Effect Measure

One of the enduring mysteries is what causes traffic jams. Sometimes it’s obvious — sort of. I remember having to make a daily trip from New York to Bellevue Hospitals in New York down FDR Drive. At one spot the three southbound lanes suddenly widened into five lanes because of some construction and then, after about 100 yards, narrowed again to three lanes. If you didn’t know better you’d think the extra capacity of the roadway wouldn’t be a problem but in your mind’s eye you can see exactly what happened. All those cars that filled up the extra space had to reconverge to three lanes. The roodway aneurysm caused a terrible mess.

More often, though, the cause isn’t so clear. Every year we drive about 1000 miles to a vacation down Interstate 95 and every summer, reliably as clockwork, we hit a bad traffic mess just south of Washington, DC in northern Virginia, usually just after midday. It’s always the same. Traffic flows at about 30 miles an hour, then suddenly jams to a standstill, then a few miles an hour, then back to 30 for a short period, etc. It’s like those old slinky toys, coiled springs that go down flights of stairs (if you’ve never seen one you have no idea what I’m talking about and if you have, you know how hard it is to describe; but there’s a great one on Wikipedia here). Slinkys had clear and obvious waves of compression-decompression moving up and down them and that’s what the traffic situation in Virginia felt like. But there never seemed to be a clear cause for this problem. As quickly as it appears it just stops, after about 20 or 30 miles of driving hell. Now a team of mathematicians at the University of Exeter have analyzed it and come up with what they think is a model that explains it:.

The team developed a mathematical model to show the impact of unexpected events such as a lorry (tractor trailer) pulling out of its lane on a dual carriageway (divided highway with median between traffic going in opposite directions). Their model revealed that slowing down below a critical speed when reacting to such an event, a driver would force the car behind to slow down further and the next car back to reduce its speed further still. The result of this is that several miles back, cars would finally grind to a halt, with drivers oblivious to the reason for their delay.

The model predicts that this is a very typical scenario on a busy highway (above 15 vehicles per km). The jam moves backwards through the traffic creating a so-called ‘backward travelling wave’, which drivers may encounter many miles upstream, several minutes after it was triggered. (Science Daily)

Essentially the model says the problem can start when the reaction of a single driver is propagated down the line when traffic density and flow is sufficient, somewhat like what happens in a smoothly flowing liquid that becomes turbulent when it reaches a certain point (as measured by its Reynolds number). But because this models driver behaviors rather than an abstract continuum, it is more comprehensible:

This model takes into account the time-delay in drivers’ reactions, which lead to drivers braking more heavily than would have been necessary had they identified and reacted to a problem ahead a second earlier.

Dr Orosz continued: “When you tap your brake, the traffic may come to a full stand-still several miles behind you. It really matters how hard you brake – a slight braking from a driver who has identified a problem early will allow the traffic flow to remain smooth. Heavier braking, usually caused by a driver reacting late to a problem, can affect traffic flow for many miles.”

Fascinating work I will enjoy pondering the next time I am stuck in a traffic jam. Which will probably be tomorrow on the way to work.

Addendum: Coturnix (Blog Around the Clock) alerted us to an excellent post he wrote about a year ago on this topic with some good links therein and some interesting observations of his own. Recommended if this topic interests you (as it does me).

Comments

#1 Melanie
December 20, 2007

revere, it isn’t just I95. All of the rest of DC area hiways are parking lots for a substantial part of the day.
#2 Colst
December 20, 2007

“Drivers and policy-makers have not previously known why jams like this occur,” (from the sciencedaily article.

Bull. I read the same explanation in Newsweek; I think about a decade ago.
#3 Dave Briggs
December 20, 2007

Fascinating work I will enjoy pondering the next time I am stuck in a traffic jam. Which will probably be tomorrow on the way to work

Yes, fascinating! I am old enough to know what a Slinky is so that helps! LOL! I wonder how many other phenomenon we deal with are analogous to the Slinky? LOL. Perhaps you have hit on something that could be just the tip of the iceberg? Maybe there is some way we can incorporate the Slinky Phenomenon for that next trip to the moon, or to finally get some human boot marks on Mars? Time will tell! Thanks for the info!
Dave Briggs :~)
#4 Ambitwistor
December 20, 2007

What’s new in this study? Traffic engineers have known about traffic waves for some time (see Bill Beaty’s page for some nice animations).
#5 Ahcuah
December 20, 2007

Colst wrote:

Bull. I read the same explanation in Newsweek; I think about a decade ago.

Now that I think about it, back in the late 1970s I was taking a class from Gordon Baym dealing with solitons. One of the lectures took some traffic assumptions, including driver-reaction time, and with a few simplifications derived a very nice soliton equation.

While this new thing might be more sophisticated, I guess major features have been known for quite a while.
#6 revere
December 20, 2007

I have a couple of responses to the “what’s new” complaint (which may be valid; university PR depts. are doing this all the time). But what seems new here is that it is not a description of what we all see but a model that generates what we see. The model here is discrete, so it isn’t the same as a soliton solution, which is continuous (and involves non linear PDEs); and seems to be in terms of actual parameters of the roadway and the behavior of drivers. This, I think, is different, although others may know more about it. If so, I’d like to hear about it. There is other work with the same flavor described by Philip Ball in his very interesting book, Critical Mass (which I recommend), so this may indeed not be that new.
#7 Colst
December 20, 2007

I should be clear. I don’t doubt that the study has some novelty to it; I just think that statement in the Sciencedaily article (which probably came from a press release) is bull. This may be a more sophisticated model, but the cause was known.
#8 Coturnix
December 20, 2007

This may be interesting to you – I am still completely naive about the entire science of traffic.
#9 Ahcuah
December 20, 2007

Revere,

I agree that the discrete analysis and specific explanation of an overreaction to the initial braking is (probably?) new.

What actually is kind of interesting is how much of the behavior was still captured after doing all of the approximations that lead to solitons.
#10 M. Randolph Kruger
December 21, 2007

We have the same problem here in Memphis and the radio stations suggest that we turn into “pace cars” to keep it moving. Whenever you see a grouping of red lights starting to come on within line of sight in front, the cars are to slow behind it without hitting the brakes and drop back 5 mph and at least five car lengths and let the distance open up by about 1/4th mile. NO BRAKES! So most of them get it and three or four abreast we are rolling happily along and the morons that originally caused the problem that are trying to do 80 in a 55 up in front start to pull away from you. It opens up about 1/4th or 1/2 mile of clear road.

Each time they run into the red lights they are slowed and we are still rolling behind them with a lot of rolling distance in between. It keeps us all moving. It works and the traffic jam will go away after two or three passes from doing it. You get great participation and even if there is an accident to clear the pacers keep it moving. The helicopters even cite the cars on the radio that are doing a good job and tell them to speed up a bit or slow as they can see up in front. All anyone wants to do at 8 and 5 is either get to work or get home. Full stop is not an option and no one minds going 45 as long as its rolling.

Try it in just your lane and see if you dont get rid of that road rage… Have to here in Memphis, we all have 12 gauge pump guns in the back window on our pickup trucks and are packing under the right to carry law.
#11 Sarah
December 21, 2007

Kruger’s right. I do this all the time in Houston (don’t brake, just let off the gas) and it works for me. I figured out myself a long time ago that all it takes for a big traffic jam is some ramrod switching lanes too quickly, causing the guy behind him to slam on his brakes, and the guy behind him, and behind him, and so on, then people try to get out of that lane and cause the same ordeal in the lane next to them.

Tell me it didn’t take a room full of scientists to figure this crap out. I’m a 24 year old secretary. Come on guys. Go build a rocket or something.
#12 Ellen
December 21, 2007

Living in Baltimore, I travel down I-95 South fairly frequently, and there is ALWAYS a traffic jam just south of DC. No matter what time of day, it is always there. It is incredibly frustrating!
#13 Holly
December 21, 2007

I produce traffic reports for a newstalk station and its TV affiliate during the morning commute, so this stuff happens all the time. Idiotic drivers, that is. Not only is it the slamming on the breaks that creates instant back-ups, but volume, speed, distractions within the vehicle, weather conditions, and even the kind of car. We see more SUVs and semi-trucks involved in more accidents than anything, which isn’t surprising if you consider the general attitude of those drivers (which has also been studied and the results were obvious).

It’s the same concept of what happens at stop lights. You’ll be sitting behind say, a dozen cars at a red light and the light turns green. Of course you don’t get to go through the green light because by the time you get to the intersection, the light’s red again. Here’s the concept: if everyone started going at the exact same time after the light turned green, you not only would be able to get through the light yourself, but about twice the number as stated above would also get through that light.

Downtown Cincy if you hit one red light you’ll hit all of them.. BUT only if you accelerate to the speed limit and stop at the lights. We tested this out the other day, actually. My boyfriend, instead of stopping at the light, waiting ’til it turns and accelerating to the next light only to stop, he went an even 20mph and made all the lights! It was neat. BUT I agrgee with Sarah: I can’t believe scientists wasted their time on something that seems like common sense. Go build a rocket. lol.
#14 Ambitwistor
December 21, 2007

Revere,

“The model here is discrete, so it isn’t the same as a soliton solution, which is continuous (and involves non linear PDEs); and seems to be in terms of actual parameters of the roadway and the behavior of drivers. This, I think, is different, although others may know more about it.”

I’ve tried to track down the actual study, which I believe is this one.

Neither discrete models nor models which parameterize driver behaviors are new. What appears to be new in this study is an analysis of how traffic waves can appear in stable traffic flows. Evidently, it was previously thought that stop-and-go traffic waves should appear only when the traffic flow destabilizes.
#15 AGS
December 21, 2007

The speed of a car represents a curve that is steeper (is that a word?) on the braking side and less steep on the acceleration side (kind of a Chi square shaped curve). That is, cars slow down faster than they speed up. When you put a bunch of these curves side by side (like cars one in front of the other), you can imagine the effect of one car on the braking slope, requiring the cars behind it to brake, thus slowing their rate of progression (rate of speed change?). If cars speed up as quickly as they brake, there would, theoretically, be fewer traffic jams.
#16 RBailey
December 21, 2007

As someone who drives that nasty part of I-95 everyday, braking is only the tip of the iceberg here. Some of the other factors include:

1) Northern Virginia lacks secondary roads. The only road that parallels I-95 is US 1. And that route has been overdeveloped to the point it cannot handle its own traffic. One fender bender on either of these roads brings the entire I-95 corridor to a screeching halt.

2) The area south of Washington D.C. lacks safe and affordable housing. There’s safe housing (Starting about $1 million), or affordable housing (if you want to live in a neighborhood controlled by MS-13). The result, more people move out further, longer commutes, more traffic.

3)The bottleneck of too many on ramps in one place. The worst part of the 50 miles below D.C. is the end of the HOV lanes north of Quantico Marine Corps Base (traffic merging on left side of the highway). Combine this with the fact that there is an exit/entrance ramp almost across from it on the right side of the highway and the situation just gets worse. And to top it all off there are truck scales right there as well. Which means the trucks have to re-merge into traffic. Whatever momentum the truck had is lost, and it takes a while for them to get up to speed.

4) Virginians do not understand the concept of passing lanes and merging lanes. At any time of moderate traffic on this highway the center and left lane are full of cars not passing. This makes the speed demons jump into the right lane than back into the center, then the left, across three lanes to the shoulder… I think you get the point. But all that lane changing suddenly creates a whole lot of braking, see the entire article above.

The other concept, merge lanes? The Virginia Dept. of Transportations has actually put out signs lights saying don’t merge here… merge up there. When you have 5 different cars on different points of the merge lane trying to get into the main flow at the same time, you get 5 times as much slamming on the brakes.

Or you get the guy who doesn’t want anyone getting in front of him. So he moves half into the merge lane, shortening the merge area. When the lines that distinguish the merge lane as a seperate lane end… That’s the merge point.

There are however times you can avoid the worst traffic when passing through this area.

Summertime; If travelling south on a Friday or Saturday if you can’t get south of Fredericksburg, VA by 12 noon, wait until 6/7 PM. Strecth that out to 8:30 PM for any holiday weekends. Sundays, be north of Washington by 2pm or forget it until Midnight. The rest of the week, 5:30-8:00 AM avoid the inbound roads, from 2:30-6PM avoid the outbound roads.

During the winter peaks 5:30-8 AM (IN) / 2:30-6PM (OUT) seems to be consistent. Except for Thanksgiving and Christmas.

That’s why I’m stuck at work now until at least 7 tonight!
#17 etbnc
December 22, 2007

To me this illustrates the value of understanding our individual roles in a larger system.

The solutions mentioned here involve understanding that our individual decisions create consequences for other people in a larger system. The behaviors that exacerbate problems involve reacting to a single event or a single bit of information with no regard to potential ripple effects.

It seems to me there’s value in applying this insight to other aspects of our political, economic, and personal lives.

Thanks for bringing this to our attention (again, or for the first time).

Cheers
#18 Monimonika
December 22, 2007

I wonder, given the information provided by this and previous models of how traffic jams develop, how do those traffic jams (both preventable and non-preventable) eventually get resolved? In what ways can a full-stop (like due to a major vehicle crash that needs to be towed out of the way) traffic jam be turned back into smooth traffic in the shortest amount of time possible? In other words, what’s the reverse of this process?

Going by some “well, duh” wisdom, there eventually come times of the day when there are very few cars entering the roadways, thus creating extra space for the cars already on the roads to maneuver in. I have a feeling this is a significant part of resolving traffic jams, but I could be wrong.

Talking about “well, duh” wisdom, those who say that this study (and maybe others) was a waste of money due to the conclusions being “obvious”, are falling into the same kind of trap that alternative medicine supporters fall into. The trap is to accept conventional wisdom/common sense ideas at face-value without testing to see if your personal experience actually is universal/common/correlating.

As for the reason to do newer studies on phenomenon that previous studies have already been done on, well, there’s not only the part about testing new aspects of a phenomenon, but also to reconfirm and add more evidence to what was found out from the previous studies. It’s better to have several (good!) studies supporting a conclusion, rather than just a single (again, good!) study. You know, repeatability and whatnot.
#19 Tony
December 23, 2007

I second Kruger and Sarah’s assessment. Is this really a discovery? To me this is common sense. Of course, if the person ahead of you even taps their brakes, you’re going to, and in turn, will the person behind you. Duh!

The same patient, non-knee-jerk reaction works for me as well. Just let up off the gas, let the momentum keep you moving forward but at a decreasing speed as the space opens before you. The person behind you has no need to break suddenly or drop to an even slower velocity. (Oh, and if this wouldn’t work for it, you’re following too closely.)
#20 Monimonika
December 24, 2007

Tony wrote:

“Is this really a discovery? To me this is common sense. Of course, if the person ahead of you even taps their brakes, you’re going to, and in turn, will the person behind you. Duh!”

To me, it’s common sense that vaccination causes kids to become autistic. Kid gets vaccination when very young, soon after gets diagnosed as autistic. Duh! There can’t possibly be any other possible factors involved. So, it’s a waste of time and money to scientifically collect data to verify this very obvious, common sense, “well, duh!”, Truth. Why do more studies when we already have the perfectly good study from Andrew Wakefield that confirms this Truth?

If it’s not clear, the above was me being sarcastic. I do not subscribe to the “vaccines/mercury lead to autism” screed. Nor do I have any kids.

Although I do agree with Tony about whether or not this can be considered a “discovery”, I just can’t let pass his (and others’) notion that “common sense” things shouldn’t have to be tested or studied. Do Tony and the others think that it was obvious or common sense that a feather and a bowling ball fall at the same rates in a vacuum? That the flow of time is relative to how fast one is traveling?

There are a lot of other simplified examples that illustrate how “common sense” gets challenged, debunked (or confirmed), and then replaced (or refined) with another version of “common sense”. That saying about hindsight making things clearer also applies to Tony (and some others).
#21 Charles Roten
December 25, 2007

Sigh.

The things that get cited as “new” research these days.

Anyone who has driven for more than a year or two on the Metro Seattle freeways knows about the consequences of a single vehicle irrationally slowing down. And if they can be seen here, they can be seen on the DC Beltway or any other highway system running close to saturation.

I read the observation about soliton-like behavior about five years ago. It was referenced in a comment made to the old Netslaves web board, and the actual piece cited dated from almost 10 years ago: Traffic Waves.

The logic is pretty elementary for anyone who cut their teeth on nonlinear hyperbolic PDEs in grad school. Or got introduced to compression zones, rarefaction zones, and shock fitting in any other systematic way.