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Crosstown Traffic

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In the 1993 film Falling Down, Michael Douglas plays William Foster, a.k.a. D-FENS, a recently divorced engineer who has been laid off from his job with a defense agency. We first meet him when he’s on his way to his daughter’s birthday party on a hot summer day, stuck in a traffic jam on a Los Angeles freeway with no air conditioning and an errant fly buzzing about the baking interior.  The stress builds until Foster snaps, abandoning his car on the freeway and heading off on foot, eventually going on a violent rampage across the city as he unleashes all his anger and frustration at being a forgotten man.

It’s road rage, writ large, and while we certainly can’t condone Foster’s behavior, who among us hasn’t felt that slow burn of frustration and impotent rage when trapped in a seemingly infinite line of cars creeping along the freeway? I spent two years commuting from the east side to the west side of Los Angeles, and I assure you that Dante’s Ninth Circle of Hell is that stretch of I-10 between Crenshaw and Robertson Boulevard at 8:30 AM (although other commuters might point to the I-405).

Nor is this merely a Los Angeles problem, although the city of angels frequently tops the list of places with the worst traffic in the country, along with Washington, DC, San Francisco, New York City, Atlanta, Chicago, and even Seattle. Traffic flow is a big problem in most major urban centers. The average US motorist spends 36 hours every year in traffic delays.

Fortunately, physicists are hot on the case, and have been busily studying traffic patterns and trying to build mathematical models to devise some kind of solution to keep us all from snapping and turning into D-FENS.

Going With the Flow

Conventional scientific wisdom has compared traffic jams to the process of freezing — namely, a phase transition between a liquid to a solid. Think of it this way: On a sparsely populated highway the cars are far apart and can move at whatever speed they choose while freely maneuvering between lanes — much like the movement of molecules in a gas. In heavier traffic, the “car molecules” are more densely packed, with less room to maneuver, so cars move at slower average speeds and traffic behaves more like a liquid.

If the “car molecules” become too densely packed, their speed is reduced, and their range of movement is restricted, to such an extent that they can “crystallize” into a solid. So traffic jams aren’t random. There’s a threshold “value” to the flux of cars traveling along a highway, and if that threshold is exceeded sufficiently — if local perturbations are large enough — then the flowing “liquid” traffic jams into a “solid,” akin to the critical temperature/pressure point threshold where water turns into ice.

It’s a useful but rather crude analogy. The situation is a bit more complicated than that, and scientists would love to understand the phenomenon in far greater detail. A major breakthrough occurred in 1998, when a physicist named Boris Kerner with the Daimler Benz Research Institute in Stuttgart, Germany, published a paper in Physical Review Letters. (Kerner has written an entire book on the subject, a massive, highly technical tome called The Physics of Traffic: Empirical Freeway Pattern Features, Engineering Applications and Theory.) Kerner analyzed data collected from several years of traffic monitored along German highways and found that traffic tends to follow the physics of self organization.

Based on that data, he developed a model that essentially broke traffic into three basic categories: freely flowing, jammed (solid state), and a bizarre intermediate state called synchronized flow, in which densely packed “car molecules” move in unison, like members of a marching band. When this happens — when all the cars are traveling at close to the same average speed because of the vehicle density on the roadway — they become highly dependent on one another. A physicist might compare the relationship to the correlated motion of electrons in metals, which gives rise to weird phenomena like superconductivity.

Highly correlated traffic means that a tiny perturbation — a butterfly flapping its wings, or a single driver braking unexpectedly  — will send little ripples of corresponding slowdowns through the entire chain of cars behind him/her. That’s one reason why slowdowns and traffic jams occur most commonly at merge points, especially exit and entrance ramps, or when lanes are closed due to road construction.

A state of steady synchronized flow, punctuated by these tiny ripple effects (“narrow jams”) can persist indefinitely, but the balance is delicate and highly unstable. If the volume of cars continues to increase, the density continues to increase, and eventually you get a “pinch effect” — that frustrating “stop and go” phenomenon, in which you escape one narrow jam only to encounter another a little further down toe road, until they all converge into a single wide jam. Traffic comes to a standstill. Collective road rage may ensue, and the next thing you know, Michael Douglas is on a shotgun-toting rampage.

Kerner’s self-organizing model would seem to indicate that while drivers think they are acting of their own accord, they are really just behaving like a tiny unthinking particle, a single grain of sand in an enormous sand pile, unconsciously following the “rules” of self-organized flow.

But that’s not quite the case: driver behavior can impact traffic patterns in significant ways. The unpredictability of human behavior is one reason why many traffic models aren’t as accurate in their predictions as they could be.

In 2004, a team of German scientists led by Michael Schreckenberg (University of Duisberg-Essen) sought to rectify that. They came up with new predictive models that took realistic driver behavior into account: you know, all those jerks on the highway who keep changing lanes and cutting in front of you just when your lane is starting to move, which in turn arouses your competitive instincts so that you (a) honk angrily and tailgate him for a few yards, determined not to let any other “cheaters” infringe on your valuable space, or (b) switch over to a new lane in turn, thereby causing another slowdown. Not that we’re bitter. As team member Robert Barlovic put it, “Real drivers tend to hinder each other when doing things like changing lanes.”

The model was quickly put into use to forecast traffic along the autobahn network around Cologne, based on real-time traffic data gathered by  embedded sensors in the road. The problem is that this broad access to more accurate information actually changed traffic patterns. People modified their behavior based on the new information provided by the forecast models: they all flocked to the same exits to avoid upcoming congestion, for example. This in turn made those models less accurate in their predictions. More information is not, as it turns out, the answer to all our traffic woes.

Other cities are trying similar methods. In May, San Francisco started up its Smarter Traveler Research Initiative, which combines real-time traffic data with databases of past traffic patterns — information already collected by numerous companies like Microsoft and Google — to predict jams “up to 40 minutes into the future. Drivers are then automatically sent an email or text message of conditions on their regular commute before their trip begins.” That way they can alter their routes and avoid the problem areas. Only a dozen or so drivers are currently enrolled in this test program, and MIT engineer Moshe Ben-Akiva told New Scientist that when all drivers have access, you’ll likely get the same flocking effect as in Cologne, Germany. “You inform them of congestion in one location, and the congestion just shifts to another route.”

Phantom Traffic Jams

Most maddening of all is that there doesn’t always seem to any good reason for the congestion. Granted, it’s always heavier near an exit ramp, but more often than not, you creep along, expecting to pass some god-awful wreck… and there’s nothing. Traffic suddenly starts to pick up just as mysteriously as it slowed down.  In 2008, a team of Japanese scientists at Nagoya University came to the somewhat obvious conclusion that there are just too many cars on the road. It’s a density problem. There’s a certain critical threshold for traffic, and once it’s reached, even tiny fluctuations can cause a chain reaction that eventually results in a jam.

They tested their theory by studying 22 cars driving around a circular track, asking the drivers to move at a steady 19 MPH. Twenty-two cars was the magic number to achieve critical density on the track. The drivers did their best to maintain the requested speed, but there were still tiny fluctuations of braking and speeding up, and this reverberated around the track. The result: occasional brief standstills. Get enough of those over the course of rush hour on a weekday morning (or evening), and eventually you’ll get a traffic jam.

A bunch of MIT mathematicians were so intrigued by the Nagoya researchers’ findings that they developed their own models for these kinds of phantom traffic jams (or “jamitons”), publishing their conclusions in Physical Review E in May 2009. Those equations are very similar to the ones used to describe the shock waves produced by explosions, adding specific variables such as traffic speed and car density to calculus the precise conditions these “jamitons” are most likely to form. Just as with shock waves, jamitons have a kind of “sonic point” that divides the flow of cars into “upstream” and “downstream” segments. Those segments can’t communicate with other. That’s why, if you’re in a car stuck “downstream,” you have no way of knowing if there’s an accident or some other obstacle impeding traffic flow further “upstream” — or if conditions are about to just as suddenly improve.

Gabor Orosz of the University of Exeter is a mathematician who has also concluded that “the effect of spontaneous jam formation (caused by tiny fluctuations above a critical traffic density) is the main reason for traffic jams.” He has studied the reaction time delay of drivers and found that a late reaction of just one second by a single driver can have a major impact, particularly at faster speeds. A vehicle dropping its speed from 80 MPH to 65 MPH may cause a ripple that later vanishes, while dropping its speed from 80 MPH to 62 MPH may cause a ripple that is amplified and leads to traffic jams.

So by now, physicists and mathematicians have successfully defined the problem of chronic traffic jams. Alas, a solution has proved more difficult to come by.

The Ants Go Marching One by One

Perhaps we can take a few lessons from the Formicidae family, a.k.a., the humble ant. A paper appeared on the arXiv in October 2008 demonstrating that ants might be better than humans at regulating their own traffic efficiently. Dirk Helbing is a “congestion expert” at Dresden University of Technology, who teamed up with a few colleagues to build a tiny ant motorway in the lab, featuring several “carriageways” between an ant nest and a source of sugar.  It didn’t take long for a few ants to find the shortest route to the sugar, leaving a handy chemical trail for their friends to follow. And eventually so many ants were following that trail it became saturated with ants.

Now, if this happened on the I-10 (or a tiny ant version of it), it would be the point of critical density, and the tiny fluctuations in driver behavior would build up and form traffic jams, especially at the interchanges. But that’s not what happened with the ants. At those critical interchanges, just when the route was about to become too clogged, ants returning to the nest would physically block the way for ants on their way to the sugar source. Not consciously, mind you — there just wasn’t enough room. The other ants had to find an alternate route.

As result, traffic jams never formed. Somehow the humble ant has cracked on of the most challenging problems in traffic physics, not to mention the routing of data over the Internet and other networked systems: “the efficient distribution of limited resources by decentralized, individual decisions.”

Helbing realizes that it’s not practical to let cars collide with oncoming cars to control traffic, but he figures that you can force cars traveling in one direction to alert oncoming cars to the traffic conditions ahead, so they can take evasive action if they need to. The problem with this, as mentioned above, is that the evasive actions can cause their own clogged conditions.

So why not build more roads, or widen the highways to accommodate more cars? It turns out this might not be an optimal solution, either, according to a paper in Physical Review Letters in August 2008 (2008 was a banner year for traffic research). A collaboration of Korean and US physicists conducted a study and concluded that building more roads can actually make traffic congestion worse. It’s a paradox, stemming from the fact that individual drivers act solely in their own best interest — say, the quickest route for them — and instead end up slowing traffic as a whole.

How many times have you seen someone drive along the shoulder or an exit lane during heavy traffic to sneak a few spots ahead in line, thereby slowing the methodical merging to nearly a standstill? If someone cut in line in the grocery store, they would be shamed into at least feeling a twinge of guilt about it, and I’ve seen cashiers actually toss those customers to the back of the line in retaliation for their rudeness. But in a car, you have the protection of privacy — mobile privacy — and the offender doesn’t stick around long enough for the social peer pressure to kick in.

It’s basically a conflict of interest between individual and collective benefits — the researchers dubbed it “the Price of Anarchy” — and the result is 30% longer commute times overall. How do we change human nature, which seems to act counter to the collective best interest when it comes to traffic? Well, you can try to force a change in behavior, like the ants. The Korean/US team found that by simply shutting down a few select streets, they eliminated certain travel options, thereby bringing the interests of single drivers more in line with the interests of collective commuters as a whole.

Here’s their illustration. Select starting and ending points linked by two different routes: one over a short but narrow bridge, and a longer one over a wide freeway. If half of the drivers choose the bridge and the other half choose the highway, the combined travel for all is minimized — except many more drivers opt for the shorter route over the narrow bridge, which quickly becomes clogged. When it gets clogged enough, some of the drivers switch back to the highway.

This process plays itself out over time until the traffic reaches some sort of equilibrium, a state in which no one driver can reduce their commute simply by switching to the other one. But the combined total commute time is significantly longer even after all that switching than if the drivers had just split down the middle over each route to begin with. Shutting down carefully selected streets can encourage drivers to make the optimal choices — without realizing they are doing so.

Once again, the ants turn out to be smarter than humans, at least when it comes to optimizing traffic for the good of the collective whole. French biologist Vincet Fourcassie (Paul Sabatier University in Narbonne) set up his own tiny two-way ant highway with a bridge of varying width between the nest and a foraging site to study the behavior of both garden and leaf-cutting ants. And he observed very definite “rules of the road” that came into play — the ant equivalent to not cutting in line at the supermarket. For instance, when the bridge was narrowed so that only one garden ant could pass, an ant can’t enter the bridge if another ant is moving towards it in the opposite direction, but the same ant can follow another ant directly in front of it. Leaf-cutting ants have more practical concerns: here, if an ant is carrying a leaf (food) back to the nest, that ant receives right of way on the bridge; the non-leaf-bearing ants will yield, and/or refuse to pass the ant bearing food.

Basically, ants are better at regulating their behavior for the common good. They even will use their tiny bodies to plug potholes in the trail leading back to the nest, for faster, more efficient delivery of food. Human beings, in contrast, constantly struggle with the conflict between the common good and “What’s in it for me?” We could learn a few things from the ants.

[NOTE: This post was adapted from two older blog posts from the Cocktail Party Physics archives: "Crosstown Traffic" (January 2009) and "Road Rage Redux" (August 2006).]

Jennifer Ouellette About the Author: Jennifer Ouellette is a science writer who loves to indulge her inner geek by finding quirky connections between physics, popular culture, and the world at large. Follow on Twitter @JenLucPiquant.

The views expressed are those of the author and are not necessarily those of Scientific American.

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  1. 1. Mike W. 9:35 am 08/17/2011

    Does that mean if people had a ‘traffic density’ function on their satnavs or smartphones, people would start driving to avoid congestion that they otherwise wouldn’t know about and traffic would dissipate over many routes more efficiently?

    I wish I had the money and resources to write that smartphone app!!

    Link to this
  2. 2. Larry Ayers 10:33 am 08/17/2011

    Pretty cool that you could incorporate two old posts (which I hadn’t read) into one new one, with current research added. Interesting comparisons between vehicular traffic and ant traffic!

    Link to this
  3. 3. Jennifer Ouellette 3:50 pm 08/17/2011

    @Mike: So far, no — more information about congestion available to more people just results in more clustering on the alternate routes, per the second section of the post. Although that app would likely be a money-maker, so why not? :) Really, the only solution is lowering the density of the cars on the road. More telecommuting, more folks living within walking distance of work/school and other resources, etc. might make a difference. But people do love their cars!

    @Larry: I’ve been following traffic physics for several years now. 2008 was an especially good year for papers on the subject, and I expect we’ll be due for another flurry of them at some point. The nice thing about having done the blog for so long (5 years and counting) is that over time, stuff I wrote about in, say, 2007, becomes relevant again as new research gets done.

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  4. 4. a_grade 5:42 am 08/18/2011

    “Fighting traffic congestion by building more roads is like fighting obesity by loosening you belt”
    Lowering the number of cars on the road is the best way to increase average speed.
    I remember finding webpage in 1999 that demonstrated the reaction time being the dominant effect with human drivers. I’ve long since lost it though.

    Would there be a solution by sending random/targetted green and red roads to GPS users to actually send the traffic elsewhere even though some of their red roads weren’t too bad.
    This would be something like the random back-off on ethernet collisions – ethernet gets congested when there’s too many users too !

    I guess people wouldn’t like it because they might think it would be like Singapore’s Odd and Even number plate road rationing.

    Nothing is common sense when it comes to humans.

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  5. 5. Mike W. 11:14 am 08/18/2011

    @Jennifer: I’ve been thinking this over and I don’t think what you say would necessarily have to be the case.

    If the most efficient way for traffic to flow is to disperse over choke sites relative to the capacity of each site, then it would be easy to do that with smart devices. Obviously devices with identical programmes that compute routes based on the same information, they’re all going to come up with the same recommended route. But to solve that issue, the app could be designed to rank best routes by how preferred, then assigning each a value to add up to 100 (or any arbitrary large number), then offset those values depending on how fast a choke point is going to become jammed, then having the app use a faux random number generator to select the route, proportions of those smart devices would divide traffic flow ahead of time to distribute the traffic efficiently.

    As long as you kept the software updated with information about how many cars are likely to be using the app at any given time, the values could be kept at an optimum.

    Theoretically it seems, to me, to be a workable solution for traffic inefficiently, and not just a money spinner.

    I would love to hear your thoughts.

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  6. 6. Mike W. 11:27 am 08/18/2011

    It reminds me of game theory in a lot of ways. The best result doesn’t necessarily come when all players are rational and have common knowledge. It’s a game only with thousands of players making a payoff matrix with millions of squares.

    Link to this
  7. 7. denisosu 9:37 pm 08/19/2011

    Great article! Your solid/liquid analogy reminds me of a comment by an Italian friend about traffic in Rome. In Rome, you have many more cars on narrower roads, and the driving seems crazier, yet the traffic flows much better than in many US cities. His explanation was that Italian traffic is like a liquid, while US traffic is like a particle flow. During my time in Rome, I came to realise this was true.
    For example, consider the case of a side-road entering a busier main road. In the US, cars wait their turn to enter the main road. Either they wait for a gap in the traffic, or a car on the main road stops (stopping all the cars behind it) to let them enter. In Rome, cars from the side-road enter the main road even when there isn’t a gap, and the cars on the main road slow down slightly, just enough to avoid hitting it. A similar pattern occurs at traffic lights, where instead of the three lanes that are marked, cars will go between lanes to get to the front.
    It looks like total chaos at first, until you realise, as my friend did, that it is in fact a much more efficient way of helping traffic flow – following the example of a fluid by effectively narrowing the streamlines at points where there is a contraction in the flow cross-section.
    It should be noted that this works wonderfully in Rome, where the drivers have been doing this all their lives – and where mostly they don’t see a minor bump as a reason to stop – in LA, you’d probably end up with multiple accidents, blocked highways and an overworked highway patrol …

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  8. 8. seanacoy 12:57 am 08/20/2011

    The comments about gps traffic alerts and anti-congestion apps reminds me of experiments I read about years ago to automate cars with instructions passed to them along wires imbedded in the roadways. Presumably this would remove people from the equation and produce synchronized flow. But I would posit that the synchronized flow would be not much more reliable than the syncflow with people doing the driving – because minor differences between individual cars (a defective mechanical or electronic part) and other butterflies (a gust of wind, a deer detected by radar, etc.) might still trigger solid states.

    I do like the idea, if algorithms are used to alert drivers of impending jams, that they are modulated/randomized so that not all drivers are sent the other way. Additionally, there could be a psychological feedback, so that drivers who consistently don’t follow directions would also get the “other” direction!

    Also, what happens when analogies are made to air traffic controls. In theory, minimum separation distances are mandatory – in three dimensions. To a certain extent, this is controlled by controlling take-offs. A traffic jam ala LA in the air would be impossible, since the planes would not stay airborne. (Of course, unlike cars, they could temporarily use a wider air lane.) The only situation I know where a similar kind of control is used for cars is on some major highways where on-ramps have lights to prevent more than one or two cars at a time coming on to a highway. This tends to reduce the interference with the syncflow but build up congestion on roads leading to the access points.

    Will solving the traffic flow problem mean saved fuel and an improved economy? If so, DARPA should get started on this.

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  9. 9. R.Blakely 4:26 am 08/20/2011

    Backward traffic rules, that is one of the reasons for traffic jams. Slower traffic should pull over for faster drivers to pass, instead of blocking traffic.
    Dual-highways should be used instead of multi-lane highways. This would permit use of the alternate highway when one highway is blocked. Barriers between the highways would prevent accidents from blocking both highways. Gaps in the barriers would allow movement between the highways.

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  10. 10. Dreaded Anomaly 5:26 pm 08/23/2011

    I think the solution here is to automate all traffic. Google has invented reliable cars that drive themselves; if all cars did this, that creates an entirely controlled system, and dealing with inefficient human reactions is no longer a problem.

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