can do nothing to aid the "evaporation" at the far end. If I cannot predict where jams will arise, then I'd better drive all the time with a huge empty space. (Which is just what many truckers do. Did they figure something out that I didn't know?)
Just one single car, if it decelerates while approaching a jam, can change the behavior of everyone behind it. And soon these people behind that single car will take the place of everyone in the jam. Your single car can bite a huge chunk out of the region of stopped traffic. If one car refuses to pack together with everyone else to form a "parking lot," the jam can be made smaller. Or if one driver gradually builds up lots of empty space before encountering the slowdown, perhaps that driver can "eat" the whole slowdown just as the many traffic waves were "eaten" by my own car.
[[!img standing_wave.gif size="433x" align="center"]]
STANDING WAVE: a "rubbernecker slowdown" ...without rubberneckers! Traffic-waves need not drift backwards. Sometimes they become pinned in one place. Once this type of traffic jam is established, it can last nearly forever. It can also grow to enormous size as more cars arrive from behind. New cars MUST slow down as they enter, and that's what makes the jam persist. You cannot dissolve the jam by accelerating out at the end, since you're still blocked by the driver ahead of you. The solution: bring a huge space in as you approach it. This temporarily cuts off the flow of incoming cars which feeds it and keeps it alive. A single driver can easily erase a small jam, removing the bottleneck and turning it into a wave which moves backwards.
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 changed to the exit lane as I approached that distant jam, and I 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 one single driver was able to take a huge bite out of it.
Just Moving Jam Around
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 caused a slight slowdown behind me. After I arrived at the jam, the jam was smaller. When all was said and done, part of the dense traffic jam had been removed. However, it was changed into a mild slowdown, and it was spread backwards upstream over several miles of traffic. Traffic behavior was changed. 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 average traffic flow might have improved, but also it might have remained unchanged. But the nasty, frustrating part of the 2-mph jam was converted into a large "fuzzy" area of reduced speed. And after I made these changes, drivers as a whole would find it much easier switch lanes to avoid becoming trapped in the jam, since the solid-packed region was much smaller. 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... that is, if other drivers didn't simply go around my slow car.)
Another thing that happened: by shrinking the region of solid-packed cars, I made it easier for other cars to merge into the exit lane, so I probably removed part of the backup in the through-lane as well. By moving the jam backwards, I unplugged the merge zone at that exit. The jam was mostly caused by drivers trying to merge across lanes to reach the exit. Drivers already in the exit lane weren't letting anyone in, so the merging cars sat unmoving in the thru-lane, waiting for a space to open, and stopping everyone behind them. By inserting a large empty space, I wasn't only taking a bite out of the jam ahead of me. I was also easing the jam in other lanes. At best, moving the jam backwards would entirely remove the bottleneck and halt the growing queue of stopped cars. With the jam broken up, the clot of cars behind the merge zone becomes a wave which freely moves backwards. The traffic jam was like downtown city "grid-lock," and I was breaking up the gridlock and promoting free flow by putting spaces between all the cars.
Here's a general principle I take from the above. (I guess it's obvious in hindsight!) ANTITRAFFIC DESTROYS TRAFFIC. Empty spaces can break up 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" ahead of me. When my antitraffic 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 fuzzy smudge behind. The fuzzy smudge behaves very differently than the original bottleneck: it travels backwards and moves off into the distance.
My next thought: if I took several friends along on my experiment, we could have repeated the same jam-erasing process. Each of us could have allowed a big blob of anti-traffic to appear, and then the repeated impacts of the antitraffic could have completely erased the traffic jam at the Lynnwood exit. Traffic at the exit would start flowing freely, and the long backup would drain away. When traffic is sparse, we cannot keep a large space ahead of us, since it's too easy for cars to pass a slightly-slow driver. But several separate drivers could bring less-enormous 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 affect them by first making my way through the jam and then "peeling out" at the end. 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 as a commuter I'm encountering the same traffic jams every day. I know what to expect ...so if I planned way ahead and brought a big empty space along with me into the jam, I could use that space to manipulate the jam. I can control the traffic only by applying the brakes. But 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.
But won't other drivers simply go around me and fill my big empty space? Hmmmm. After trying this many times, I find that they usually don't. I wonder why? (see the FAQ.)
And here's a final lesson: a bit of math! (This part took me years to figure out.) A traffic jam is a pattern in the cars, but what exactly is a traffic jam? Simple: it's a traffic pattern where the outflow from the pattern has become constant. Drivers can't affect the outflow rate from a traffic jam (they can't dissolve the jam by "peeling out.") And amazingly enough, that's the key thing that makes a jam be a jam. In normal un-jammed highways, the outflow from a piece of road is affected by the inflow. If inflow rate gets larger, then outflow rate gets larger too. But once the jam-pattern appears, the outflow rate becomes constant, and the jam will grow larger and larger if the inflow rate is a tiny bit bigger than the outflow. (And of course the jam may shrink to nothing if the inflow is a bit smaller.) And finally: once the jam has been triggered, the outflow must be less than the outflow from an un-jammed highway. (Think: if the outflow from a jam was better than the outflow from a normal highway, then the sudden improvement in outflow would drain out the cars, and the jam would instantly evaporate before it had a chance to really get started.)
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 it was still moving, not jammed.) Nobody would let me in. I drove like this for a long while, then started driving fairly slowly 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 for no good reason. But I had an excuse, I had to get to my exit! To make matters worse, I had nearly come to a complete stop, and brought two entire 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 exact same thing that I did, and this would make the "wave" near the exit worse and worse. Our inability to change lanes would create a "dynamic bottleneck" which hovers near the exit. Obviously the simple cure is to give up; not merge, and miss the exit. I should never have forced the issue, I should have let my exit go past. And so should all the other merging drivers. 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 swerve into it during their quest to cheat by running to the front of the line. But this sort of "closed-gap" 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 "dynamic bottleneck" and screws up the traffic at highway ramps. The gear teeth cannot mesh, so the whole machine grinds to a halt. The "zipper" becomes jammed because the "teeth" of the zipper are resentful about new teeth moving into the space ahead of them.
The jammed merging lanes are almost a city's gridlock. Smart city drivers never block intersections, since blocked intersections will freeze all traffic permanently. But we highway drivers are ignorant. We close up the gaps when others need to merge. And our behavior creates needless "highway gridlock" during every single rush hour.
So, if I keep a few carlengths of space open ahead of me, then not only can I use it to help vaporize waves and jams, but I also eliminate one of the major causes of waves and "highway gridlock." I eliminate the "solid wall" of traffic at merge areas, and I let people merge without slowing down and creating traffic waves behind them. Take a look at this animation on page three of this article. Ideally a merge-area will act like gear teeth. But suppose that everyone starts defending themselves against opportunistic drivers by eliminating all gaps in traffic. In that case the valid merges cannot take place either. A fight develops, and a traffic jam is created. The jam appears at the merge zone, while a huge region of empty roadway is created downstream. Sometimes this jam is the fault of people like me who panic while missing their exit and who come to a complete stop. Sometimes the jam is the fault of the huge blinking yellow 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 the guy behind you doesn't want any merges either. Everyone in the whole lane is saying the same thing! It's a solid packed wall of hostility. Poking a hole in that wall can make a difference.
Delusions of Grandeur
Seattle suffers from many separate rush-hour traffic jams. Why should I stop with the jam at the Lynnwood I-5 exit? 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?) This could be a "flash mob" organized via email. [NOTE: IN TORONTO, TO PROTEST THE LOW SPEED LIMITS, SEVERAL PEOPLE FORMED A ROLLING BARRIER DURING RUSH HOUR. THEY DROVE AT JUST UNDER THE SPEED LIMIT FOR HOURS, CREATING A HUGE SLOWDOWN. THEY WERE ARRESTED BUT LATER RELEASED WITHOUT CHARGES.] 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 entire I-5 and I-90 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 never open up ahead of me because nothing stops other drivers from passing me. In my experiments, I could create my "antitraffic" spaces only because traffic was very heavy, and because only a very few people had the opportunity and the ambition to leave their lane and move into my 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 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 city traffic jams simply stops arriving. There is no new traffic for many minutes. The huge jam trickles away. Just as the last of it is gone, the row of State troopers and the 55-mph traffic arrives, and the jam has been transformed into miles and miles of slightly slow traffic upstream from the old location of the jam.
The BIG Question
But does this increase the throughput of the highway? YES!!! It allows people to merge again! It actually changes the 'capacity' of the highway. It wipes out a 'dynamic bottleneck.' By removing the close-packed region, the two lanes of traffic at the exits and entrances are able to merge... so even though the close-packed region is now a big fuzzy slowdown, the flow of traffic does greatly increase.
On the other hand, the situation is not so simple if lots of extra traffic is entering from numerous on-ramps. The "rolling barrier" can't affect these extra inputs, and if nearly all of the traffic is from on-ramps, then the "rolling barrier" idea would be worthless. In that case it can only control the main highway and not all the on-ramps.
Ah, but what about "rubbernecker slowdowns" at accident sites? 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 dunno. Sometimes "rubbernecker slowdowns" persist for hours after the accident has been cleared. This suggests that the slowdown is self-perpetuating. Rubberneckers only trigger it, but they don't keep it going afterwards. 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 for the police 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. However, 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 120MPH afterwards. Also, some jams act like "virtual bottlnecks" which create huge backups behind the jam while also creating empty highway downstream. Removing the jam will remove the bottleneck and increase the flow. (Note: if this is common, if jams commonly act as bottlenecks, it means that highways don't have a known capacity. The highway's maximum capacity is different whether a jam is present or not.)
A One-man Multi-lane Rolling Barrier
In driving with huge empty spaces during rush hour, I find that the space ahead of me doesn't just instantly fill up. Other drivers don't change lanes to fill them. Weird! What's going on? First, if I'm driving with a big empty space, sometimes the car directly behind me will pass me. Sometimes it happens twice. But this removes the lane jumpers from behind me, and forms a row behind me of nonaggressive drivers. Those drivers are like a plug, since any aggressive drivers several cars back can't even SEE the big empty space ahead of me.
But what about the adjacent lane? Won't they all fill my empty space? Nope. A few do change lanes, then they rush to the end of the empty space. This filters out the aggressive drivers from the adjacent lane, letting them move to my lane at the end of my space, and leaving sane ones next to my empty space. They don't change lanes. They don't care that there's a huge empty space growing and shrinking right beside them. They form a big plug, and aggressive drivers behind them cannot get to my big empty space.
This "plug effect" only happens when traffic is highly congested. When traffic is light, I can't maintain a big empty space, since aggressive drivers can easily swerve around to jump into the space. But when traffic is light, there's no traffic jams, so there's no need to create an antitraffic bubble and perform jam-busting.
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 the slowdown, the same way I did it with the jammed sections in the "traffic wave." But the genuine "bottlenecks" seemed all too rare. Then finally I noticed 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 sloooooooowly come together. Then you race off at 60 mph! No downstream congestion! The merging lanes formed a terrible bottleneck, yet the open lanes ahead were not a 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, obviously because there's too many cars on one road. And because everyone must take turns slowly merging together. WRONG! Wrong wrong wrong. Even during extremely low-traffic conditions, everyone still takes turns, yet everyone merges as a high speed flow,like a zipper. 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 suddenly comes to a near halt. The "gear teeth" jam up, the "machine" halts, and a bottleneck is created. The pile of pebbles can no longer pour through the funnel. Traffic on the highway turns into a city street intersection, where people merge at a "four way stop sign."
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... and the close-packed cars keep the bottleneck in existence. And the bottleneck makes drivers all pack together.
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 incoming traffic slow down.
- Go back to the top of this loop and repeat.
- This is absolutely fascinating because 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 this loop and repeat.
At a merge zone, fast traffic causes traffic to remain fast, while slow traffic causes a jam to persist. 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, sometimes they can switch from one to the other. A smooth flow can hit a glitch and turn into a traffic jam. Or somebody can switch them intentionally.
Suppose the traffic at a merge zone was flowing fast as in Loop 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 prevent any cars in the other lane from merging into the closely-packed lane. Cars in the merge-lane would pile up too. Then I drive off laughing evilly, because I have just CREATED MASSIVE LONG-TERM TRAFFIC JAM! The exit might stay jammed for hours.
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 of cars 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 those old Ranier Beer ads, pretty cool, eh?