Traffic Waves

EARLIER COMMENTS (back to 2007)

I take a weekly trip north on I-93 and for a while got stuck in traffic every week. Like you, it gave me plenty of time to watch the patterns of traffic around me. Where pinch points happen and where the waves of traffic seem to emanate. Picturing it in my head and creating "rules" allowed me to observe how my own actions can affect other drivers behind me. (And sometime around me too)

Eventually I began to practice the same scenarios that you describe. Slowing down gradually to create a gap in between my car and the car ahead of me that would be caught in the jamb first. I certainly noticed a difference after practicing a few weeks in a row.

I began to notice that drivers behind me would start to emulate my behavior. They would stop changing lanes often and remain in their spot. The biggest kick i got out of the whole experiment was watching aggressive drivers fly up to the jam weave through a few people and then get stuck as I coast by. (This was not always the case but in most instances I found that I would maintain a semi-permanent position in relation to aggressive drivers.) It was also a thrill to look to my right (I am usually in the far left lane) and see that people around me were doing the same thing. Within a 20-yard radius the cars were behaving in a similar manner, eating up the waves that we came up against.

I just want to add a few notes from my own experience.

1. I believe it is easier to "eat" traffic waves in a car with a standard transmission.

a)Breaking automatically alerts the person behind you that you are slowing down. In a standard you can slow down without breaking by down-shifting so that the person behind you must become conscious of their own speed and position within the group.

b) Shifting gears and attributing certain speeds to what gear you are in helps you identify the severity of the traffic jam and the period of each traffic wave

2. You mentioned that at first you thought it was a philosophical solution, ie maintaining a "cool-head" and driving with patience, but later abandoning that reasoning and adopting a more scientific view of upholding certain driving habits. I would counter, and say that it is both.

a) I don't think one is capable of doing one without the other. If I had not let go of my own ego and released myself from the recurring negative thoughts that I must be first, and that I must continue to pass people to make headway in traffic, i would not have been able to observe the laws that were governing the traffic jam. Thus, I would not have been able to improve my driving and (since conscious driving alleviates the traffic for those behind me) the drive for those other people with whom i share the road.

b) if you "project" your good driving behavior you cause other drivers to become aware of their own driving and, perhaps, improve themselves. Which would cascade into better drivers all around. (we all know Massachusetts needs more of those)

Lastly, I just wanted to say thanks for taking the time to put together your essays and post them publicly. This is a great resource for others. Peace.


Morgan Lawless <mmmorgan.lawless@gmmmail.commm>
Boston, MA USA - Wednesday, December 26, 2007 at 09:15:09 (PST)
Hi Bill

You might want to check out these two links:


Someone should have spent a little time on Google searching for "traffic waves"...

I blogged about it here:

Dave Halliday <dh@synthstuff.com>
Maple Falls, WA USA - Saturday, December 22, 2007 at 19:07:24 (PST)
I've personally seen this work. When I lived in Hurricane, WV and they were doing major construction on the interstate (it has major traffic flow between Charleston and Huntington, and I know this is no big city traffic) but when people fought to merge traffic slowed to a crawl. Since a lot of trucks move through the area they started forming roving barriers that increased traffic flow. Other drivers noticed the improvement and formed barrier partnerships with cars beside them. Worked wonders, cleared up hours of traffic hassle at least for the people doing it and those around them. Since I've moved up to Morgantown I've noticed the people don't do this and are very competitive (due to the high student to town population ratio). For a "smaller" town traffic is hell here mostly because of this competitive behavior.
Morgantown, wv USA - Friday, December 21, 2007 at 16:46:53 (PST)
I don't have a question. But I read your "theory" a couple of years ago and follow it on a regular basis on the 10 or 405 with much success. It takes some of the stress out of traffic jams when you can single-handedly improve traffic flow. It really does work and I've never had a road rage incident.. Thanks!
james <stoptimela <@> gmail.com>
los angeles, ca USA - Saturday, December 15, 2007 at 01:35:10 (PST)
This is why I believe now that traffic lights are far inferior to roundabouts. If you think about it, traffic lights promote a hurry up and wait system. Roundabouts promote average speed driving. What you?re describing is driving the average speed. When I see a red light way ahead, I begin to slow down. Ahhh? look at all those fools continue racing toward the light, some even come into the lane in front of me (I?ll get to that in a bit). I rarely ever actually stop at red lights, unless the light turns red right in my face, which is the worst! Because if I had known that it would be red, I would have slowed down a long time ago. This is why I mention that traffic lights promote a hurry up and wait system. Also, since traffic lights work in letting everyone through in this half of the time and the other half people build up the queue, if you are driving the average speed to the light and someone is behind you and unable to make it to the left hand turn lane because you didn?t feel like stopping, there is obvious peer pressure for you to go faster to a light that is red. This is why roundabouts are much better. No left turns at a roundabout. With a roundabout, I can actually drive the average speed, slow down early to a long line of cars, and I?ll only piss off totally ignorant fools who have no idea about anything, but they won?t actually have any point to be mad. Where as, in the traffic light with a left turn lane example, the guy behind me kind of has a point, after all, it?s not his fault that the traffic light is designed for me to move up as fast as possible allowing him to go left.

But getting back to the point I said I would get back to, if I?m going the average speed and some guy goes around me, (ESPECIALLY if he does this when no one else is in front of me and he just wants to get to the front spot) when the light is green and I?m prepared to move past everyone at 20mph since I didn?t stop and he?s the only one holding me up, I usually honk my horn, flash my high beams and pressure this person to get on their horse. After all, they were in such a rush to get to the light, I assume they?re in a mad rush like all hell to get to wherever they?re going. And if he wasn?t there, when the light turns green, I?m zooming past everyone because I wasn?t stupid enough to stop. I ?used my space? to keep my speed and my lane didn?t stop behind me. I do this ALLLL the time, drive the average speed that is. One night, it was CLASSIC when a cop (late at night, no one else on the road) did this to me on a 2-lane (each direction) road. The light turned green, I started to accelerate but not that fast, on a 45 mph road I slowly accelerated to about 30 mph and then started to cruise. The cop behind me was clearly pissed off because he raced around me at 50mph and then? yes that?s right, his brake lights turned on and then came to a complete stop. I was still going 30 mph and approaching a red light where he was stopped at. Light turns green, and before it even turns green I accelerate to 35mph and on my way to 40mph as he?s only just starting to move. Without speeding (I don?t ever speed past the speed limit), I had gotten about 15 cars lengths ahead of him, it was sooo funny. And the best was, once I got through, I started to slow down again because I noticed the light was red again ahead, stupid cop raced past me trying to show me he?s faster and I have a slow car, and I did it to him AGAIN! He then passed me again going about 55 mph on a 45 mph road, he passed me at 10 mph faster. Good for him?

Simon Hartigan <simonhartigan@cox.net>
Mission Viejo, CA USA - Thursday, December 06, 2007 at 20:50:47 (PST)
It's always nice to see someone thinking about traffic dynamics. The discussion here has addressed mainly highway traffic, but I'd like to point out that the application of some intelligence can make city driving easier, particularly with respect to stop-light behavior.

Chris from Sierra Madre (Nov. 26, 2006) asks us to imagine how much better it would be, when a red light turns green, if all the stopped vehicles could begin at the same time, like the linked cars of a train. He suggests that everyone start moving together and "accelerate quickly" as soon as space is available. It should be obvious that this is a risky strategy in dense traffic, where the failure of even one driver ahead of you to behave as you wish can create a chain of rear-endings.

Ed from San Diego (June 21, 2007) describes the "red light shuffle," by which drivers who have already stopped at a light compress the open space between their vehicles, moving up one at a time as if being slightly closer to the light itself will enable them to get a head start when the signal changes. He mentions brake wear, but doesn't really address the shuffle's effect on traffic dynamics.

The answer, of course, is that compressing distance at stop lights has exactly the opposite effect of what the drivers are presumably seeking. It slows down everyone (except the very first car), because each driver, practically sitting on the bumper of the next car forward, must wait for that driver to move before he can. The next car, in turn, must wait for EACH preceding driver to get going, one at a time, and so it builds. With enough vehicles on the road, you eventually get the frustrating situation in which the light turns red again before everyone in front of you has gotten through.

The simple solution is this: NEVER CREEP UP at a red light. Stop a modest distance behind the stopped vehicle in front of you, and STAY THERE. Let the vehicles in front of you creep up. Let the vehicles in adjacent lanes creep up. Let people give you funny looks because you are not seizing absolutely every last inch of "available" asphalt. Watch the signal light. The instant it turns green, begin rolling forward slowly, past those people who gave you funny looks as they crept up and passed you while the light was red. They will be waiting for those in front of them to get going.

When this move works to its fullest, the vehicles in your lane will be under way before you catch up to them, and you will be able to put some gas on while adjacent vehicles are still barely moving, if at all. Accelerating at this stage is much safer, because everyone in front of you will have had several additional seconds to pick up speed and disperse themselves back to cruising distances. Everyone behind you in your own lane will benefit too. Their benefit will be have been reduced by some creeping of their own, although your action will have reduced the harm they could do to themselves. Maybe one of them will notice what just happened, and stop creeping at red lights themselves.

Erik <spark240@excite.com>
Floyd, VA USA - Saturday, December 01, 2007 at 12:19:40 (PST)
I am an undergraduate physics and math student at the University of Cincinnati, and this past quarter we have been pounding away at everything that is periodic--from the simple harmonic motion of a mass on a spring, to the behavior of RLC circuits, and ultimately, the physics of waves.

To my surprise and immense delight, as I sat down tonight to work on this week's problem set, I opened my book, Vibrations and Waves, turned to the end of chapter seven, which is titled "Progressive Waves," and read the first problem that was assigned, 7-22, which goes as follows:

"You are given the problem of analyzing the dynamics of a line of cars moving on a one-lane highway. One approach to this problem is to assume that the line of cars behaves like a group of coupled oscillators. How would you set this problem up in a tractable way? Make lots of assumptions."

Thanks to this website, my response has just become much more interesting--I am even going to suggest to my professor that he include it in the syllabus!

Also, for the curious, this book written by A.P. French, and was first published in 1966 by the Massachusetts Institute of Technology.

Aaron Eiben <hawk22@gmail.com>
Cincinnati, OH USA - Monday, November 26, 2007 at 19:48:55 (PST)
One factor I believe you have ignored is that of grain-size. Traffic can indeed be modelled by fluid dynamics, however in order to accurately model actual traffic flow you must also account for the varying sizes of the individual vehicles. The understand the significance of this, just imagine this: You are pumping ready-mixed cement into the basement of a new house. If there are any over-large stones in the mix, then the flow is constricted and a "cement jam" ensues. Applied to a real-world traffic problem, if there is a large bus broken down in the middle of a lane, only smaller vehicles will be able to get past it. Having driven cars and motorcycles thru many cities around the world, it always surprises me how little this principle is understood. In the city I live, the urban planners seem to think that buses are a better idea than cars. They think that getting ten people out of their cars and into a bus is a good idea. They don't seem to realize that a bus has to stop very frequently. This results in a reverse wave travelling backward through a crowded city, causing traffic jams miles away from the actual location of the bus. This is why I prefer to ride a motorcycle thru congested traffic - so why don't planners ever consider this????
Patrick Magee <patrick_magee@hotmail.com>
San Francisco, CA USA - Wednesday, November 07, 2007 at 00:20:45 (PST)
"Merge now, or get out of my way!" I could almost hear the driver shout. The situation was this: we were heading into Bristol, England along the M32 when we started to see signs saying "lanes merging, keep left". So we dutifully merged, as did most drivers, into the left lane. This meant the left lane started moving slower and slower, and the right lane became virtually free of traffic, except for a few ignorant drivers who didn't see the signs, or worse, the "cheats" who chose to ignore them. The left lane got slower and slower, and almost came to a standstill, while drivers on the right whizzed past to the front of the merge. Frustrated by this, the driver in front of us waited for his moment, signalled right and cut into the right hand lane. We thought he would simply speed up and head to the front of the merge so we got ready to occupy his space, but instead he simply drove at the same speed as us, stopping when we stopped. Seeing his intention, we left the space he had previously occupied empty so he could move back into it when we reached the merge. "Why not?" we thought, he is clearly acting for the common good, and it might actually work.

A few moments later of course, a few drivers started to jam up behind him, parping horns, waving hands from side to side, asif to say "what on earth are you thinking of?" Then a few moments later, to our amazement and glee, the traffic in our lane started moving much faster. Clearly we had unlocked the merge for an instant, freeing up the traffic ahead. Before long, we were through the merge, we gave eachother a visual "hi-five" and went on our way. What came after us was anyone's guess, certainly we had helped to free up the traffic ahead, but whether that would carry on was anyone's guess.

My guess is that the right hand lane filled up a little more, the cheat drivers saw there was little to be gained from being in the right lane any more and merged, the ignorant ones slowed down enough to notice the signs. Once again the right hand lane would have become emptier and the cycle may have started all over again. But the point is, being in the correct lane IS important, and often there is nothing to be gained from queue jumping, collectively and perhaps even individually, as the lane you are jumping into may be the cause of the delay in the first place, and certainly can't guarantee a quicker route through the merge ahead.

Henry Bainbridge <henry@dubstudio.co.uk>
Bristol, UK - Wednesday, September 19, 2007 at 05:37:50 (PDT)
I'm an old math and science teacher. I figured this stuff out over a few months when I was about 26. Now 16 years later, I find that I've persuaded about 15 people to drive this way--a frequency of about 1/yr. The method of building lead space and trying to adopt a very uniform speed works well in cities and (normally) on the autobahn. It works in Korea and Japan as well. It does not work in countries in which drivers are seemingly suicidal such as France, Italy, Greece and Mexico. Where it works, it solves all sorts of problems, but it cannot, ultimately, resolve the issue of super-aggressive drivers. Germany has perhaps 20-30% super-aggressive drivers (normally these folks are found in high-performance gas guzzling cars). This results in their wonderful highway system being plagued by "Der Stau". As in a Wagner opera, Der Stau is a traffic jam of truly epic proportions. Imagine a 20km line of closely packed traffic with 20km until the next exit. In one stau near Aschaffenburg I becamse so overheated, dehydrated and helpless that I was on the verge of a medical emergency. Four hours after the authobahn stopped there it began to move again. I've suggested solutions to the Germans, but they will not listen. I'll try here as well. 1) Emergency exits, 2) Gated stau relief exits, 3) gated autobahn entrances, 4) electronic signs to reroute traffic prior to entering the autobahn, 5) strictly enforced speed control and exit advisories ahead of staus, and 6) teach your population to increase their following distances to that needed at their target speed.

Just two days ago I broke a traffic jam on the B13 in Ansbach by letting an about 100m gap build ahead of me and then trying to keep my speed constant. I was moving at 20km/h for about 2 minutes and up to 50 km/h in another 2 minutes. I observed MANY cars turn left across my path, lots of traffic was also able to merge into my road. In short I had created usable anti-traffic. For this service I was flashed perhaps 100 times by the gentleman in the BMW behind me. Fortunately blowing the horn within city limits is tantamount to calling Der Polizei--so German city traffic is quietly seething :-)

Scott <4dr3sp0ns3@googlemail.com@whatit.com@deletethisandwhatit.com>
N?nberg, Bayern Deutschland - Tuesday, September 18, 2007 at 16:08:14 (PDT)
You are obviously a very thoughtful person and want to make things better for everyone, so I hope this post helps.

First, we have to mention a make clear a few properties of roadways. Roadways are like a high-density fluid. For example, imagine a funnel. If the hole at the bottom of a funnel is 1 cm, and one pours water into the funnel from an opening that is 2cm, then a "traffic jam" will form in the funnel due to the capacity restriction.

Second, it helps to keep in mind that roadways are inherently unstable for two reasons.

1) They have low throughput of only about 2250 cars per hour per lane of travel. This is because people almost follow the "two second rule" when driving at speed. Actually, each person maintains a "comfort zone" that consist of roughly 1.5 seconds plus about two car lengths.

2) Because of this minimum distance between cars, as the rate of travel slows, the throughput of the system drops, too, as described here:


Think about that for a moment. Even with a freeway with 4 lanes of peak direction traffic, only 9,000 people can get to work during the peak hour of travel.

So, what happens when person number 9001 comes down the on-ramp? Everyone is already traveling down the freeway, maintaining a comfortable 1.5 second comfort zone, and there are no extra gaps for a new car to fit. The inevitable result is that someone will slow down to accommodate the merge and regain that 1.5 second comfort zone. But since the highway is already at capacity, everyone behind the merge also experiences a 1.5 second delay. But it doesn't stop there. Since the throughput of the highway decreases as speed decreases, there is also a corresponding loss of throughput for the lane, as well. In fact, assuming travel of 60 miles per hour prior to the merge, and assuming a speed decrease of just 1.5 miles per hour for just one second, the throughput for that lane of traffic would have dropped by 34 cars/hour during the merge, thus creating a rippling effect all the way down the lane to some point where the bandwidth of the roadway is no longer saturated.

Of course, the effect of this one merge is not much. But multiple that by 20 cars per minute coming from 10 on-ramps?
Well, we can start with a 300 second (5 minute) delay just to accommodate the space taken by these cars (at 1.5 seconds separation per car) and the throughput for the lane after the merge drops right to 0.

So there's really not much one can do to ultimately unwind the traffic jam except to avoid driving during peak periods. And even though people want to blame others for the traffic jam, it's a simple matter of physics -- too much water poured into the funnel all at about the same time.

With all that said, your suggestion to create an "anti-wave" is helpful. In addition to reducing stress and saving energy caused by unnecessary brake/acceleration cycles, you may increase the throughput of the roadway by spending less time driving at the speeds with the least throughput.

I do have a suggestion for to consider regarding merging for lane reductions. Allowing extra space for all the aggressive drivers to merge in front of you at the merge point creates a moral hazard by rewarding the anti-social behavior. The net result is a net increase in travel time for yourself and all the rule-abiding people in your lane of traffic, while the anti-social behavior is rewarded with a net decrease in travel time. An alternate approach is to drive in the lane that is about to merge until it ends, while driving at the same speed as the cars in the other lane. Once your lane ends, you can merge in a saw-tooth pattern when a space becomes available. You'll find that people will be happy to let you in, since they didn't have to sit and wait for a dozen or more sociopaths to merge in front of them. This reduction of tension also contributes to people allowing a comfort zone of space to develop between their car and the one in front, which contributes to the average speed (and throughput) by eliminating some unnecessary stop-and-go driving. Further, this method makes the most efficient use of the roadway.

I want to end by amplifying the suggestion to minimize the amount of driving done during peak periods. If people can give a lift to a friend, coworker, or neighbor, that would double the throughput of the roadway. Better still is to sit back and relax on a bus or train while someone else takes you to work. Not only does that the environment, the economy, and national security by reducing dependency on foreign oil, it gives you a chance to read a book or magazine during time that would otherwise be wasted driving. Finally, the best suggestion is to work from home if you can. This reduces energy consumption the most, reduces stress from commuting, lowers costs all around.

Thanks again for so thoughtfully considering this issue.

Almost Got It <almost@gotit.com>
Chicago, IL USA - Friday, September 07, 2007 at 01:13:11 (PDT)
Great article, I was gripped all the way through! I've practised your -ve traffic jamming for several years now, although never really thought about it. Alas I can't do it all the time as I get a bit worried about the guy behind me getting out at the next lights to ask 'what's up?'
Needless to say I think it's a good idea if more people do this, saving tyres, brakes, engines, road-wear, emmisions and (hopefully) stress levels.
Actually I've never had anyone get (visibly) mad with me, I hope that's because they can see I'm approaching the car in front as it's starting to move off, or the lights (sometimes :-P) as they're changing to green. During my commute to/from work I combine this with letting in a driver or two from side roads and bikers overtake (because they always do) safely.

Have you tried getting your car and a car coming from the opposite direction through a tiny gap as quickly as possible?
I will slow if they're nearer the obstruction (say a parked car on a narrow street) than me and flash my lights several times to get them through, or speed up noticeably and agressively if I'm definitely closer to the obstruction - they'll always see me speeding up and will only have to slow a little before I'm through and waving 'thanks' like a lunatic!

Justin <justinclark61@hotmail.com*&^%$>
London, UK - Wednesday, August 22, 2007 at 12:09:56 (PDT)
Great article on traffic! I came up with most of those hypotheses on my own from my experiences driving up and down California and experiencing many of those mysterious phantom traffic jams (no accident - no apparent cause). You did a great job explaining how this can happen based on driving behavior.

In my opinion, drivers in heavy traffic areas are far too jaded by constant traffic jams and accidents for the looky-loo's to be the problem. And yet, the putative notion is that rubber-necking causes ALL traffic jams to persist. I think most people never really think about it. I don't deny that rubber-necking is a factor, but I think its blown way out of proportion.

Another phenomenon I find strange is something you could call the "red light shuffle". Here's how it works:

1. When cars stop at a red light they leave a certain amount of space in front of them and behind the car in front of them. For some reason the guy in front is almost always about 8 feet from the line.

2. After 20 seconds or so, the people in front start creeping forward and making the spaces they've left in front of them smaller and smaller as if they've suddenly become unhappy with the amount of space the left originaly.

3. This makes the spaces for the cars behind them bigger and bigger and then all the cars behind them start shuffling forward as the space in front of them gets larger and larger.

4. If you are near the back of the line of cars and you don't move, you end up with a car-length or two of empty space in front of you. You may feel uncomfortable about this and creep up closer, thus perpetuating the shuffle.

5. Everyone puts more wear and tear on their brakes from all the shuffling.

I also think it may be possible for highway traffic jams to creep forward, but I don't know how this would work. It just seems to me that I've been through a bunch of jams that only cleared up a significant distance after the site of the accident that caused it.

San Diego, Ca USA - Thursday, June 21, 2007 at 13:58:49 (PDT)
Excellent information.

Instead of a wall of state troopers, how about "Pace Cars"... :)

TN USA - Wednesday, June 20, 2007 at 10:21:13 (PDT)
As reassurance in the correctsness of your basic "Truckers Figured It Out" trope: I drove big trucks for several years, and the tenants of Big Spaces, Let Others Merge, and Go Slower To Go Faster aer all nearly instinctive in that World. Most of us would call it "being polite" and leave it at that, since, lumped up, that is essentially what it is.

The Left Laners are jerks with a justification and probably all own Corvettes and Hair Plugs.

USA - Monday, May 28, 2007 at 22:49:09 (PDT)
Read some of your ingenious ideas. You might want to throw this into the mix and pass the word along to help reduce the "pressure waves". Thanks...

News Release

Dateline: April 23, 2007... Portland, OR
Web Address: http://www.leftlanedrivers.org

Enough with slow drivers in the left lane! ?As traffic gets increasingly congested, it?s time for citizens to reclaim the left lane,? says J.A. Tosti, spokesman for Left Lane Drivers of America, a grassroots effort to get slower traffic to move right. ?More and more these days, you find slow drivers in the left lane, causing no end of headache and frustration to those of us who have places to go and people to see. Some of these offenders are timid and tentative, some are completely oblivious to what?s going on around them, and some are self-appointed ?hall monitors? regulating what they alone have determined to be proper driving speeds. Whatever be the case, it?s time for us to trumpet the message, ?If you?re not a Left Lane Driver, get out of the left lane!??

In order to actually help slower drivers move right, Left Lane Drivers of America offers copyrighted windshield decals which boldy and prominently display their unified sentiment in the offending driver?s rearview mirror. The decal, which reads ?MOVE OVER? also has a large arrow showing them where to go. The words and arrow display backwards on the windshield so that they read properly when seen in the mirror (go to www.leftlanedrivers.org to see picture). According to Tosti, ?Although the message minces no words, the idea here is not to be rude or pushy but to offer slow drivers a gentle prod, reminding them of the need to either pick up the pace or make room for those who choose to drive a bit faster.?

In fact, slow drivers do need to move over. In many states, the left lane is supposed to be the passing lane and slower drivers can be cited for obstructing traffic. Those who stake out permanent positions for themselves in the left lane tend to provoke those wanting to drive faster, often giving them no other choice but the dangerous strategy of passing on the right in order to get ahead. Slow drivers can easily become slow moving safety hazards.

Bottom Line: Moving over is a matter of courtesy. It is a matter of safety. It is a matter of doing one's part to help traffic flow smoothly. And it is the law in many states: ?Stay to the right except to pass?. Left Lane Drivers of America is doing something positive to help improve traffic flow on today?s overcrowded, pressure-packed freeways. Their ?Move Over? message has the potential of helping reduce instances of road rage, hazardous driving and untimely, often deadly accidents.

J A Tosti <jat@teleport.com>
Camas, WA USA - Monday, April 23, 2007 at 20:46:57 (PDT)
Awesome site! Really interesting to read about. (:
Honolulu, HI - Sunday, April 08, 2007 at 14:45:21 (PDT)
Hello. I have some very naive questions:

1) wouldn't the rolling barrier idea have the supposed effect of everyone braking and creating another jam?

2) If all of this is just science, then why don't we have scientists figure out how to help traffic instead of building more infrastructure. If it requires certain behaviors on the part of drivers at large, why don't they just tell people that on the news and on commercials, etc. I've never seen any information anywhere about how I should drive on the highway to prevent jams. According to you, there is a solution, but people just need to do it. But nobody knows what the solution is, because most people don't go researching all this stuff on the internet. So why don't big cities go on a campaign to just get the information out to everyone?

3) I'm sure the answer to this is very obvious, but I'm curious: why wouldn't raising the speed limit help traffic? If everyone got on and off the highway faster, wouldn't that do something to clear it up?

4) Since you're from Seattle, I have another question -- the backup on I-5 Northbound at the Mercer exit --- isn't this all because of the traffic lights once you get off the exit? I know that if I turn right at the first light, then there's another light. And I've noticed that there's often much less traffic going crossways at that second light. This seems to just back everything up on the highway. Why don't they just put traffic lights with sensors at places like this? So that the light is only green when it needs to be? Wouldn't solutions like that be cheaper than exansions?

richard pellegrin <pellegrin42@yahoo.com>
seattle, wa USA - Sunday, April 01, 2007 at 21:47:34 (PDT)
Hey Mr. Bill Beaty,
Your site is so cool. thanks very much for your insights into this traffic thing. Experiments, analysis, animations and a good spirit of finding solutions for ALL OF US ! Whoa, behaviour on the roads is so bad, largely through ignorance I hope (and not malicious intent ..) and so the light you are throwing on the subject is potentially very useful. Only "potential", since it is up to us drivers to adopt some higher principles of action on the road, beyond ME FIRST.

I wish you fun and success in your explorations.


Carlos Bagnales
Toronto, CANADA - Saturday, March 24, 2007 at 20:54:44 (PDT)
It was very noticeable to me while driving in the Seattle area last year that people there tended to drive at a steadier pace than drivers here in South Florida. For years I'd tried slowing down traffic to ease the wave problem. It only seems to work to a small extent when there is only one person doing it. Perhaps many more people in the Seattle area know about this idea and try to implement it themselves. I've never come across any such conversations here but will begin mentioning it from now on to see if it helps on I-95.
USA - Wednesday, February 28, 2007 at 11:01:41 (PST)
There doesn't seem to be much talk about the "safe space" factor in your explanations. Maybe I missed it, and sorry if I did. Here's what I'm talking about. For a given speed, drivers have a "safe space" that they will try to maintain between them and the next car. At high speeds, this space is relatively large. At low speeds, this space can be as small as a few feet. Anyway, the point is, by leaving space for people to merge into, you aren't necessarily gaining anything, because you'll have to slow down to maintain your safe space when they merge in front of you. If it's 100', when someone merges in front of you, you'll have to slow down 50' (relatively speaking). When you slow down, then the person behind you has to slow down, and on and on--and we have the beginnings of a jam.

To me, the key to efficient traffic flow is attaining highest speed with the littlest amount of space between cars. However, if you make the space too small (or the speed too high), then the slightest disruption (as you have mentioned) will cause a jam. Raise speed limits and drive safer cars. That's my advice. Maybe those gigantic SUV's going 95 MPH aren't so bad after all...

In my opinion, part of the reason why traffic is so hard to figure out is that every driver has a different "safety zone" vs. speed program in their head. When going 65 MPH, granny requires 300' of space, while you may only require 100'. If someone merges in front of granny, she's going to slow down to what she considers a safe space vs. speed ratio, and so will you.

As for weaving in and out of traffic--I've often wondered if I could sneak through the holes in traffic without affecting the system at all. There's all this space--even in congested traffic. Is it possible to use that open space without adversely affecting the flow? Is it possible that I'm helping out the situation by using space that no one else will use? On a 4 lane highway, is there a hidden "5th lane"? A 5th dimension--the empty space between all the cars?

Just remember, wherever you go, there you are.

cheers, andy

Andy <andrewRneumann a t sign gmail com>
Dem. Rep. of Congo - Monday, February 26, 2007 at 10:58:08 (PST)
I love this page. Generating anti-traffic can make the experience of being in a traffic jam almost bearable.

Your car is acting as a low-pass filter for traffic change (slow down) and because there's inevitably some lag in a driver's moving from stop to start, by driving at the average speed (a bit below) you are removing an amount of delay equivalent to that lag times the number of cars' space you're introducing to the bottleneck (I think.)

Another way to look at it: by slowing down before a jam, you are propagating information as to the u coming jam more quickly to following drivers, allowing them to adjust their speed more efficiently than stop/start, and hence allowing them to avoid the jam.

On the subject of information propagating upstream: in Qingdao city Shandong province in China I noticed they have large LED signs on each traffic light visible for 100s of meters, giving the remaining time to the next light change. I'm not certain *why* they do this, but I think it could contribute to anti-traffic.

Finally, thanks for giving meaning to traffic jams!

Colin <colinZAP a t sign POWchinixDELETE com>
Sydney, Oz - Thursday, February 01, 2007 at 06:05:57 (PST)
I'm fortunate that I don't have a long commute, but I do take long trips several times a year. This explains something I've noticed in the past few years: I haven't encountered any significant construction merge-lane stop-and-go congestion, and I think it's because I got into the habit of getting into the thru-lane as soon as I saw the lane-closure signs, and then slowing down to the work-zone speed limit when those signs appeared. Since most other drivers were still going faster, this had the effect of creating the traffic hole you describe, the cars in the merge lane could merge, and by the time I got to the lane closure any prior congestion must have evaporated.

My philosphy is, you don't fight the traffic, you learn to flow with it. If you're in the interchange lane and someone's approaching on the on-ramp, you act like a gear tooth and let them in ahead of you if they're ahead of you. (I do get pissed when some jerk passes me and immediately exits, though.)

Peter Kappesser
Syracuse, NY USA - Sunday, December 03, 2006 at 19:54:24 (PST)
One very strong argument that would encourage folks to use your suggested techniques is fuel economy.

Travelling at 20mph for 20 minutes is far more efficient than travelling at 40mph for 10 minutes and then idling at 0mph for 10 minutes. Every time you use the brakes, k netic energy is being converted into heat. So the less you use the brakes, the better fuel economy.

Also, coasting in gear is always more efficent than coasting out of gear with the engine idling. When the car coasts in gear, no fuel needs to be added to the combustion chamber. Once you take the car out of gear, fuel has to be added to prevent the motor from stalling. Note this only applies to manual transmissions.

Slow and steady saves you money and potentially gets every to their destination quicker.

Dan Charlton
Seattle, WA USA - Thursday, November 30, 2006 at 14:01:28 (PST)
I have a pretty crappy commute to and from work everyday. Although I have not thought as much about this problem as you have, I know that the "gap" that you crated to erase waves actually works. Infact, if you drive in traffic where there are a lot of truck traffic, you are much better off following them because truckers naturally follow the "gap" rule so that the dont run over other cars if they do need to brake hard. When following trucks, I hit my brake a LOT less often and am generally end up being much faster than the idiots who keep merging in and out just to claim any small gaps.
Dub Specialist <mc68302 (at) yahoo (dot) com>
Dirty Jersey, NJ USA - Monday, November 27, 2006 at 06:21:20 (PST)
I agree with most things written here. Though there's one major correction: When merging two lanes into one, if traffic maintains the same distance between cars, then it's straightforward to see that traffic must go half as fast than it was going before the merge.
[No, that only applies if two lanes running at half capacity must merge into one at full capacity. And in that case, the entire single lane which is downstream from the merge will contain close-packed cars. Yet in nearly all the merge-jams I've seen, the single downstream lane is totally empty. It's not overloaded. Once I've gone past the jam and entered the single lane, I can take off at the maximum speed. This happens because congested traffic moving at a crawl is a very low flow. Within the jam, the incoming lanes are flowing at *far* below 1/2 of full capacity. When combined at the merge zone, the two flows don't instantly cause a traffic jam to fill the single downstream lane. Their combined flow is just too low (and that's why the single downstream lane remains unjammed and empty.) But whenever the jam already exists, the congested cars will keep it alive because the merging of two solid-packed lanes is such a slow process. On the other hand, high congestion can create permanent jams which nobody can fix. If the two lanes feeding the merge zone are really running at greater than 1/2 capacity (like close-packed cars moving at 35MPH,) then this is a genuine overload which will trigger a massive backup, and individual drivers cannot "un-trigger" that kind of jam. -billb ]
We should do what we can to educe artificial waves that exist for no reason other than psychological reasons. However, when a road suddenly has half its capacity, that's a basic physics problem that you can't solve with psychology. If you take a water hose or an air tube, and constrict it in the middle, the stream through it is going to slow down simply because it has educed capacity. That's all there is to it.

Interiot <amasci com [at) paperlined [dot) org>
Chicago, IL USA - Monday, November 27, 2006 at 00:03:08 (PST)
Like many people have pointed out, I've been doing this also for many years.

Another thing I thought of, and which you may have mentioned in your too-long-for-me-to-read-the-whole-thing article, is that of accelarating quickly when the car in front accelarates.

The best way to illustrate this is like a train. Even if there are 100 cars all attached to one engine, when the engine moves, so does the last car.

This principle can equally be applied to traffic. Especially at red lights.

Imagine how many more cars could get through the green light if everyone that is behind a car would not wait several seconds before they increase their speed.

They should immediately begin moving and then, once through the intersection, slowly allow the car in front to create a larger gap.

Happy thinking.

Chris <barophobia a t sign gmail com>
Sierra Madre, CA USA - Sunday, November 26, 2006 at 18:55:07 (PST)
One of the CAUSES of traffic, is by people NOT driving with the flow of traffic, or driving too slow for their lane.

For instance, you have a car going 50mph in the far left lane, and a car going 60 in the middle lane, the car going 50mph will automatically cause a jam because people in the far left lane are going at or above the 65 speed limit. this causes the standing wave effect.

EVERYONE should YEILD to faster drivers, and if someone passes you on the RIGHT, you should CHANGE LANES. This will certainly limit traffic flow problems.

joshj <joshjx a t sign gmail com>
San Francisco, CA USA - Sunday, November 26, 2006 at 10:03:54 (PST)
I thought of this same theory just this last year since i started commuting an hour to work each way. I works best when cars next to you begin to mimic this because then cars are unable to pass and mess up your space causing it to not work. Glad someone write this out so that hopefully this idea spreads to more people on the road, specifically the people i commute in with.
Germantown, MD USA - Sunday, November 26, 2006 at 09:18:06 (PST)
During the Carter administration, when the 55 mph (double nickle) highway speeds were implemented, some troopers did the coordinated cross-the-highway driving. People were passing on the sides of the road, the backup was miles long. I think I prefer the single driver independently operating in one lane. This way there is less of a sense of hazard, and desperation. If they want to go faster they can, but they can also be orderly.

I'm just concerned now that I'll over-think my driving. I instinctively leave the space in front of me, but now I'll pause to think about it. I'm not sure that's a good good thing.

From a traffic calming perspective perhaps we need smart 'flow speed' signs every mile or so, showing the r commended speed to maintain to smooth out traffic flow. This would replace the fixed 55/60/65/70 mph signs we have now, and they could be updated by the minute.

Nick <nradonic at comcast net>
Derwood, MD USA - Sunday, November 26, 2006 at 08:56:18 (PST)
I am an Industrial Engineer and have worked on several Queuing Theory models in my time. This experiment seems to favor Queuing Theory dynamics. In fact I have even thought of this in the past. I just never thought, like you, to perform experiments on it. I really enjoy your thorough analysis and reporting on your experiments.

I believe you could mathematically describe the "traffic jam" as a Queuing Theory problem. The "traffic jam" could be seen as a queuing line with stoichastic interactions. The jam itself could be a server and the i coming traffic could be arriving at different interarrival times. I would love to explore this more. You can look up more about Queueing Theory from Wikipedia. http://en.wikipedia.org/wiki/Queueing_theory

larry <larrydag a t sign sbcglobal.et>
TX USA - Sunday, November 26, 2006 at 07:57:37 (PST)
That is just an awesome idea! You are encouraging other people to do this, get this theory out to the world!
chipdip <chipdip a t sign verizon.net>
Ronkonkoma, NY USA - Sunday, November 26, 2006 at 07:27:04 (PST)
LOL! I line in Winnipeg Canada, and your theories fall apart here. For some insane reason, drivers here do things different than where you live. They:

- do not close the space ahead to prevent cars changing lanes
- let signalling drivers change lanes ahead, or already beside you, then they speed up so they can get in behind

Honestly, I can change 3 lanes in 500 feet in rush hour traffice doing 50 km/hr just by signalling and waiting for the cars to move. Its a small city, in a cold place, but the rest of Canada is the same mostly.

Interesting stuff. I'm an IE. :-)

Dave C. <davec//at//shaw//remove//.ca//remove//>
Winnipeg, MB Canada - Sunday, November 26, 2006 at 07:23:49 (PST)
Very interesting analysis! I have often applied this logic during my commute to work. I try my best to go at an even speed, minimizing the taps on my brakes. Often a long open stretch of road opens up in front of me, but I resist the urge to close it up. If more people did this, wouldn't traffic improve?
David Rubenstein <dave.rubenstein a t sign verizon net>
Reston, VA USA - Saturday, November 25, 2006 at 18:12:20 (PST)
Many years ago I was skimming through my grandfather's stacks of Popular Mechanics and similar magazines from the 1940's and 50's.

I vividly recall an article from 1950 or so, about "The New 'Freeway' Systems" in the US. An engineer was asked about the traffic jams that were already b coming a part of the freeway experience, and he answered something like, "These systems were designed with the assumption of rational, consistent behaviour by drivers. But that's not what we're seeing. If people would just drive at steady speeds, and especially, leave enough room for other drivers to merge on and off, these systems would be much more efficient."

(It's always dangerous for engineers to assume rational -- engineer-like, in other words -- behaviour on the part of the, um, masses.)

I've been commuting for 20 years, and have observed all the same phenomena identified here in Traffic Waves. In the mornings I come down a long shallow hill on the freeway that gives me a view ahead of about two miles -- and it's very easy to see the tail-light wave patterns created by sudden braking, or by agressive drivers filling the spaces other drivers are trying to leave open ahead of them, and so on.

Too bad I couldn't convince the 100,000 or so people sharing the freeway with me each morning to read Traffic Waves. We'd all be much happier, calmer people if even just a fraction of us started driving as advocated here.

Brent Eades <beades a t sign ~almonte.~com>
Almonte, ON Canada - Saturday, November 25, 2006 at 03:19:48 (PST)
On the production of traffic jams from merges (or nowhere). On average, drivers assume a minimum comfortable headway of about 2 seconds in a traffic stream. However, at a merge, many drivers will accept a gap between two vehicles of about 3 seconds, creating two headways of about 1.5 seconds. This will not be tolerated as the cars move along and adjust to 2 second headways. Given enough of these merges in a medium short time, traffic can end at a standstill to cope. In a way drivers "shoot themselves in the foot".
Alf <arhoward34 a t sign yahoo com84/.,=111>
Boston, MA USA - Wednesday, November 15, 2006 at 06:37:10 (PST)
Its fun to read an article that I have been thinking about for a long time. Living in Washington DC, I see this time and time again. I have been doing the "space-buffer" in front of me for awhile now, and I can see the differences it makes. The only problem around here is that, the space in front of me will get eaten up by aggressive drivers who merge at the last minute. It is extremly difficult to keep that buffer when it occurs. Anyways, Great article.

Washington, DC USA - Monday, November 13, 2006 at 08:05:31 (PST)
What a great site! congratulations on all the effort, specially in hours and hours of experimentation (even if you were 'forced' to do it :P ).

Just for the record, I'm not sure if there's a fully developed theory about traffic waves specifically, but there is some theory about traffic dynamics anyway, and according to theory, perhaps (just perhaps) things should behave just as the way you have discovered (that's one of the greates things about science, anybody should be in possibilities of trying it)

I'm a master's student from my country, and I'm specializing in studying traffic phenomena, using cellular automata (CA). My theses was about the analysis of the probability of occurrence of vehicular accidents in some CA models for traffic flow. Anyway, I'm currently developing some software for the simulation of traffic flow, using the basis of a model called the Nagel and Schreckenberg model, and a generic derivative that I've done for it. When I make my degree exam, I'll try to make a webpage for it and let you know, ok?

congratulations again!


Javier Novoa C. <jstitch a t sign gmail com>
Mexico, Mx Mexico - Tuesday, November 07, 2006 at 15:45:04 (PST)
The main problem is people don't know how to drive. START BLOWING THE HORN at the onset of a traffic jam, everyone must do it, everyone should be deafened with the noise, then whomever is causing the jam will get moving. Put up buildboards at choke points, saying, "You are not supposed to be stuck in traffic at theis point. Get moving or start blowing the horn".
herb stone <stoneh200 a t sign yahoo com>
reading, pa USA - Tuesday, November 07, 2006 at 08:34:17 (PST)
I found this site about five years ago and i have been systematicly using its suggestions on motorways, and local roads and i have found that as i have started maintinaing slow approaches to traffic congestion and obsticals i have found that other drivers have learned the behaviour by example (i am not taking credit for teaching everybody how its done) but if you do it in heavey traffic every day then the guy behind you starts to realize its a good idea and quits hasseling your bumper, relaxes and backs off and boom you have a mirror full of slow moving traffic and a windscreen full of stop start stressed out bumbleheads, it relaxes me and i can take in the scenery and relax, while my car gets a better milage on fule and my brakes and tyres last longer. It works!

A final point is that if you are in multiple lane's if traffic then buddy up with a car in an another lane, they will begin to see the wisdom and you can facilitate a rolling road block at a sensible and constent speed smoothing out the traffic flow and negating pressure waves. I love it and do it all the time - thinking about the car's behind and not the cars in front.

As a final point if this was taught in driving schools then there would be no problems with heavy traffic - why rely on ACC when the human brain when taught correctly is far more responsive and powerful?

good job for making sense of heavy traffic - maybe you could come and teach the local government that traffic lights cause more problems than they solve!

Douglas <stickygoblin a t sign hotmail com>
Hereford, UK - Sunday, October 29, 2006 at 03:09:58 (PST)
When a vehicle is "merging" onto a freeway off of a ramp. Who has the right of way?? PLease respond, I say, already flowing traffic in their own lane should not merge to somebody coming off of a ramp??
CindieLee <tubbie a t sign telus net>
Edmonton, ab canada - Monday, October 23, 2006 at 14:30:46 (PDT)
I cycle to work and frequently pass clumps of held up traffic. I am frequently amazed at the triviality of the event which has caused the clumping.

Thanks for a very lucid explanation of the dynamics of these situations; I'll be r commending it to anyone interested.
London, UK - Thursday, October 12, 2006 at 23:52:46 (PDT)

Hills, overpasses and turns can also trigger traffic waves. Cars (drivers) have a tendency to slow down going up hill (or up an overpass)l, and speed up going downhill. The result is compression of cars on the up hill and a rarefaction downhill. Cruise control can cancel most of an individual's variation.

Turns can also trigger traffic waves. Inside turns tend to be more compressed than outside turns (differences in radius). Drivers on "autopilot" - those who drive reactively relative to toher cars - will try to match speed with the adjacent lane.

BTW: In Seattle the east end of 520 past the bridge provides an example of curve compression and expansion.

Carlos Salinas <andreeasalinas a t sign mac com>
Santa Clara, CA USA - Sunday, September 17, 2006 at 00:50:59 (PDT)
I would like to say this is such a brilliant technique. The main problem is simply the arrogance, haste and ignorance of these drivers who think of themselves before others.
A lot of the cause is "No-one let's me out, I'm not letting anyone else out" and that is the only thing which is stopping this solution.

Brilliant advice. More people should know this site. Do whatever you can to advertise. :]

Carl Papworth (13) <JoeP021 a t sign aol com>
Watford, n/a England - Thursday, September 14, 2006 at 08:30:47 (PDT)
I've been doing exactly as you describe - pacing into an u coming jam - for years on my drive up RTE3 from Burlington to Nashua. It works at least in the sense of establishing 'laminar flow' and decreasing or eliminating jams. I learned it from watching truckers. Second point: when traffic is moderately heavy and beginning to 'wave' but still allowing cars behind to easily pass I try to drive about 1 mph slower than the 'average' speed. This makes virtually everyone either follow me or pass me without causing jams. I can do my commute end-to-end on cruise control and never touch the brakes while the average commuter is speeding and braking the whole way. The fastest guy is at the mercy of everyone, the slowest rules the road. net commute time difference end-to-end is about a minute - see ya at the light at the ramp. Third point: your zipper theory is spot on. Here in Mass the genius professional traffic engineers use the 'crossover' merge cloverleaf, that is the traffic getting on has to merge through the traffic getting off (and vice versa). Talk about jams. The tendency is for drivers to follow too close and to attempt to force the merge too early (probably out of anxiety that they will miss the crossover). This ALWAYS jams up traffic in both directions. If you watch carefully though there are periods when drivers who do not follow closely meeting drivers who do not cut in too soon and the speed up is dramatic. It really happens, too bad it's basically random. education needed ....
GregC <gregon77_S_P_A_M a t sign hotmail com>
Burlington, MA USA - Tuesday, September 12, 2006 at 14:12:24 (PDT)
Great site! What a grand idea! And for the record, for those people who don't think it will work, etc., they obviously don't understand the idea fully (proven practice, not theory!), and are probably impatient drivers, and therefore jam causers themselves.
Moscow, ID USA - Wednesday, May 03, 2006 at 16:33:28 (PDT)
This is an incredibly interesting theory. I can hardly wait for my next commute, to give it a try. I don't think it will work, but it sounds worth a shot.

A fairly frequent objection I noticed is that: "You're just pushing the wave farther back." An expirement comes to mind, where you do your well practiced anti-jamming, and someone else monitors traffic behind you - way behind you -to see whether the overall situation is actually improving or ... doing the other thing.
[This article is really about experiments, not theory. I commute every day and often can unmistakably see the effects of my changes. Pushing the wave away from a merge zone is the whole point. Pushing the wave back will usually make the merge zone flow faster ...sometimes stunningly much faster. On my commutes there are a couple of places where my large empty space causes a mile-long backup to totally unplug and start flowing. When it occurs, it always strikes me as unbelievable. But the effect is unmistakable so I have no choice but to accept what my eyes are telling me. Yet as you say, what I still don't know is how long this "unplugging" will last. And I haven't kept records to see how often my efforts just redistribute the clots without increasing the flow. Fortunately the unplugging happens IN FRONT OF ME, so I get immediate direct benefit. Even if the jam gets triggered again later, this won't happen until I've zoomed ahead through the fast-flowing merge zone. -billb]
One thing you failed to mention, or at least mention strenuously enough, is the mechanical aspects of driving in a more sensible manner. Gun 'n' slam is hard on cars, while sensible driving is easy. Have you noticed any detectable difference in your fuel or mechanical bills since you implemented your new driving style?

Jim <jb17703kresge@wavehjsldahcable.com>
USA - Monday, April 17, 2006 at 14:49:31 (PDT)
I have been driving like this for years, and use the same technique with stop lights. I am completely off the gas if there is a red light blocks ahead of me. Actually, I find it actually a FASTER way to get from point A to point B, at night, when traffic is light. Routinely, a frustrated driver will pass me, then speed ahead to stop at the red light. As I approach the light turns green and I pass him as he is at a dead stop.

In stop-and-go driving in LA freeway traffic, I rarely touch the brakes.

At 180,000 mi, the brake pads on my mini truck have never been replaced and still look fine. I am now convinced that brake pads can easily last the life of a vehicle.


Phil Hobie <hobiephil@excite.com>
Los Angeles, CA USA - Saturday, April 15, 2006 at 22:45:59 (PDT)
Excellent observations and speculations. I do not claim to be an expert in this field, but your ideas seem to make sense, and in my experience, ideas that make sense after you fully understand them usually are correct. I am impressed with your experiments and I hope to conduct some of my own. Your "theory" is "right"! ;)
Alan Hensley <misternethead gmail com>
Houston, TX USA - Saturday, April 15, 2006 at 19:18:11 (PDT)
For almost two years I commuted from Edmond, OK to Norman, OK on a daily basis. I can tell you that these techniques have almost always worked for me during rush hour traffic. I learned about "advanced driving" from my father who was a truck driver for many years. One of the things he taught me you do not mention. Did you know you can influence the speed of the driver in the lane next to you? Many times if a driver is distracted or is "in the zone" they will stay just in front of you without realizing it. It works best if you are on their right side. This is also known as "Why the hell can't I get out of their blindspot?" By using this idea you can succesfully create a two car rolling barrier. Also you can just get next to a semi and pace him. Even better is to pace a semi on your left with the 'zoned' driver on you right creating a three car barrier. I've only done that once, but it was really cool.
David H <avid.dp@gmail.com>
Edmond, ok USA - Monday, April 10, 2006 at 14:05:48 (PDT)
I noticed this fluid-like behaviour in the 1970s as Motorway traffic started to become (occasionally!) congested. I also noticed a "Venturi effect" where traffic speeds up as the 'pressure' drops after a blockage. The result is a much lower traffic density for a reasonable distance, and higher speeds - sometimes higher than 'normal'. Whilst it could be explained as a psychological thing (people are impatient to catch up, relieved at the unblocking, etc)it looks for all the world like a venturi

Dr. peter lennox <p.lennox[at]derby.ac.uk>
USA - Tuesday, March 28, 2006 at 03:28:26 (PST)

In the UK, these obeservations are basic advanced driving skills. Nothing new really. Then again in America you don't wear seatbelts, you hardly have any roundabouts and you use mobile phones while you drive. Finally, hardly any of you know how to drive a manual transmission (stick shift you call it).

Basically, you Americans don't drive, you just cruise in your extra-large vehicles along your extra-large "highways". Most of you do not have the skills to negotiate hazards effectively because you "have it too easy".

Although there are some terrible drivers in the UK as in any country, most of them are forced into driving better than you lot in the USA.

Just my opinions. Sorry if you don't like it! ;)

London, England - Wednesday, March 08, 2006 at 10:04:26 (PST)
thats just a good example of INERTIA, the same thing happens when the red light turns green, being back in line will you
make it through before the next red?

chris <@@Bert-chris@worldnet.att.net>
Mt Vernon, IN USA - Friday, February 10, 2006 at 18:26:44 (PST)
What a great site, a scientific explanation for what i've been trying out for years. I drive the A428 from Cambridge to Bedford most days at rush hour, and yes leaving a large gap to the car in front does mean me and everyone behind goes at the average speed, we don't stop/start and so are less stressed and SAVE FUEL!

I've tried it on three lane motorways as well, it would work really well if most other drivers would behave and not keep jumping into the gap in front.

I watched a BMW on the M42 the other week, he was choping and changing at every opertunity. Me, I just stayed in the inside lane (or Lane 1 as the poilce refer to it) and NOT THE SLOW LANE as most idiot drivers in the UK call it. Anyway, he and I made exactly the same progress, we entered at the same time, and got to the M6 at the same time, a journey of about 20miles or so, but I bet he used more fuel than me, taking into account relative mpg of our cars.
Cambridge, Cambridgeshire UK - Tuesday, February 07, 2006 at 11:06:06 (PST)


I agree with everything on this site. I've noticed an increasing trend lately in the UK of outside-lane-blocking by vigilante lorry-drivers to prevent "queue jumping". This depresses me as this results in wastage of road space. Some brief thoughts on the optimum point at which to start "merge-in-turn":

If we assume it takes say, 10 seconds to merge into the inside lane and the inside lane is travelling at approx 20mph (9 metres / second), the optimum point to start merging is therefore only about 90m from the lane cut-off.

However people tend to queue single-file a mile or more from the roadworks, which is obviously excessive.

Robert Tuck <robt_a_majormajor_O_me_O_uk>
Wokingham, UK - Tuesday, January 17, 2006 at 13:56:18 (PST)
Thank you for finaly proving that this works. I have been doing the slow steady driving after school when all my classmates are racing to eachothers bumpers and i continue to slowly move and use as little brake as possible. I have often wondered if this is the most efficient way to drive or if the other way was better and you proved to me that I am doing the best thing. Thanks...now if other drivers would realize this!
Huntingdon, PA USA - Wednesday, December 21, 2005 at 15:23:41 (PST)
For the record, my own experiments with driving substantiate the intuitions captured on this web site. I think an appreciation of William Beaty?s observation rests on the ability to be able to discern the difference between simple, mechanical, closed systems, and complex, organic, open systems. Simple systems can be known purely from a knowledge of their parts, additively, while complex systems manifest synergistic properties, in which ?the whole is seen to be greater than the mere sum of its parts?. Simple systems change at the margin, gradually and incrementally. Complex system may well change discontinuously. Traffic flows can be usefully thought of in both ways, depending on one?s purpose. Many of the skeptical comments on this web site by traffic engineers are driven by a world view that is restricted to a mechanical understanding of systems. Specifically, the idea that ?capacity? is some numeric fixity that can be computed for any particular highway configuration, and that remains unchanged irrespective of individual driving behavior, is a mechanistic view that is not borne out by empirical evidence.

In the years that I have been driving in Southern California, I have conducted some experiments into the effects of alternative driving behavior on traffic flow, average speeds and fuel economy. In 1992, when I moved to Los Angeles and became interested in understanding systems behavior from within an environmentalist perspective, I began to maintain a log of fuel consumption, so that I could attempt to establish, for my own satisfaction, whether and how driving behavior might affect fuel economy. My purpose, in initiating these experiments, was three-fold?one, to maximize my fuel economy, two, to make sure that I was maintaining my car as close to a state that would give me the highest fuel economy, and three, to make sure that system behavior was captured in my driving habits. (In actual fact, and in retrospect, a fourth benefit accrued to me as well, in that I was able to minimize the psychological stress of driving in frequently congested traffic by changing my understanding of ?normal? behavior?in which traffic jams are not abnormal aberrations, but rather signals of system states, and cues for us to either act on or ignore, depending upon our state of enlightenment.)

Here is a summary of the three rules I?ve come up with to control my own behavior from within a systems planning perspective. (Actually, they can be reduced to two, with the third manifesting itself merely as a corollary of the first. But it is still useful as a mnemonic device.)

1. Drive as close to the average speed of traffic flows for your current trip as possible. Alternatively put, minimize acceleration and deceleration to the maximum extent possible, as these are the driving events that most affect fuel economy.

2. Always maintain the 55 mph speed limit. This is as close to optimal for fuel economy as you can get. From a standstill, fuel economy improves with increasing speed until about the 55 mph threshold, and then begins to drop increasingly as you accelerate beyond that speed.

3. Always maintain a speed-proportional spacing, sufficient so that another car can merge into your lane in front of you without your having to step on your brakes. Not only does this reinforce the first law, by minimizing braking and acceleration, but it also allows cars to maintain flow speed while changing lanes.

Besides my concern with the environmentally optimal driving behavior, intended to maximize fuel economy, I was also driven by my realization that my impulse, to close the gap between myself and the car ahead, so that others would not be able to get between me and my destination, was counterintuitive, as, for every car that got ?in front of me?, a few cars up, some other car was getting out of in front of me. As a driver in traffic, my sensory inputs were limited by my actual field of vision, and so always had incomplete information about the actual behavior of the traffic system I was participating in. Following the three rules I set for myself, I am able to actually optimize my fuel economy, I am able to maintain my car in a state that I get the best fuel economy possible, and I am able to influence others behind me, to at least some degree, to actually improve flow conditions for the system, if only slightly.

I am also able to verify the observation, noted by Beaty at this web site, that I can influence the traffic behind me by changing my driving behavior. In Southern California, and in spite of various popular legends about congestion being impossibly bad here, I find instead that, more often than not, I am the slowest car on the road when I attempt to maintain a 55 mph speed limit on my won driving. However, I observe that if I do drive at that speed, cars behind me will at leaste some times slow down as well, rather than opting to overtake me. To the extent that even a few cars do this, for any measurable duration of time, I have improved fuel economy, however slightly, for the regional transportation system.

It has occurred to me that one transportation control measure?one that would benefit traffic flows, air pollution and fuel conservation at the same time?would be to post actual and current average flow speeds for each highway segment to make it possible for drivers to adapt their driving behavior to traffic conditions that they simply cannot sense for themselves, purely on the basis of their very limited field of vision. Couple this with a system of voluntary ?pacer? cars, visibly marked, and nearest-neighbor theory assures us that it may be possible to influence more people to drive for these optimalities, rather than on the basis of the imperfect information available to them through their windshields. Increasing information content is always a useful way of managing systems adaptively.

Vasishth ashwani@csun.edu (818) 677-6137
Department of Urban Studies and Planning,
California State University, Northridge

Ashwani Vasishth <vasishth@usc.edu>
Hollywood, CA USA - Monday, December 12, 2005 at 19:18:48 (PST)
Atlanta has some of the worst traffic in the country. So sitting it in gives one time to think, and I have over the past couple of years developed similar theories. It was music to my ears when I heard that there is a website that illustrates these ideas (quite eloquently, I might add). Keep up the good work. I always leave a gap, and I encourage others to do the same. The funny thing is that the problem results from the human factor. People are not naturally inclined to be considerate, so they do not want to leave a gap because, oh god, that car might get there 5 seconds faster than I do. This attitude, however, is ultimately self-defeating, and they end up being 10-15 minutes later then they wanted to be. So your theories have practical application in the moral tangle which is consideration. When people ask me why they should leave a gap, this is the answer I give.

Logan <???????Rauchdrachen@hotmail.com>
Newnan, Ga USA - Tuesday, December 06, 2005 at 10:51:06 (PST)
Just to say, if your theory about jam-waves is accurate (and it does seem to be) then what you are doing is a well known technique in physics, where a wave of opposite energy is used to cancel each other out (this is used to eliminate background vibrations in heart-rate monitors in hospitals I believe) and therefore makes perfect sense. It's an interesting application of the theory, its just a shame so few people seem to have noticed it (with the exception of Belgium apparently)

Actually, now that I think of it this is alost identical to the cancellation of sound, since sound works through high and low density patches of air particles travelling along and your theory (in the scientific sense of the word) just replaces air particles with cars. OK, maybe not exactly the same since it isn't really possible to overlap cars, it's more like sending a constant signal which is only slightly negating the average energy and therefore adding to the negative energy of the wave (the gaps between cars) and draining the positive energy (densely packed cars) enough for things to level out to a steady signal (no jams or gaps, just constant streams). Even so, maybe looking into sound and audio might further your research more?

kitsuken <kitsuken@yahoo.co.uk>
UK - Sunday, December 04, 2005 at 15:41:02 (PST)
Not sure if you are still posting comments, but here goes. In my early 20s I was a messenger, driving 350-400 miles per day between Baltimore and Washington, DC, and noticed early on what I called the "compression waves" of traffic. Being a musician and sound engineer, I've always wondered what traffic "sounded like."

Now, I drive a much shorter commute, and usually drive 30-year old classic cars with older braking systems. I therefore naturally follow less-closely than the average driver. However, with today's drivers, that extra space in front of me does not last long. It is invariably filled up by every manner of driver to whom "speed limit" means go as fast as you can until you are about to run into someone.

What can WE do living in a town where these space cushions are immediately erased?

Great site, by the way!

Mike Lascuola <mike@mrNOSPAMdos.com>
Colorado Springs, CO USA - Friday, September 23, 2005 at 21:01:20 (PDT)
Love your site! Excellent discussion. A couple of things I have seen in action that support your approach, that I didn't see mentioned in a quick skim:

1) putting lights on entry ramps to freeways. During rush hour, stoplights at the end of the entry ramp only permit 1 car to go at a time, feeding them to the highway at a steady but spread-out pace, and preventing traffic from slowing on the main freeway. I've mostly seen these in cities in California.

2) signposting lane closure well in advance. I've noticed that when the "right lane closed ahead" signs show up at 5 miles out, 4 miles, 3 miles, etc, that drivers are likely to sort it out themselves in advance and keep a gap knowing people will want to merge, and traffic remains moving through the lane closure, although it still slows down.

USA - Friday, September 23, 2005 at 13:33:32 (PDT)
1st: I love your site. (The WHOLE thing!)

2nd: About traffic: I drive ALOT (I put about 65,000mi on my car in an average year), and I must say that your observations agree with mine. As for the elimination of waves, why not take advantage of the cameras that run along the highways? how?

1. monitor the trafic waves at "trouble-spots"
2. have electronic advisement signs 1-5mi prior to said "trouble-spot"
3. when bottlenecks form, sign will advise driving at "X" mph lower than speed limit.

Therefore, assuming that at least 3 or 4 people follow the advisement, the bottleneck is cleared, and the advisement sign is turned off.

P.S. The person or persons responsible for timing some of the surface streetlights in the Denver Metro area needs to be slapped.

Daryl S <hippy_of_the_90s@yahoo.com>
Lakewood, CO USA - Friday, September 23, 2005 at 09:03:04 (PDT)
I noticed that you (as well as other sources) state that waves either move backwards to the flow of traffic or at a stand-still. I'd just like to not that waves may also move with the flow, it's just they're a bit harder to spot.
For example, if you use M. Treiber's simulator you have in your links, one can be created.
Start the simulation with the main inflow near or at the max while the ramp inflow is at zero. Let it run for a moment as to let the traffic be mainly consistent near the ramp. Now, with the ramp inflow slider, bring it to the max and back down as to let 4 or 5 vehicles in. Once most of the ramp-cars have entered main traffic there is some congestion. It seems to clear up fairly quickly, but if you look closely, you can see the congestion wave is actually moving with traffic away from the ramp. The cars never stop, but they do need to slow down a little bit. It's not very noticeable, but it's there.
Just though you'd like to know. Sorry if you already did.

James <zhatt(dot)zero(at)gmail(dot)com>
Vancouver, BC Canada - Monday, September 19, 2005 at 14:03:33 (PDT)
With all due respect, I think you've really misunderstood the fundamental problem of traffic.
[ Good point. However, read the title. Does the title say "speeding up traffic flow?" Nope. And, do I devote lots of paragraphs to the problem of aiding traffic flow; or of commuter trains and bus-riders and bedroom communities? Nope. I don't even mention those things. (It's even questionable whether traffic jams *always* cause drops in system-wide flow rates.) This article is not about increases to traffic flow. It's about the strange ability of individual drivers to smooth out traffic jams. The consequences of this ability are a secondary topic. Years ago my conscious goal was to speed up traffic by individual action. But my goal has evolved since then. The point of this article is, first, that traffic dynamics are very cool, and a little knowledge can turn it into a long time hobby, transforming a soul-destroying commute into ...an intentional search for "fun" traffic jams with which to play! My second point is that: we are not meaningless molecules in the flow, since our individual actions sometimes have immense repercussions for both good and for "evil." It's an important lesson, since traffic psychology is a miniature model for everyday ethical questions and especially for national and global politics. But WHY are traffic jams 'evil,' and WHY is it a good thing to remove traffic jams, especially where this doesn't affect the net flow rate? (This question is asked only by people who haven't been trapped in lots of traffic jams.) -billb]
Yes, people do things that slow down traffic. Yes, you've probably found strategies that individually and in groups can increase the capacity of existing roads. But they don't get to the root of the problem! Let's say existing capacity doubled, or tripled. Shorter commute, right? Wrong! People will start to realize they can live farther away from the "unwashed masses" in the city and have about the same commute time. Also, people from other cities start to take jobs in yours because of the "shorter commute". But then everyone does it, and more people are coming and from farther away, clogging up any new capacity you created!

The problem is that most people either have really skewed values, or they haven't really thought about the tradeoffs. They just don't realize that if your commute is potentially two hours each way, that's like making 33% less per hour (!) than if you lived near work or had a short commute. Or maybe they do realize it and don't mind it, or the stress of commuting at all! If people actually thought about this, would they be willing to suffer the "indignities" of public transportation for an effective increase in pay? I think they would. But they don't.

(Note: I am not an environmentalist, and I have no stake in herding people into public transportation. I'm just stupified at the tradeoffs people make that lead them to live lives of twice-daily traffic jams. Luckily, I live in Waco, where traffic is non-existent.)
[Heh. What if peoples' values suddenly became un-skewed? The cities would vanish, and I bet the population of places like Waco would increase by 10,000x. Does this mean that the REAL problem is overpopulation? Are people who have three or five kids the "evil" ones? :) I prefer to think that the REAL evil is the people people who look at problems and only complain, or only bemoan how inferior is everyone besides themselves, yet who do little to educate others or to improve the world. -billb]
Silas Barta <hearts_sysopNO@SPAMyahoo.com>
Waco, TX USA - Thursday, September 15, 2005 at 18:54:08 (PDT)
I find your theory interesting, but disagree with some of your theory.
[It's not a theory, if you mean "just a theory." Please read the FAQ. This site is an explanation of events I've repeatedly noticed out in the real world. I'm trying to explain why I'm personally able to bust traffic jams at some merge zones. If you're certain that jam-busting is impossible, well, then nothing I will say will have any impact on such a prejudice. To change your mind, you'd first have to try practicing my suggested techniques for a few months in order to repeatedly observe the jam-busting effect yourself. If you won't do that, then all discussion is useless, since you're trying to argue that a real-world phenomenon cannot exist, yet I have personally seen the phenomenon many times, while you have not. In other words, theory cannot disprove the simple obvious results of an experiment, and if they conflict, it shows that the theory contains a hidden flaw. -billb]

Although your traffic techniques may cause a more comfortable pace, they do not eliminate traffic jams. Obviously, the highway has a fixed number of lanes, therefore the only variable that can be changed is the velocity of the cars moving through the lanes.
Wrong. Each point on the highway contains another variable. Also, I personally see traffic jams evaporating and the cause is fairly obvious. Whenever it occurs, it's unmistakable. But only aerial photographs could act as convincing evidence for others. I don't own a plane! But onwards: is speed the only variable? No, and that's where your argument falls apart. Another variable exists: a merge-zone may currently contain a pinned standing wave, or perhaps there is no wave, so the cars all merge fast in "zipper" fashion. Single-variable thinking will utterly fail, since each point on the highway has a certain traffic speed and a certain traffic density, and therefore all sorts of oscillations and coherent patterns can arise. This is the "nonlinear thinking" which I keep talking about. If a dense standing wave does appear at a merge zone, then the merge zone becomes a very bad bottleneck, and there are two results: the lanes downstream from the merge zone are almost empty, and there is a constantly-growing backup in the upstream lanes leading into the merge zone. Individual drivers will experience this as a traffic jam, but it's a strange jam where, once a driver passes slowly through the jam, there are suddenly miles of empty road ahead and nothing apparently responsible for the jam. The problem is that an unmoving standing wave has a major effect on the flow rate in the merge zone. Specifically: the downstream edge of the standing wave is pinned in place, but the upstream edge is not pinned, instead it moves backwards as more cars arrive and the jam becomes bigger. It goes without saying that in the midst of the wave, cars are packed together and can barely merge, so the merging drivers intentionally creep ahead very slowly while trying to find a slot. The jam sustains itself once triggered.

Your "safe zone" argument only becomes relevant during extremly congested conditions, where the flow in the two incoming lanes is large enough that the single outgoing lane WOULD be overloaded. In that case a standing wave (traffic jam) is spontaneous and unavoidable. Perhaps you're looking at my animation and assuming that the incoming lanes always overload the single outgoing lane? If so, then you're wrong. As traffic density rises, usually something triggers a standing wave long before the single outgoing lane becomes overloaded. Perhaps a dense travelling wave has passed through the intersection. Perhaps two merging drivers were jockying for the lead. Or perhaps a "vigilante" was driving slow in order to block a "cheater." Many events can trigger a jam under conditions where no jam would otherwise arise. These "pinned-wave merge jams" are quite common in my experience, and are not the rare "perfect conditions" you seem to believe they are. And most important: when common events needlessly trigger a merge-zone standing wave, and if other drivers manage to remove it again, that standing wave will not instantly reappear. Yet once the standing wave has been triggered, it grows continuously and can become enormous. Though again, I do agree with you that under much higher traffic flows, a jam is unavoidable, and fancy driving techniques will have no effect. -billb]

As the velocity increases, so does the ?safe zone,? or comfortable distance between the cars any given speed.

The animation on the ?MERGE-JAM? page shows two lanes of traffic traveling at a constant speed with a comfortable ?safe zone? between the cars. As the lanes come together, the cars seamlessly merge while maintaining a constant speed.

The problem with the animation is that it did not account for the cars ?safe zones? that have been compromised. As the cars merge, they will apply their brakes until a comfortable distance has been reached from the car in front of them. This will breach the safe zone of the car behind them and they will be forced to slow until their safe zone is achieved. Etc, Etc. This will ultimately cause a traffic jam.

Furthermore, any amount of space between you and the car in front of you (other than the safe zone) is wasted space and increases the inefficiencies of the traffic jam.

I agree that your theory (in perfect conditions) will help normalize the average speed of the traffic, but will it decrease the overall travel time?

Mike Deisel <mikesig7@yahoo.com>
Dallas, TX USA - Monday, September 05, 2005 at 13:56:18 (PDT)

Very Interesting Site.

I drive 355 in Chicagoland. I see people opening up gaps in the left lane during the evening southbound commute. But it gets out of control too. To the point where there are 1 mile long gaps. They are doing this to average out to the tollgate jam some miles down the road. But many off us who leave the highway before the jam get some penalty. This practice backs up traffic north from the entry tollgate back up to a few miles north on Route 53. I'm sure this situation is one of those that resulted in the Illinois law that now prohibits left lane traffic vehicles from driving slower than the traffic ahead. I think a reasonable threshold of distance to the jam to begin anti-traffic action would be 3/8 ths of a mile. Any further assumes one knows there is a jam beyond their sensory capabilities. This is many times not the case and many times there is no jam at all in the distance to the next exit.

But, the methods in the website have merits. In the morning the right lane is a lot quicker, as the left lane drivers are setting up nice standing waves before the curvy parts of the road. This is usually due to the SUV curve handling capability. An SUV just cannot keep safely proceeding at 75 MPH when it comes to the curves. This causes the reflected traffic wave and the standing wave pattern. Oh, did I forget to mention I am an RF/Microwave EE. Meanwhile traffic in the right, even with merges is travelling along at 65 to 70, and with a good group of drivers merges are seamless and have a better average time.

My dad is in the C.E. departement at a university. He told me about a traffic study done in the deparment on the Dan Ryan expressway in Chicago. They found the best solution to the problem was to drive over the 55 MPH speed limit at 62 MPH. Faster resulted in reaction time accidents, slower resulted in the 2 second distance most people drive being too short for the smooth merge phenomina you point out. This resulted in the best overall system thruput.

The 2-second following time is the source of the problem you had trying to exit. A line of cars doing 45 MPH in the right lane has a 2 second following distance on the order of 2 or 3 car lenghs. Dangerous to merge into, and easy for somebody to accelerate to block. At 65 MPH that distance opens up to 4 to 5 car lengths, and the gears mesh as you put it. Additionally, sight lines when following at 2 to 3 car lengths in overcast conditions (no shadows to cue off of) are quite poor. Thus the reaction of many in such a right hand lane situation to over react to cars "swooping" in from the left and behind.

My approach to this problem is this. I get out of the fast lane, into the center and get about 1 second behind traffic, and try to line up with a gap in the right lane. I then turn on right blinker. You got three reactions to this. Those that will slow down and let you in, and those that accelerate and block and those that do nothing. When the accelerating person hits his gas, its relatively easy to hit the brake and fit into the gap left behind him. You see, the car behind him has limited sight lines, and being 1 second behind traffic means there is 3 seconds of following room behind me. The other possibilty is the guy who does nothing. These are the ones on usually on a cell phone or for whatever reason do not react to the right turn blinker. Lately, I let the blinker run for as much 10 seconds before an action is taken because of this. Its difficult to see the cell phone from the left foward position I am in when I start the blinker. His arm is hidden by the A pillar, and the oblique sight line through the windshield can be problematic. Then one is forced to merge into a 2 car length gap from a lane moving faster than the gap, hit the brakes hard and waste gas.

Don <do@*nver@sbcgLlobAal.net>
Naperville, IL USA - Sunday, August 28, 2005 at 14:23:31 (PDT)
I read an article (it might have been in Wired) that experimented with traffic through computer simulations. Simulated vehicles would accelerate or decelerate depending on the car in front of it. Basically, they found that traffic flow was always smooth if the relative speeds of vehicles are the same. This in mind, I think when you went the average speed of the stop-and-go traffic and saw no "waves" of traffic in your lane behind you, it was due to this sort of phenomena. When driving at slow, yet constant, speed, what reason does the person behind you have to behave any differently? You've become a sort of pace car. This should work at faster speeds as well. Tailgaters are as much a boon to traffic flow as the grandmas that can barely see over the wheel. That flicker of the brake light can set off one of your waves. Very interesting site by the way.
Withheld <brainmeltdownATyahooDOTcom>
Salem, OR USA - Saturday, August 06, 2005 at 22:20:10 (PDT)
I like your website and I wish everyone would read it, especially people who drive on the FDR Drive in Manhattan. Unfortunately although your technique is a good one it never works for me -- people in New York will sneak into the smallest space and close that gap, and I feel it makes it dangerous sometimes for me to drive that way.

I'm interested on your comments on the recent outbreak of aggressive, self-righteous drivers who ANGRILY flash their brights at you when they think you are going too slow. I drive regularly late at night on a stretch of three-lane highway (well, six lanes, three on each side). I usually drive in the middle lane because people are exiting and entering in the right lane with some difficult spots to see. I drive about 65-75 in a 55 MPH zone, and almost every night one or two people will come up right on my tail and violently blast their brights at me in the mirror. They do it with a certain angry rhythm, not like a friendly "BLINK BLINK" but a "BLAAAAAAAAAST BLAAAAAASSSSTTTT". Why do they do this? They can pass in the left lane. What's the problem? I'm not even driving slow.

New York, NY USA - Saturday, July 30, 2005 at 21:47:41 (PDT)
You concentrate on traffic waves as blocks, but you neglect the the difference in speed between the lanes. I noticed years ago that the fast lane becomes the slow lane whenever traffic slowed down below about 3/4th or 2/3rd of the posted speed limit. I experimented by staying in each lane for a week and discovered that I could save about 2-3 minutes for each lane I moved away from the center divider. That's not bad for a 15 mile stretch of freeway.

During light to medium traffic when everyone was driving at or above the posted speed limit, the center lane does go faster. For some reason drivers all want to switch lanes to the "fast" lane whenever traffic starts to slow down, slowing down that lane even more. During the week I was in the "fast" lane, I noticed that just as traffic slows down, almost everyone in the next lane tries to cut over. During my week on the far right "slow" lane, I found that most people who just entered the freeway would immediately try to cut over to the center "faster" lanes. I found that by moving 2 lanes over, and mingling with the traffic entering and exiting the freeway, I was able to consistantly go faster and save time for the entire commute. It's strange that everyone thinks they are faster drivers than everyone else.

Eventually, I was able to figure out the best local roads to use and save a total of 15 minutes on my normal commute. Many drivers are just not paying attention to their surroundings. Fortunately, they are mostly idiots and are afraid to get off the freeway, otherwise my commute would have sucked even more.

You also dismissed the idea of slower traffic keeping right. While this doesn't work during medium to heavy traffic, during light to medium traffic, people shouldn't be driving in the passing lane unless they are passing. The blocks of traffic occur during light traffic because a few drivers are inconsiderate and block the faster moving traffic. It only requires one person to generate a slow moving block. There are frequently times when traffic could be moving faster if that one driver would just speed up or slow down and pull over instead of blocking the passing lane. I've seen solitary drivers sitting in the fast lane when there is no traffic around and everyone is passing in the slow lane. There's no reason for them to be driving all the way in the center fast lane if everyone is passing them.

berkeley, ca USA - Monday, July 04, 2005 at 15:56:21 (PDT)
Yeah, I like your thinking, however, all it takes is one idiot to ruin this utopia of highway control. In otherwords, they would have to outlaw rubbernecking (which i would LOVE to happen) but it wont. Also, this would have to reach everyone in the US to actually work and everyone would have to follow certain rules for a "zipper" effect to happen. I like your thoughts on all this, but lets face it, as long as people are individuals, there is no way out of traffic jams.
Adrian <morrow_snow_bro@hotmail.com>
Sanger, CA USA - Thursday, June 30, 2005 at 19:58:43 (PDT)
i thought exactly the same way... how ever.
your just thinking exactly the same as every one else...
how ever im sure you will get close to the car ahead of you or go at the same time rather than when they leave off of you. this theory (which is quite fact) is known by many but there is no real way to fix the problem minus the block traffic method to create blocks of traffic.
you cant just all go at once because no one can see the first car except the second and third cars and no one can see the third car except the 4th and 5th cars... etc...
it is a problem. however it is unavoidable without spending more time more money etc... on traffic regulators... ie motorcycle cops going about 55mph. :)
other than your preventitive idea's the theory is very sound an im impressed to learn im not the only one out there with this feeling...

Randy schultz <Dijasom@hotmail.com>
Arlington, wa USA - Monday, June 27, 2005 at 13:48:16 (PDT)
I just happened to stumble upon your website during a boring day @ work, and I must say it has been both interesting & informative.

Having been in a terrible and near-tragic accident myself, I am a very patient driver and find that I naturally use these sort of "driving principles" for my own personal safety. I will certainly reccommend your site to my friends, and my younger sister who is just learning to drive as well.
Louisville, KY USA - Monday, June 27, 2005 at 10:22:03 (PDT)

I am struck by the comment "Cheaters are not problem, but the people who want to punish the cheaters are". I think this would make for a fascinating Nash Equilibrium matrix. For the most part, I think you have found the Nash Equilibrium already by driving with an open space in front of you, but I wonder if it might payoff more to be one of the cheaters from time to time. An analysis of how often cheating causes traffic to adversely affect the cheater, compared to how often the cheater is not directly adversely affected by his own cheating would be necessary.

The more anti-traffic out there, the more the behavior of the cheater would be rewarded, the more cheaters out there, the more the anti-traffic driver would be rewareded. Most curious.

[ Cool idea! I recently started harnessing just this concept on my daily commute. Some days I behave as a "cheater" who speeds ahead and merges late. But on most other days I maintain my large empty space in the long queue, while letting lots of "cheaters" merge ahead of me. (How many "cheaters" must I help, before I can become a "cheater" myself?) There's added complexity because a "cheater helper" gains direct rewards, since in the long run their behavior raises the speed in the whole queue upstream of the merge zone. The queue becomes unplugged because I'm removing many "cheaters" early. These drivers would otherwise drive to the head of the queue and slowly push their way into the very front. By letting them in early, I remove a major cause of the backup. On other days I merge late myself, but not so late that I have to come to a stop, force my way in, and thereby participate in causing the backup. (And note that many apparent cheaters *want* to get in early. They only became "cheaters" because nobody in queue would let them in. Which driver is worse, a "cheater" who goes to the queue head, or all the drivers in the queue who adopt an "I've Got Mine" attitude, and who block all early merges?) -billb]

Frank Benson <mfbensonnospam@comcastnospam.net>
Dallas, TX USA - Friday, June 24, 2005 at 15:03:59 (PDT)
The simple rules of traffic etiquette necessary to prevent jams are, on the whole, not followed due to selfishness. Now I ask "Why then can individuals and corporations be expected to self-regulate for the long-term good of the economy and the environment?" Republicans who overestimate the human animal need look no farther than the daily traffic jam.
James H. Burnette <***jhburnette@hotmail.com***>
Lackawanna, NY USA - Wednesday, June 22, 2005 at 22:29:01 (PDT)
I won't say that I am never an aggressive driver but this paper pretty much validates my usual driving pattern which is: maintain an oversize empty space in front of my car if possible (this is good defensive driving that allows more options in panic situations); establish myself in the lane I need for a turn or exit well in advance and stay there; merge with other traffic as soon as I identify an unexpected blockage in my lane (accident or construction); when I identify an unexpected blockage in another lane, shift to a lane not involved with merging as early as possible; drive at speeds slightly less than the posted speed limit.

Good article.

alan <amoerdyk@earthlink.net@@@>
phoenix, az USA - Friday, June 17, 2005 at 12:31:06 (PDT)
I can hardly believe that //all// truckers just happen to learn the anti-traffic technique because of their experience. I wonder if its taught to them when they get their trucker liscence. Why not just teach a uniform traffic technique to anyone that gets a liscence.

Also, would metered break lights that intensify depending on the intensity of the break possibly prevent more accidents, or even help people to glide along with your speed even if they chose not to free up space behind you?

What's your take on handling people that use the shoulder lane to beat traffic? Obviously it creates more traffic problems because they end up cutting people off when they get to their exit ramp, but is blocking up the shoulder lane as revenge a good way to increase or decrease traffic?

Charles <dreamquixote@yahoo.com>
Mamaroneck, NY USA - Thursday, June 16, 2005 at 01:40:27 (PDT)
Great article on traffic waves, a phenomenon I've often noted but never seen analyzed so cogently. I've seen the same thing referred to as "accordion effect" in the context of marching armies. In the early days of the Civil War when troops were not well trained to maintain spacing, long columns would sometimes get so screwed up that troops would have to stand in one place for hours, then run to catch up with the unit ahead to avoid losing contact with them altogether. I think the term "accordion effect" is nicely descriptive of the general phenomenon.
Lee Creech
Frankfort, KY USA - Tuesday, May 24, 2005 at 13:22:57 (PDT)
Well, obviously it's a non-linear phenomenon: some of these traffic waves are damped naturally, for a given density, others seem to be amplified. what is the amplifying mechanism, is there a resonance frequency?
consider the following: a fast group of cars approach a slow car, the first car reacts only when quite close to the slow car, the car behind has to brake more, etc. a small perturbation therefore causes the cars behind to come to a full stop.

Oakland, CA USA - Saturday, May 21, 2005 at 12:59:40 (PDT)
Fascinating stuff!
I'd already been driving slowly when approaching queueing traffic but that was only because approaching a jam slowly is psychologically better than getting there quick and then having to sit in motionless traffic. I had sometimes wondered though whether what I was doing might have a positive impact on the cars behind.

Andrew Johnson
UK - Wednesday, May 11, 2005 at 15:04:31 (PDT)
It is slightly misleading to focus on the backward-traveling congestion without considering the forward-traveling gap. In fact, the occurrence of a jam is more like a "pair creation" of these two local irregularities. Optimal robustness against density fluctuations is achieved when the density of cars is as uniform as possible. Thus the best strategy for an individual driver is to equalize the respective distances between his car and the cars behind and in front of him. This means that you should reduce your speed when the traffic behind you slows down! The increased distance in front of you will reduce the chance of jams there. I will be hard to convince drivers to accept this driving style ;)
USA - Monday, May 09, 2005 at 06:51:29 (PDT)
Great site and fits in with some of my own observations.

A dynamic that I have had alot of experience with is what I call "The Slinky Effect". I spent six years in the Army National Guard and have driven in many 100+ vehicle convoys. Now with Military convoy driving most of the other drivers on the road don't merge into the convoy. In the convoy you need to keep an appropriate distance between vehicles whether stopping, accelerating, or at constant speed.

I have noticed that driving near the front of the convoy everything would be easy and smooth, whereas driving in the rear of the convoy would include almost complete stops and high rates of speed to catch up. At rest stops, I would get permission to change my position in the convoy to test this out. The farther towards the rear of the convoy you get, the worse the stop and go becomes.

What happens is this: Driver 1 barely taps the brakes because of whatever. Driver 2 taps his a split second after driver 1, but increases his total braking time and braking pressure because he doesn't know how hard Driver 1 braked and waits a moment after Driver 1 releases the brake to see what he'll do.

Braking Time = X
Braking Pressure = Y
Total Braking Amount = Z

D1: X + Y = Z
D2: (X + 1) + (Y + 1) = (Z + 2)
If there are 100 vehicles in the convoy then:
D100: (X + 99) + (Y + 99) = (Z + 198)
The braking amount of Driver 100 is just about 200 times that of Driver 1!!!

Then you get to the acceration phase which uses the same mathmatics.

A light tap on the brakes by the convoy leader, can cause the rear vehicle to come to a complete stop! I have noticed this effect work in lesser degrees in civilian traffic. Call it Entropy in the Traffic/Antitraffic equation.

Peter Farland <peterfarland@alltel.net1111>
Houston, Tx USA - Wednesday, May 04, 2005 at 00:04:00 (PDT)
Damn, I saw the page was huge, so I thought maybe I can just add my comments in the hope that noone has done one before.

I have been frustrated by the slow drivers here in NZ and have spent many hours checking out why traffic jams and what causes them.

Now, here's a way to smooth things out.

The space between cars MUST be increased as you stated, BUT, there MUST also be additions.

Because NZer's are mainly stupid, the road traffic authority should put a series of signs on the motorways to teach drivers how to handle the inbound traffic.

Two kilometers out, signs should read, "increase your space to 3 car lengths", and closer to the merge zone, "adjust speed to slide into space. While at the merging lane (or 2), "glance right adjust speed to slide into space".

Bingo, problem solved.

I do it, and slide into spaces easily. BUT, we have heaps of Chinese, Indians, and Polynesian drivers, all of whom cannot drive at the speed limit in NZ. The slowest driver ( a Polynesian lady) I came across was doing 30k in the middle lane of a 3 lane highway. Lots of space and no traffic jams in front of her, yet she was driving at 30K ina 100K zone.

How can you maintain speed with this type of driver on the road?.

It comes back to this: motorways were designed to move lots of traffic from A - B. But here in NZ where there is no slow speed restrictions on the motorway, there will always be traffic jams. And now the city council, with it's bunch or slow thinking morons want to build another motorway to ease the traffic jams.

Useless thinking.

The whole idea of the motorway is out the window in this backward country, where we gave the slow suburban drivers a motorway to play on. So now they drive on the motorway at 60k. Stupid.

We must legislate to have a minimum speed on the motorway and if not met, you're outa there, unless of course, you're a truck or similar.

Rubberneckers will be caught on camera (installed at an accident or other using a camera on a tripod) and fined $500 for even glancing at a prang.

Choppers will hover over the merge centers and shoot (to analyse) the reasons why traffic slows, and if possible, record the culprits numbers and fine them $500 for slowing down without reason.


ric chan <ric@wickeddotnetdotnz>
Auckland, New Zealand - Tuesday, May 03, 2005 at 03:57:53 (PDT)
Hi there,

I was thoroughly impressed with your observations. As we don't have such highways in my country, but a far higher vehicular density, your methods will not be applicable, but all the same, they outline the very fundamental approaches of the Queuing Theory.

It was nice to come across such a page.

My regards,

C A <cax#####@softhome.net>
India - Wednesday, April 27, 2005 at 04:29:00 (PDT)
Hello to all.....I find your site very interesting, but not sure that it is going to help ease traffic. It is an unrealistic idea and other people are just going to pull in front of you (constantly)!! I want to try your suggestion (slowing down and keeping a distance) but I just can not help myself! I admit I am an aggressive driver. I hear Seattle has some traffic problems.....I am excited to see for myself as I will be there next week. Actually, traffic jams never really bothered me....more interesting. Trying to compete with other drivers to get the headway is like my recess time. The more horns I can get to sound the better!...hehe.....Thanks...Be well!
Dan W. D. <crazydjdannyboy@msn.com>
Cleveland, Ohio USA - Thursday, March 10, 2005 at 07:52:25 (PST)
Interesting article.

The EASY way to create a nice, large space in front of you is to drive just a little slower than the crowd (best done in the slow - right - lane). A nice, large safety cushion appears in front of you, and suddenly driving is no longer a white-knuckle experience. I have driven for hours on end using this approach without having to touch the brakes - and enjoying the ride all the way. With a big open space ahead of you, "crises" melt before you reach them.

I am convinced this is the trick of truckers who stay in the business - they can stay in the safety cushions they build and enjoy miles of smooth driving.

So if you want to enjoy your ride, set your cruise maybe 2 to 3 MPH below the average speed of the other dirvers. You will feel like you own the road.
Bob Cassidy <rcassidy123q@warwick.net>
Warwick, NY USA - Thursday, March 03, 2005 at 15:53:24 (PST)

Cyclists are very famaliar with this type of vehicle flow. We have real problems with stop and go traffic because we must literally come to a complete stop, touch the pavement for balance, then push off again to continue on. To avoid this we are always looking ahead, varying our speed to allow for constant forward movement. So if you want practice, try riding a bicycle in a group, and wear a helmet.

I've been using the gap ahead in my car for quite a few years and can atest to it's effectiveness. Here's another bit of advice; stay in the right (exit/entrance) lane when stuck in traffic and use the gap. It works better here because as traffic exits with the gap the lane moves faster and as it approaches an entrance, it allows the oncoming cars to merge in better. Those merging in also have a better chance of moving left into another lane thus further opening up the lane your in.

One last bit of advice, never do this when a cop is around or they will ticket you with obstructing the flow of traffic. I recall road signs in Washington stating no more than 2 cars lengths between cars allowed. Never try to educate our law inforcement officers with this wave breaking logic, they're not much open to new ideas unless the courts tell them otherwise.
Gary <bluecyclist@yahoo.com>
Mt Clemens, MI USA - Thursday, February 03, 2005 at 07:35:58 (PST)

I love your site. I have been thinking about this here and there for years. As a math guy I invisioned an equation or two which probably exist. I knew that the summation of acceleration caused waves after a flow interruption. I have observed that when a strong wave is initially started with heavy fast moving traffic that the deceleration needed to avoid collision increases up stream (since time decreases by the summation of reaction times)unless people like you are downstream to absorb. Your antitraffic spaces absorb these types of problems.

Traffic is somewhat of a prisoner's dilema. I think this can turn normally good people into Jerk drivers believing if they don't defect, they will be defected against. Also the anonymity driving allows only squashes the normally good person's guilt or punishment for defecting. I like how you point-out that the Always Punishing drivers cause more problems than the Jerk Drivers. I have to admit I've been a punisher before, but mostly I take turns. Now I will drive absorbing more waves than I cause.


Michael McConville <***mikemc314***@hotmail.com>
Minneapolis, MN USA - Friday, January 14, 2005 at 23:48:05 (PST)

I surmised that these principles can be applied at traffic lights as well. By leaving just over a car length infront of you at a red light, you should be able start moving as soon as the car a few ahead of you starts moving. If everyone did this they all could start moving exactly as the light turned green and there wouldn't be a delay ripple through the stopped traffic. Of course this would cause the traffic engineers to have to rewrite the timing of the lights as their models would havve to change.
Terry L
Canada - Wednesday, January 12, 2005 at 07:05:03 (PST)
I read through your FAQ section as well as the comment section, and I was astounded that you failed to properly address a fundamental problem. Several people correctly raised this issue in the comment section, but they were arrogantly brushed off.

The problem is this:

There is a limited amount of physical road space and an upper limit to the speed of traffic flow, so therefore there is an upper limit to traffic flux. The greater the space between cars, the lower the traffic density, and therefore a higher traffic speed is necessary to maintain constant traffic flux.

In other words, once the number of cars trying to enter traffic flow reaches a critical density, it is physically impossible for traffic speed to maintain reasonable speed without reducing the space between cars (and thus increasing traffic density). Hence your solution is untenable for most traffic jam scenarios, ie jam scenarios caused by high density traffic throughput.
[So jam-smoothing techniques in theory cannot ever work? Heh! Better tell that to those behind the multi-million-dollars project in London which uses such techniques on their enormous M-25 highway. Also, anyone who actually tries these techniques can often see them work with their own eyes. They're that obvious. But before further rebutting your comments, I must first point out some important facts which I think you've missed: congested traffic is not a traffic jam. A traffic jam is a density wave which can either travel over time, or it can remain "pinned" in place. Usually traffic jams only appear in congested conditions, but also they can be triggered early and then persist even when traffic becomes very light. Another important point: during extremely congested traffic, sometimes no "waves," no traffic jams arise. If most traffic jams require a certain level of density before they can be triggered, then it SEEMS like traffic jams are simply a form of extreme congestion. But this is wrong. Congestion is linear; it is analogous to compressed gas which becomes denser and denser. Traffic jams are not linear; they are analogous to nondispersive soliton waves, or to gas which spontaneously changes state to liquid or solid. Congestion is linear, while traffic jams are a nonlinear effect. Or in more detail: on the Fundamental Diagram of traffic flow versus density, the slope of the curve becomes negative at high density values, and as I understand it, this gives an effect where small noise sources are amplified. It produces "turbulence" in the form of standing waves, stop-and-go driving, etc. Individual drivers can have little effect on the Fundamental graph, while they can have enormous effect on the turbulent regime in the negative-slope portion of the graph.
Now about your comment. In most traffic jam scenarios, the road which is downstream of the "standing wave" traffic jam is nearly empty. The traffic jam is not just a high-density region. Instead it is acting as a bottleneck which produces a huge backup in the upstream highway, and leaves the downstream roads empty. Since a "standing wave" can either exist on a congested highway, or it CAN NOT EXIST ...and since traffic jams appear because either "traffic noise" or a highway incident triggers their appearence ...then if we could just remove a traffic jam, then the bottleneck would vanish, and the cars trapped in the backup would suddenly race forward. (All this is known traffic theory, and is the basis of professional jam-busting systems based on electronic speed limit signs as well as stoplights at highway entrances.)
But perhaps you're imagining some road conditions which always trigger a traffic jam spontaneously. In these situtions, if the traffic jam were removed, it would immediately reappear. Such conditions do arise. But other conditions are also common: conditions where something has triggered the formation of a standing wave, and where this standing wave will not instantly reappear if it is somehow removed. -billb]

O. Harris <dr_tube@yahoo.com>
Santa Rosa, CA USA - Saturday, January 01, 2005 at 02:06:13 (PST)

I know for a fact the the techniques you talk about DO work, and have been practicing them myself for many years. One entry in the book mentioned some formulas regarding FLUID DYNAMICS, and on this point, I would urge you to study something known as PROPROTIONAL-INTEGRAL-DERIVATIVE CONTROL SYSTEMS (also called PID as an acronym). These systems are used in process control (any "process", but I know of them from oil refineries) plants world-wide. The "CRUISE CONTROL" in your car uses the technique, by the way. Look up the terms: PROCESS VARIABLE, SETPOINT, MEASURED VARIABLE and find the analogy of your driving technique! Thanks for the cool website! I wish everyone would read it, and could understand it!
JB <j e f f p i c k s @ g m a i l d o t c o m>
Eatontown, NJ USA - Wednesday, December 29, 2004 at 15:05:02 (PST)
Thank you for the traffic congestion science. Not to easy to put this all on a website and then get Yahoo to feature the link for kicks.

Question: If I'm driving in Seattle, WA and the vehicle is traveling at the speed-of-light. OK .... can I use my headlights to blind the driver that I'm tailgateing ????
XP Dork <xp_dork@yahoo.com>
Earth, CA USA - Sunday, December 26, 2004 at 18:27:46 (PST)

I wonder if anybody has applied the mathematics of "velocity modulation" as applied to microwave tubes to a study of traffic flow?
Don Shannon <donald.shannon@nsc.com>
Sunnyvale, CA USA - Thursday, December 02, 2004 at 11:28:06 (PST)
Interesting stuff. I've come to similar conclusions trying to save my brakes by figuring out the average speed of the traffic and sticking to it. Perhaps a good idea would be to create a "society" of sorts of concientious drivers who would adhere to these principles. They could affix stickers to their vehicles proclaiming their membership to this society with a link to a website that would explain these ideas, and hopefully create more converts to the technique. If the computer controlled highways in Germany work, it is because the people understand that it is in their best interest to observe the suggested speed limit (or enforcement is really good ;) ), so maybe if we can get people in other places to figure it out to, things will improve for all!
Josh Ong <jishcat@hotmail.com>
Elmsford, ny USA - Thursday, November 25, 2004 at 19:40:01 (PST)
Nice page! I briefly went through the links, but have only found very few references to the simple exclusion type models the investigation of which I am involved in. On one hand, these models are not optimized for traffic modeling, and I am sure some more sophisticated ones are analyzed in the literature. On the other hand, the model is so simple that one can describe it in a few lines: cars are placed at distinct sites, and each can advance on sites one by one. They each try to do so in random times, independently from each other, but only succeed if the neighboring site, where they want to advance to, is not occupied by another car.
Many properties of this model have been investigated and are now known rigorously (i.e. not only by simulations or approximations) by mathematicians and physicists. In particular, this simple model already leads to a differential equation developing wave solutions (in some sense).
These waves are similar to the ones observed on these pages, but are different in that they are not stationary: they slowly disappear by themselves. We know exactly their shape and motion (yes, they can move in the direction of the traffic or in the opposite direction) in the model.
One can for example read from these solutions that we meet a traffic jam suddenly: it is not like we are going slower and slower, but we rather meet the traffic jam all at once and have to brake intensively. However, leaving a traffic jam is just the opposite: we do not suddenly see a clear road in front, but rather go a little bit faster and faster until we notice that we finally reached our cruise speed. And that is what we see in real: we meet jams at once, but it might very well take minutes until we get completely out of a traffic jam.
The positive effect of decreasing the car density behind a wave can also be seen, although it doesn't help in our question of interest: the time by which we get to a given further point on the road.
Of course, these simple models can not take closed lanes and freeway ramps into account, where making waves disappear can really help. One advantage of them is that, by their simplicity but rather complex behavior, they make the phenomenon more understandable for people interested in the subject; both scientists and non-scientists.

Marton <balmar@freemail.hu>
USA - Sunday, November 14, 2004 at 20:32:32 (PST)
I was very interested in your observations and I think some of your solutions, such as creating a larger area of slower moving traffic in front of a jam, are actually being put into practice on the motorways in the UK.
Although there is no mechanism to actually create an area of anti-traffic there are now numerous electronic signs near known traffic jam areas which are activated during a jam instructing drivers still many miles away from the actual jam to drive 10 - 20 mph below the speed limit. This should have the effect of delivering less traffic to the end of a jam and thus allow it to dissapate sooner.

Joe <joe@gravychain.co.uk>
Birmingham, UK - Tuesday, November 09, 2004 at 09:15:54 (PST)
Creating gaps between myself and the car in front works even down here in the quiet counties of Dorset, Devon and Cornwall, Only trouble is the gaps are never that big as there is usually a bend in the road ahead less than 1/4 mile ahead, even so if there is a wave build up around the corner and I get caught I can still control the traffic behind me by opening up a gap once I start to move again. This is normally at about 5MPH until the gap opens considerably (about1/2M) or the evaporating end of the jam is within sight. If I get it right I can gradually accelerate as the jam dissipates and almost eliminate it altogether hopefully having left behind me lots of not so unhappy drivers. I find if I get cut up the best thing to do is drop back to open a gap and by doing both of these things my average speed of a journey tends to remain fairly constant. Having now your website I have been inspired to study this for my own benefit at least, I could tell others and just hope they listen. Nice one!
Neil Lockie <coastalskipper.nl@btopenworld.com>
Weymouth, UK - Thursday, October 21, 2004 at 15:58:36 (PDT)
I think that for a full explaination you have to look at gaseous flow. Consider turbulent flow and boundary conditions stagnation pressure.
Carl <carl_tunich@sbcglobal.net>
Clinton Twp, Mi USA - Thursday, October 21, 2004 at 10:44:00 (PDT)
Thanks! Like many here, I've had many of these same thoughts myself -- this is far and away the best formulation I've ever seen.
Morgan Venable <nope>
San Francisco, CA USA - Tuesday, October 19, 2004 at 08:59:09 (PDT)
I noticed on vacation in Holland that the highway(s) leading in to Amsterdam had 'dynamic' speed limits displayed on overhead electronic billboards. At first it made little sense to me why the speed limit constantly varied during rush hour, but on the other hand, traffic never really slowed below the given speed limit. A nice straightforward engineering solution similar to your Highway Patrol blockers. :) Great site! :)
Jeff Dungen <jrmdunge@engmail.uwaterloo.ca>
Montreal, QC Canada - Monday, October 18, 2004 at 17:22:59 (PDT)
Fantastic read! Everyone getting a lic. should be required to read this! I've driven a truck for 25 years. Big trucks don't need their clutchs depressed when shifting gears, only when they come to a dead stop and when they start from a dead stop. The shifting between gears is easy and doesn't even require thinking. The pressing in of the clutch is nerve racking, so to keep from doing this I'd just keep an empty space bewteen me and the car ahead of me, so I could keep rolling, regardless of the stop and go patterns of those ahead of me. I didn't realize how much I was helping the traffic situation.
gary boehm <dudevato@yahoo.com>
USA - Sunday, October 17, 2004 at 08:08:05 (PDT)
See also "Traffic Zoology" by Hemming at http://www.trafficlife.com/page92.html

A similar analysis. Also very amusing.

Jim Lone <lone@conxns.net>
San Francisco, CA USA - Tuesday, September 28, 2004 at 16:01:48 (PDT)

They should have those animations running on monitors in every DMV (Department of Motor Vehicles). Every motorist in the state would be standing in line and would have to watch how traffic jams are created and how they can be avoided. Its about time we conduct ourselves as an intelligent collective when it comes to cooperating on a daily basis in traffic rather than acting selfishly which results in inefficiency for everyone. They should should teach this in every driving school.
David Chan <dchan1@cox.net>
Dana Point, CA USA - Tuesday, September 21, 2004 at 18:40:00 (PDT)
I wondered how I can make much difference since I ride a motorcycle and split lanes (ride between cars). :)
Thinking about it, I did realize that agressive lane-splitting on bikes can cause more jams - because doing this sometimes startles the nearby cars, and they'll spread out to allow me through, and sometimes it involves braking. The unexpected movement of a car opening up a space for me, because I startled him by flying by him 3 inches from his side mirror (heh heh), could also ripple a lane over causing others to startle, and slow down or swerve themselves, and it's self-repeating.
So perhaps bikers can help by splitting conservatively and slowly, so that I don't startle anyone or force anyone to alter their speed/direction.

Huntington Beach, CA USA - Wednesday, September 15, 2004 at 17:12:59 (PDT)
billb said: [Heh. Think first, THEN talk physics! In the real world, when two lanes merge smoothly into one, the two lanes slow down and no traffic jam forms.

-That's what SHOULD happen. But in the 'real world' people don't function like computers, they over brake, causing the waves you mention.-

(The two incoming lanes might move 2x slower, but that is not a "traffic jam.") On the other hand, if a traffic jam appears, then the flow in the two lanes approaching the merge zone IS NOT 2x lower than the flow in the single lane. Instead the flow drops almost to zero, and that is the problem.

-What you mean to say, is not '2x slower' but 'half as fast'. Two times slower would be backwards. :-) I'd have an easier time agreeing with you if you explained yourself in a clearer fashion. You are correct, I should myself be more clear, the slowing of traffic itself is not a jam.-

If traffic behaved like water which pours through a bottle neck, then traffic jams would not exist.

-This is an anology I was trying to use to explain capacity through a 'bottleneck' not fluid dynamics.-

Instead, traffic often behaves like stones pouring into a funnel: they grind together and stop, while the tube below the funnel empties out, while still more stones pile on behind the funnel. And within the funnel, only a few stones can grind past each other per minute.

-I think the rock analogy isn't helping. :-) -

If instead we poured oil on the stones, so that the gravel in the funnel could easily flow into the smaller tube... that is called "having no traffic jam!" Back to the cars: if there is no traffic jam, then the flow in the two incoming lanes must be twice as low as the flow in the single outgoing lane. But when a traffic jam develops, the flow is much much lower than 2x. A single driver can sometimes remove a traffic jam. But of course a single driver can do nothing about the 2x slowdown. -billb]

-okay, we agree on that, the cars have to go half as fast when moving from 2 lanes to one. But as I think I tried to explain, at 60mph, half the speed is 30 mph. Which would be nice enough, but as we've all explained and experienced, brake waves form and the actual speed is a lot less.

I read an article (in the economist I think) a few weeks ago about studies being done at some school somewhere, that they found humans have about a 1 second reaction time to braking, so they over brake thus causing the waves. They found that if people used the traffic sensing brake features (That I guess they're starting to put in cars now) which have a much quicker reaction time, 80% of the effect of the brake wave goes away if you have this electronic braking in only 30% of the cars. The proportion was surprising. Unfortunately (me included) some of us aren't going to let the car drive for us.

Stu <spamme@deadpelican.com>
White Plains, NY USA - Tuesday, August 24, 2004 at 05:33:56 (PDT)

In theory you are correct, but here is the real problem: The cars that are merging onto the freeway via an onramp should merge into traffic as soon as they can rather than SPEED UP IN THE LANE THAT IS ENDING, SO THEY CAN GET PAST AS MANY CARS AS THEY CAN, THEN JUMP IN FRONT OF ANOTHER CAR that may have already let several cars merge in.
Lissa <mdfletcher11@yahoo.com>
USA - Wednesday, August 18, 2004 at 20:33:33 (PDT)
Bill: As with most of the commenters, I have thought about these things for many years and out of curiousity found your site after an "enforcer" cut me off at a construction zone last night. Long ago I believed that best behavior was for everyone to move over as soon as possible, but eventually decided that the zipper approach is best. Recently, I have noticed that PennDOT is advising travellers to "Maintain lanes until the merge point." On two occasions at such merges, I have had drivers (both times of large pickups) pull into the left hand lane in order to force all drivers to merge into the left. Same thing happened to me last night in Ohio.

I believe that PennDOT's zipper scheme works best because of an additional factor that is not included in your simple model--the additional damping factor caused by the much longer time period it takes for tractor trailers to accelerate from a stop, particularly on an uphill grade. In a one-lane bottleneck, this damping factor can be profound, especially where there is heavy truck traffic. When the line starts from a stop, gaps of one or more truck-lengths can appear between each pair of trucks. With zipper merging, three, four or sometimes more cars can easily fit in between each pair of trucks.

The self-appointed enforcers who attempt to block the second lane may generating a great feeling of accomplishment for themselves, but they are slowing wasting everyone's time.
Jim Wiggin <wigREMOVE TO MAILgin@attglobal.net>
Columbus, OH USA - Monday, August 02, 2004 at 11:36:13 (PDT)

if a car is going 90mph on the highway and a cop is five miles behind how fast does the cop have to go to catch up?
paul <da_icon1@hotmail.com>
queens, ny USA - Thursday, July 22, 2004 at 07:55:58 (PDT)
You say in a response to a comment below:

[What?!! I think you didn't look at those animations. In the unjammed version on the right, the total flow is doubled: two cars per second go past the blinking arrow, and also the speed of the cars is 5x faster. In real life it could be more than this because it takes a very long time to "take turns" at the head of the jam. The benefits of unjammed merge zones are very large. But there is a big problem: once the jam is removed, WILL it rapidly reappear again? When traffic is even more dense, then I suspect it's impossible to maintain the "unjammed" condition. -billb]

The problem that you're having is that for every mile of road in your second animation, you've taken half the cars off of that road. All those cars are stuck back in Redmond now while your nicely oiled gears on the evergreen bridge are happily working away.

You should consider a principle that I think is a good one: You can't create antitraffic ex-nihilo.

You've acknowledged that you can't have any effect on the cars in front of you, so the bottom line is that you're not going to get home any faster by creating antitraffic, and if you're one of the cars that can't fit on this reduced-capacity roadway, then you're not going to get home faster by ANYONE creating antitraffic.
[Let me try again. At a merge zone, once a "standing wave" develops, the downstream highway clears out because the merge zone is behaving as a bottleneck. A huge backup develops upstream of the merge zone. Now as you rightly say, it's impossible to create "antitraffic" without also creating a dense area behind. Or in other words, an individual driver can only move a standing wave backwards. But at merge zones this has a profound result! If a driver can move the standing wave back a few hundred feet, then the merge zone itself will no longer be jammed. Without the solid-packed standing wave, cars can easily zipper-merge together. The original traffic jam (the standing wave) is not gone of course. But it has stopped growing. It no longer behaves as a bottleneck. So the final key to all of this is: if drivers can very early pull the standing wave away from the merge zone, then that standing wave will still be very small when its growth is halted. But if the standing wave remains pinned at the merge zone for hours, it grows enormous, and our halting its growth doesn't improve things much. It ESPECIALLY doesn't improve things if the giant standing wave is going to evaporate all by itself when traffic becomes low for the evening. So the moral is: jam busting can be extremely effective if an informed jam busting driver comes by every so often. But if a jam is allowed to grow for hours before a "buster" arrives and tries to pull it backwards, then nobody will even notice that the gigantic jam has stopped growing. -billb]
Robert Nelson <rnelson@ber.org>
Shoreline, WA USA - Friday, July 16, 2004 at 07:40:55 (PDT)

First of all, I think this is a great and actually very important theory. I have found myself thinking these very thoughts over and over. The highways are definitely NOT the place for mindless behavior! People feel so victimized by traffic jams, and obviously never stop to consider that they have more of a say-so in the deal than they suppose.

I do have a question-- I am pretty busy so didn't look at the FAQ section, so sorry if this is a repeat. I am wondering if there is any source where one can look up the "history" of the traffic jam phenomenon...? For instance, when and where was the first documented traffic jam? Is there a place where one can look up studies that have been done about traffic jams? Thank you! Great site, I'm definitely coming back. (Kristi)
Kristi <RScribes@juno.com>
Denver, CO USA - Thursday, July 15, 2004 at 15:45:14 (PDT)

Great site, and great concept. I'm looking forward to getting my license soon to try and test this theory. However, drivers in Israel are notoriously raged, so I'm not sure slowing down will work without retaliation.

one other problem I encountered while reading the site is this: what all these methods do is only make the 'traffic jam' more bearable, mentally. They won't let you get to your destination any faster, though...

for instance, when you show two variants of the traffic jam, where in one, everyone's pushing forward and condensing, and in the other, people let spaces build and drive faster. in that case, a car that is in the 50th place behind the first would get to point 'x' (point 'x' being after the traffic jam, where traffic is normal in both variants) the same time in both variants. it would only seem more fluid for the car taht's driving by your theory... am I mistaken?
Twinpraetor <Twinpraetor@yahoo.com>
Tel Aviv, N/A Israel - Thursday, May 20, 2004 at 01:54:45 (PDT)

I was quite impressed with what you have done here. I, myself am an antitraffic supporter, and have been utilizing the technique on the North Dallas Tollway for months now. I was excited to find your site and its in-depth approach to the subject. Here is my main comment....how can we organize? How can we easily and effectively get this information out to all of the commuters I see everyday.
Most drivers are so anxious to get to their destination, they punch their cars forward, riding up on the cars in front, not letting others merge...stop and go, stop and go. If there were a way to get the message across that EVERYONE would get home quicker and less stressfully if they follow a few simple rules. I would love to be involved in a re-education effort to change our rushhour habits....any ideas?

LeeDon <ashwin@anidlemind.com>
Chapel Hill, NC USA - Friday, May 14, 2004 at 17:44:37 (PDT)
This was a very interesting site, it defined Newtons First and Third laws of physics, as well as incorporated the law of inertia. Also clearly defined the geometric pathagorin theroem in which cars move at a steady rate. We're planning on commuting to Seattle to try this experimentation using several trials, to see for ourselves if you are truly full of shit!
Darwin Fish and Natalie Shrek <weluvphysics@aol.com>
USA - Thursday, May 06, 2004 at 09:25:19 (PDT)
Neat site, and certainly brings back memories of a lecture our applied math professor gave in grad school yeeeeeeears ago. He modeled traffic as fluid flow in a pipe, and when the density and speed were great enough, the flow goes "supercritical". Once it is supercritical, any random fluctuation (a driver gawking at a sign) will cause shock waves. Depending on the density or speed, the shock wave will either propagate forward through the traffic or back. I sure wish I remembered the math . . .
Jessie <carman_jessie@hotmail.com>
Manama, Bahrain - Tuesday, May 04, 2004 at 01:39:48 (PDT)
Here's another idea I had that might actually have some real effect on traffic patterns: The New York State Thruway Authority Tarp Company.
Rubbernecking on the opposite side of a highway from where an accident is, is the cause of needless traffic. There is no physics capacity problem. This is a social engineering problem. So I propose, the Tarp Company. At the site of an accident or ANYTHING 'interesting', the tarp company shows up and puts up a huge sail (there are some wind problems, I realize) but something to make the drivers quickly lose interest in what's going on, on the other side of the roadway so they don't slow down to take a look.

Stu <spamme@deadpelican.com>
White Plains, ny USA - Tuesday, April 27, 2004 at 10:46:31 (PDT)
I don't know if somebody mentioned this, but let me explain something I figured out about traffic. Actually some are here: http://nyti.dyn.ee:81/learnedcat items 30, 31 and 32. As you are, I'm an amateur traffic dynamicist and the merging problem can be explained this way. Fill up a two liter soda bottle with water, turn it upside down and watch the water pour out. There are about 5 lanes of water in the bottle, and only one that goes out the bottle (at the cap)
In order for traffic in five lanes to flow at the same speed in one lane, that one lane would have to be going 5 times as fast, but do people speed up at merges? no, the slow down making the backup worse. All that crap about "if people would just not bunch up and let people in, there wouldn't be any merge problems" is all bull. Physics doesn't allow for it. Period.

Stu <spamme@deadpelican.com>
White Plains, ny USA - Tuesday, April 27, 2004 at 10:38:27 (PDT)
I thought there might have been a chance to encounter the term "correlation length of the system". It's inversely proportional to "stress in the system" brought in by stressed drivers.
Jan Storms <jan@>
Haarlem, Nederland - Saturday, April 10, 2004 at 13:49:15 (PDT)
Someone GETS it...greetings and kudos Bill, for taking the time to inform others by posting all this.

This is a wonderful site. Chock full of interesting and informative information on traffic and flow. Especially the 'cures'.

As an airborne traffic-reporter in Los Angeles (who also drives 75 - 100 a day on those same roads), i can second your thoughts on most of these dilemas.

Our roadways are - for the most part - constant, yet the number of vehicles using them is ever-expanding. Thus, creating quite a problem. It takes a bit of thinking, planning and COOPERATION from others on the road to make this all work.

Will definitely create a link to your site for others to explore and learn from.

Keep up the great work!

...taylor (non-expert...just an observer)
M taylor baez <EyeintheLAsky at ya-hoo dot com>
Ca USA - Saturday, April 10, 2004 at 12:03:29 (PDT)

I have just found the perfect site for car mad science students in Oman. Thank you
KathyS <kathys@squ.edu.om>
Muscat, Oman - Wednesday, March 24, 2004 at 23:30:47 (PST)
For many years I have suspected the traffic wave phenomena. Your articles make it very clear. They should be required reading in any driving education program. I have pointed out your articles to my local newspaper (Doctor Gridlock at the Washington Post).
Tim Brown <tbrown59@verizon.net>
Wash, DC USA - Monday, March 22, 2004 at 10:46:59 (PST)
Honestly, I have actually thought the same thoughts as you are explaining on your web site. It is very interesting to me. I drive one hour each way to work five days a week, and I have plenty of time to analyze traffic behavoir. It really does act like one being rather than thousands of people. What really makes me wonder is why do people insist on filling the gaps I try to leave between me and the car in front of me. It is comical. We, my family, observe this all the time and it does become entertaining to us. Thanks for your scientific analysis of the behavoir of traffic. This is the coolest website ever
cflukens <cflukens@aol.com>
Fremont, NC USA - Monday, July 05, 2004 at 08:25:27 (PDT)
just a small remark on your writings about trafic jams,
You might be interested to know that the technique you call 'rolling barrier of state troopers' is used in Belgium for already a very long time (I think about 6-8 years already). We have one three lane highway that brings all the trafic to the coast, and on sunny days, we have what we call 'blokrijden' or 'driving in blocks'. Basically what happens is the following... One motorcycle cop goes on the highway and drives in front of some people, they are obliged to stay behind him. The speedlimit is 120 kph here... so the cop typically drives about 90-100 kph (slower if needed). They allow for a large 'block' of moving cars to form, but little enough not to have the wave effect. Then, when the block has a sufficient size, another motorcycle cop goes in again and forms another block... Like that over and over... so we have big blocks of cars driving on the highway... I have to say it is very effective...

Geert V
Belgium - Monday, July 05, 2004 07:21:48 (PDT)

Older Email Messages



Guestbook script from Matt's Script Archive