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What causes traffic jams? The depressing answer may be nothing at all

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  • Eric Britton
    ... From: Robert Moskowitz [mailto:robertm@knowledgetree.com] The Physics of Gridlock What causes traffic jams? The depressing answer may be nothing at all by
    Message 1 of 2 , Nov 7, 2005
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       -----Original Message-----
      From: Robert Moskowitz [mailto:robertm@...]
       

      The Physics of Gridlock

       

      What causes traffic jams? The depressing answer may be nothing at all

       

      by Stephen Budiansky, Atlantic Monthly, Dec. 2000

      http://www.theatlantic.com/issues/2000/12/budiansky.htm

       

       

      BERTRAND Russell once observed that animal behaviorists studying the  problem-solving abilities of chimpanzees consistently seemed to detect  in their experimental subjects the "national characteristics" of the  scientists themselves. A divergence in the findings of the  practical-minded Americans and the theoretically inclined Germans was  particularly apparent.

       

      Animals studied by Americans rush about frantically, with an incredible  display of hustle and pep, and at last achieve the desired result by  chance. Animals observed by Germans sit still and think, and at last  evolve the solution out of their inner consciousness.

       

      In science, Germans tend to come up with things like the uncertainty  principle. Americans tend to come up with things like the atomic bomb.

       

       The latest field to host this conflict of national styles is one that  seems at first glance to offer little prospect of a sporting contest.  Bigger and better highways are as American as fast-food restaurants and  sport utility vehicles, and when it comes to making the crooked straight  and the rough places plain, the practicality of American traffic  engineers is hard to argue with. As an American academic discipline,  traffic engineering is centered in civil-engineering departments, and  civil engineers tend to believe in solving problems by going at them  head on. A recent study funded by nine state departments of  transportation to examine the doubling in congestion on urban highways  and primary roads that has occurred over the past two decades listed in  its final report various ways that traffic engineers have tried to  alleviate the problem. These included "add road space" and "lower the  number of vehicles." This would not, as the saying goes, appear to be  rocket science.

       

      Even when American traffic engineers have ventured closer to rocket  science, with computer simulations of traffic flow on multi-lane  highways, the results have tended to reinforce the American reputation  for practicality and level-headedness. The mathematical and computer  models indicate that when traffic jams occur, they are the result of  bottlenecks (merging lanes, bad curves, accidents), which constrict  flow. Find a way to eliminate the bottlenecks and flow will be restored.

       

      Such was the happy, practical, and deterministic state of affairs up  until a few years ago, when several German theoretical physicists began  publishing papers on traffic flow in Physical Review Letters, Journal of  Physics, Nature, and other publications not normally read by civil  engineers. The Germans had noticed that if one simulated the movement of  cars and trucks on a highway using the well-established equations that  describe how the molecules of a gas move, some distinctly eerie results  emerged. Cars do not behave exactly like gas molecules, to be sure: for  example, drivers try to avoid collisions by slowing down when they get  too near another car, whereas gas molecules have no such aversion. But  the physicists added some terms to the equations to take the differences  into account, and the overall description of traffic as a flowing gas  has proved to be a very good one. The moving-gas model of traffic  reproduces many phenomena seen in real-world traffic. When a flowing gas  encounters a bottleneck, for example, it becomes compressed as the  molecules suddenly crowd together -- and that compression travels back  through the stream of oncoming gas as a shock wave. That is precisely  analogous to the well-known slowing and queuing of cars behind a traffic  bottleneck: as cars slow at the obstruction, cars behind them slow too,  which causes a wave of stop-and-go movement to be transmitted "upstream"  along the highway.

       

      The eeriest thing that came out of these equations, however, was the  implication that traffic congestion can arise completely spontaneously  under certain circumstances. No bottlenecks or other external causes are  necessary. Traffic can be flowing freely along, at a density still well  below what the road can handle, and then suddenly gel into a slow-moving  ooze. Under the right conditions a small, brief, and local fluctuation  in the speed or spacing of cars -- the sort of fluctuation that happens  all the time just by chance on a busy highway -- is all it takes to  trigger a system-wide breakdown that persists for hours after the blip  that triggered it is gone. In fact, the Germans' analysis suggested,  such spontaneous breakdowns in traffic flow probably occur quite  frequently on highways.

       

      Though a decidedly unnerving discovery, this was very much of a piece  with the results of mathematical models of many physical and biological  systems that exhibit the phenomena popularized under the heading "chaos  theory." In any complex interacting system with many parts, each of  which affects the others, tiny fluctuations can grow in huge but  unpredictable ways. Scientists refer to these as nonlinear phenomena --  phenomena in which seemingly negligible changes in one variable can have  disproportionately great consequences. Nonlinear properties have been  discovered in the mathematical equations that describe weather, chemical  reactions, and populations of biological organisms. Some combinations of  variables for these equations give rise to sudden "phase shifts," in  which the solution to the equation jumps abruptly from one value to  another; others set off truly chaotic situations in which for a time the  solution to the equation fluctuates wildly and without any seeming  pattern, and then suddenly calms down.

       

      Such mathematical discoveries do seem to be borne out in the real world.  Biological populations often exhibit erratic booms and busts that cannot  be explained by any external cause. Long-term weather patterns defy  prediction by the most powerful supercomputers. And a whole class of  chemical reactions has been discovered in which the chemicals do not  merely react and create a product, as they did in high school chemistry  class, but oscillate back and forth between reactants and products.  (Some especially nice ones cause color changes in the solution, so you  can sit there and watch the stuff in the beaker go back and forth every  few seconds.) The consistent story in all these discoveries is that the  components of the system and their interactions themselves -- rather  than any external cause -- give rise to the nonlinear behavior of the  system as a whole. A rough analogy is a dozen dogs standing on a water  bed. If one dog moves, he starts the bed sloshing around, which causes  another dog to lose his balance and shift his weight, which sets up  another wave of disturbance, until true chaos is reached.

       

      In the case of traffic, the German physicists -- principally Dirk  Helbing and Boris Kerner, of Stuttgart -- found that given a certain  combination of vehicle density and vehicle flow rate along a highway,  the solution to their equations undergoes a sudden phase shift from  freely moving traffic to what they call "synchronized traffic." Cars in  all lanes abruptly slow down and start moving at the same speed as the  cars in adjacent lanes, which makes passing impossible and can cause the  whole system to jam up for hours.

       

      In the traditional picture of traffic flow and congestion, the number of  cars per minute that pass a given point on the highway at first steadily  increases as the density of cars on the highway increases. (As long as  everything keeps moving freely, the more cars there are on a mile of a  highway, the more flow by per minute.) Eventually, however, further  increases in density will cause a decrease in flow, as drivers begin  braking to maintain a safe distance from the cars in front of them. A  graph of flow versus density thus forms an inverted V shape. The uphill  side corresponds to free flow, the downhill to congested flow. The  Germans found, in effect, that under the right (or, rather, wrong)  circumstances the solution to the equations can tunnel right through  this hill without ever reaching the top, jumping from a state of  (submaximal) free flow straight to congestion.

       

      Such a leap from one state to another is like what happens when a  chemical substance changes phase from vapor to liquid. It often happens  that water in a cloud remains in the gas phase even after temperature  and density have reached the point where it could condense into water  droplets. Only when a speck of dust happens along, providing a surface  on which condensation can take place (a "condensation nucleus"), does  the transition finally occur. Helbing and Kerner basically found that  free flow and synchronized flow can occur under the same conditions, and  that under such "metastable" conditions a small fluctuation in traffic  density can act as the speck of dust causing the shift from one to the  other.

       

      Worse, they found that it is easier to start a traffic jam than to stop  one. The phase shifts they discovered exhibit what is known in the  terminology of nonlinear phenomena as hysteresis. That is, a small and  transient increase in, say, the number of cars entering a highway from a  ramp can trigger a breakdown in flow, but even after the on-ramp traffic  drops to its original level (in fact, even after it drops well below its  original level), the traffic jam persists. Looking at actual data  recorded by sensors on Dutch and German highways, the physicists found  apparent examples of this phenomenon in action, in which a sluggish  synchronized flow came on suddenly and persisted for hours, even after  the density of traffic had dropped.

       

      If breakdowns in flow can result from such small and random  fluctuations, then the world is a very different place from the one that  most traffic engineers are accustomed to. The very notion of maximum  capacity for a highway is called into question, because even at traffic  densities well below what a highway is designed to handle, jams can  spontaneously arise. "If this flow breakdown can take place just  anywhere," says James Banks, a professor of civil and environmental  engineering at San Diego State University, "then we're in trouble,  because there's a lot more potential for congested traffic than we  thought was the case. And it makes a control strategy much more difficult."

       

      For example, it may not be enough simply to limit the rate at which cars  are allowed to enter a highway, as is now done on some congested  freeways; rather, it may be necessary to time each car's entry precisely  to coincide with a transient drop in density along the main road, thus  aiming to smooth out the fluctuations that can trigger a phase shift.  There may even be situations in which widening roads or "metering"  on-ramp flow could backfire, making flow breakdowns more likely.  Preventing flow breakdowns in a nonlinear, chaotic world could  ultimately require realizing an Orwellian idea that has been suggested  from time to time: directly controlling the speed and spacing of  individual cars along a highway with central computers and sensors that  communicate with each car's engine and brake controls.

       

      To say that not all American traffic engineers like these discoveries in  chaos theory and their implications for traffic is an understatement.  Banks acknowledges that there has been a strong, almost visceral,  reaction against the Germans' conclusion, because of its assault on  rational determinism and common sense, and also on what might be termed  culture-of-science grounds. "Scientists and engineers are human  beings,"he says, "and the first reaction is, These guys are not only  physicists -- they also have a knack for getting themselves in the  press. So right away there's an envy factor: Who do these guys think  they are?" It doesn't help that the German theoreticians' papers are  very difficult to understand. "They're written in such a way that those  of us who aren't physicists never know if it's their English, or whether  they're using physics jargon, or whether they just don't make sense,"  Banks says.

       

      The Americans also question how well the Germans' theoretical results  relate to traffic in the real world. All mathematical models involve  assumptions, and just because a model re-creates certain real-world  phenomena doesn't mean it accurately reflects reality in toto; there is  always the possibility that the weird properties of the equations are  artifacts of the model itself and its assumptions. The Germans' theory  "is one plausible description," says Carroll Messer, a research engineer  at Texas A&M University, using words that are obviously chosen  carefully, "but that's not saying it's been verified." Indeed, some  American researchers have questioned whether elaborate chaos-theory  interpretations are needed at all, since at least some of the traffic  phenomena the Germans' theories predict seem to be much like things that  have been appearing in the traffic-engineering literature under other  names for years, and these have straightforward cause-and-effect  explanations. Banks published a paper in 1999 pointing out that data  from monitors that record how many cars pass a fixed point -- the sort  of data the Germans obtained from Dutch and German highways, which they  say verify their predictions -- often fail to capture the complete  picture of what is happening on the road. He suggests that the behavior  of drivers may in fact offer a simpler explanation for the phase shifts  and other nonlinear features of the Germans' theoretical models. A  sudden slowdown in traffic may have less to do with chaos theory and  self-organizing phenomena of systems than with driver psychology.  Synchronized flow, for example, has appeared in American traffic  literature for decades, under the name "speed sympathy," and Banks says  it often happens as traffic gets heavier simply because of the way  individual drivers react to changing conditions. As the passing lane  gets more crowded, aggressive drivers move to other lanes to try to  pass, which also tends to homogenize the speed between lanes. Another  leveling force is that when a driver in a fast lane brakes a bit to  maintain a safe distance, the shock wave travels back much more rapidly  than it would in other lanes, because each following driver has to react  more quickly. So as a road becomes congested, the faster-moving traffic  is the first to slow down.

       

      Thus many American traffic engineers insist that when breakdowns in flow  occur for no apparent reason, it is only because no one has looked hard  enough to find the reason, which could be anything from a bad stretch of  pavement to a deer running across the road. Much work is now under way  on both sides of the Atlantic on a "theory of bottlenecks" that may help  to settle the matter.

       

      Even if traffic engineers manage to slay the mathematical bogeyman that  theoretical physics and chaos theory have unleashed, another bogeyman  may be lurking nearby. It turns out that the properties collectively  exhibited by large numbers of cars moving over a network of roadways  have many mathematical features in common with the behavior of other  things that flow over networks, such as data carried by telephone lines  and the Internet. The mathematics of networks is a well-studied topic in  communications research, and a recent paper draws on this body of theory  to establish an interesting paradox about the flow of vehicular traffic:  adding a new road segment to an existing network of roadways can under  certain circumstances reduce the car-carrying capacity of the network as  a whole. The safest advice for budding engineers may be, If you want  determinacy, stick to something simple -- like rockets or atomic bombs.

       

      Stephen Budiansky is a correspondent for The Atlantic. Illustration by Maris Bishofs.

       

      Copyright © 2000 by The Atlantic Monthly Company. All rights reserved. The Atlantic Monthly; December 2000; The Physics of Gridlock - 00.12;  Volume 286, No. 6; page 20-24.

       

       

       

       Links to related material on other Web sites.

       

      Institute of Transportation Engineers Home Page "ITE members are traffic engineers, transportation planners and other  professionals who are responsible for meeting society's needs for safe  and efficient surface transportation through planning, designing,  implementing, operating and maintaining systems worldwide." The site  offers technical information, conference and event listings, publication  notices, discussion listservs, and job listings.

       

      Computer Models for Traffic Flow "This applet demonstrates the simulation of traffic flow by several  computer models, some of them cellular automata, some based on partial  differential equations or differential-difference equations." Posted by  a physicist at Otto-von-Guericke University, Magdeburg, Germany.

       

      "Further on down the road," by Philip Ball, Nature, (1998) "You thought you were just a poor, down-trodden commuter. Little did you  know that you are in fact taking part in an experiment on the physics of  self-organization."

       

    • Carlos F. Pardo
      Reg. Moskowitz article, it’s easier just to start using cars less than now, instead of finding ways to move them somehow with physics or any other science.
      Message 2 of 2 , Nov 10, 2005
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        Reg. Moskowitz article, it’s easier just to start using cars less than now, instead of finding ways to move them somehow with physics or any other science. Also, the first annotation about American vs. German scientists is due to methodological procedures (early behaviourism vs. Gestalt theory), so they would obviously have different results!

         

        Best regards,

         

        Carlos F. Pardo

        Coordinador de Proyecto

        GTZ- Proyecto de Transporte Urbano Sostenible para América Latina y el Caribe- SUTP LAC
        Cr. 14 # 94A-24 of. 409
        Bogotá D.C., Colombia
        Tel:  +57 (1) 635 9048

        Fax: +57 (1) 635 9015 / 236 2309
        Mobile: +57 (3) 15 802 4115
        e-mail: carlos.pardo@...
        Página: www.sutp.org

        - Visite nuestra nueva sección de Latinoamérica y el Caribe en http://www.sutp.org/esp/espindex.htm

        - Únase al grupo de discusión de Transporte Sostenible en Latinoamérica en http://groups.yahoo.com/group/sutp-lac/join

         


        De: NewMobilityCafe@yahoogroups.com [mailto:NewMobilityCafe@yahoogroups.com] En nombre de Eric Britton
        Enviado el: Lunes, 07 de Noviembre de 2005 08:12 p.m.
        Para: NewMobilityCafe@yahoogroups.com
        Asunto: [NewMobilityCafe] What causes traffic jams? The depressing answer may be nothing at all

         

         -----Original Message-----
        From: Robert Moskowitz [mailto:robertm@...]
         

        The Physics of Gridlock

         

        What causes traffic jams? The depressing answer may be nothing at all

         

        by Stephen Budiansky, Atlantic Monthly, Dec. 2000

        http://www.theatlantic.com/issues/2000/12/budiansky.htm

         

         

        BERTRAND Russell once observed that animal behaviorists studying the  problem-solving abilities of chimpanzees consistently seemed to detect  in their experimental subjects the "national characteristics" of the  scientists themselves. A divergence in the findings of the  practical-minded Americans and the theoretically inclined Germans was  particularly apparent.

         

        Animals studied by Americans rush about frantically, with an incredible  display of hustle and pep, and at last achieve the desired result by  chance. Animals observed by Germans sit still and think, and at last  evolve the solution out of their inner consciousness.

         

        In science, Germans tend to come up with things like the uncertainty  principle. Americans tend to come up with things like the atomic bomb.

         

         The latest field to host this conflict of national styles is one that  seems at first glance to offer little prospect of a sporting contest.  Bigger and better highways are as American as fast-food restaurants and  sport utility vehicles, and when it comes to making the crooked straight  and the rough places plain, the practicality of American traffic  engineers is hard to argue with. As an American academic discipline,  traffic engineering is centered in civil-engineering departments, and  civil engineers tend to believe in solving problems by going at them  head on. A recent study funded by nine state departments of  transportation to examine the doubling in congestion on urban highways  and primary roads that has occurred over the past two decades listed in  its final report various ways that traffic engineers have tried to  alleviate the problem. These included "add road space" and "lower the  number of vehicles." This would not, as the saying goes, appear to be  rocket science.

         

        Even when American traffic engineers have ventured closer to rocket  science, with computer simulations of traffic flow on multi-lane  highways, the results have tended to reinforce the American reputation  for practicality and level-headedness. The mathematical and computer  models indicate that when traffic jams occur, they are the result of  bottlenecks (merging lanes, bad curves, accidents), which constrict  flow. Find a way to eliminate the bottlenecks and flow will be restored.

         

        Such was the happy, practical, and deterministic state of affairs up  until a few years ago, when several German theoretical physicists began  publishing papers on traffic flow in Physical Review Letters, Journal of  Physics, Nature, and other publications not normally read by civil  engineers. The Germans had noticed that if one simulated the movement of  cars and trucks on a highway using the well-established equations that  describe how the molecules of a gas move, some distinctly eerie results  emerged. Cars do not behave exactly like gas molecules, to be sure: for  example, drivers try to avoid collisions by slowing down when they get  too near another car, whereas gas molecules have no such aversion. But  the physicists added some terms to the equations to take the differences  into account, and the overall description of traffic as a flowing gas  has proved to be a very good one. The moving-gas model of traffic  reproduces many phenomena seen in real-world traffic. When a flowing gas  encounters a bottleneck, for example, it becomes compressed as the  molecules suddenly crowd together -- and that compression travels back  through the stream of oncoming gas as a shock wave. That is precisely  analogous to the well-known slowing and queuing of cars behind a traffic  bottleneck: as cars slow at the obstruction, cars behind them slow too,  which causes a wave of stop-and-go movement to be transmitted "upstream"  along the highway.

         

        The eeriest thing that came out of these equations, however, was the  implication that traffic congestion can arise completely spontaneously  under certain circumstances. No bottlenecks or other external causes are  necessary. Traffic can be flowing freely along, at a density still well  below what the road can handle, and then suddenly gel into a slow-moving  ooze. Under the right conditions a small, brief, and local fluctuation  in the speed or spacing of cars -- the sort of fluctuation that happens  all the time just by chance on a busy highway -- is all it takes to  trigger a system-wide breakdown that persists for hours after the blip  that triggered it is gone. In fact, the Germans' analysis suggested,  such spontaneous breakdowns in traffic flow probably occur quite  frequently on highways.

         

        Though a decidedly unnerving discovery, this was very much of a piece  with the results of mathematical models of many physical and biological  systems that exhibit the phenomena popularized under the heading "chaos  theory." In any complex interacting system with many parts, each of  which affects the others, tiny fluctuations can grow in huge but  unpredictable ways. Scientists refer to these as nonlinear phenomena --  phenomena in which seemingly negligible changes in one variable can have  disproportionately great consequences. Nonlinear properties have been  discovered in the mathematical equations that describe weather, chemical  reactions, and populations of biological organisms. Some combinations of  variables for these equations give rise to sudden "phase shifts," in  which the solution to the equation jumps abruptly from one value to  another; others set off truly chaotic situations in which for a time the  solution to the equation fluctuates wildly and without any seeming  pattern, and then suddenly calms down.

         

        Such mathematical discoveries do seem to be borne out in the real world.  Biological populations often exhibit erratic booms and busts that cannot  be explained by any external cause. Long-term weather patterns defy  prediction by the most powerful supercomputers. And a whole class of  chemical reactions has been discovered in which the chemicals do not  merely react and create a product, as they did in high school chemistry  class, but oscillate back and forth between reactants and products.  (Some especially nice ones cause color changes in the solution, so you  can sit there and watch the stuff in the beaker go back and forth every  few seconds.) The consistent story in all these discoveries is that the  components of the system and their interactions themselves -- rather  than any external cause -- give rise to the nonlinear behavior of the  system as a whole. A rough analogy is a dozen dogs standing on a water  bed. If one dog moves, he starts the bed sloshing around, which causes  another dog to lose his balance and shift his weight, which sets up  another wave of disturbance, until true chaos is reached.

         

        In the case of traffic, the German physicists -- principally Dirk  Helbing and Boris Kerner, of Stuttgart -- found that given a certain  combination of vehicle density and vehicle flow rate along a highway,  the solution to their equations undergoes a sudden phase shift from  freely moving traffic to what they call "synchronized traffic." Cars in  all lanes abruptly slow down and start moving at the same speed as the  cars in adjacent lanes, which makes passing impossible and can cause the  whole system to jam up for hours.

         

        In the traditional picture of traffic flow and congestion, the number of  cars per minute that pass a given point on the highway at first steadily  increases as the density of cars on the highway increases. (As long as  everything keeps moving freely, the more cars there are on a mile of a  highway, the more flow by per minute.) Eventually, however, further  increases in density will cause a decrease in flow, as drivers begin  braking to maintain a safe distance from the cars in front of them. A  graph of flow versus density thus forms an inverted V shape. The uphill  side corresponds to free flow, the downhill to congested flow. The  Germans found, in effect, that under the right (or, rather, wrong)  circumstances the solution to the equations can tunnel right through  this hill without ever reaching the top, jumping from a state of  (submaximal) free flow straight to congestion.

         

        Such a leap from one state to another is like what happens when a  chemical substance changes phase from vapor to liquid. It often happens  that water in a cloud remains in the gas phase even after temperature  and density have reached the point where it could condense into water  droplets. Only when a speck of dust happens along, providing a surface  on which condensation can take place (a "condensation nucleus"), does  the transition finally occur. Helbing and Kerner basically found that  free flow and synchronized flow can occur under the same conditions, and  that under such "metastable" conditions a small fluctuation in traffic  density can act as the speck of dust causing the shift from one to the  other.

         

        Worse, they found that it is easier to start a traffic jam than to stop  one. The phase shifts they discovered exhibit what is known in the  terminology of nonlinear phenomena as hysteresis. That is, a small and  transient increase in, say, the number of cars entering a highway from a  ramp can trigger a breakdown in flow, but even after the on-ramp traffic  drops to its original level (in fact, even after it drops well below its  original level), the traffic jam persists. Looking at actual data  recorded by sensors on Dutch and German highways, the physicists found  apparent examples of this phenomenon in action, in which a sluggish  synchronized flow came on suddenly and persisted for hours, even after  the density of traffic had dropped.

         

        If breakdowns in flow can result from such small and random  fluctuations, then the world is a very different place from the one that  most traffic engineers are accustomed to. The very notion of maximum  capacity for a highway is called into question, because even at traffic  densities well below what a highway is designed to handle, jams can  spontaneously arise. "If this flow breakdown can take place just  anywhere," says James Banks, a professor of civil and environmental  engineering at San Diego State University , "then we're in trouble,  because there's a lot more potential for congested traffic than we  thought was the case. And it makes a control strategy much more difficult."

         

        For example, it may not be enough simply to limit the rate at which cars  are allowed to enter a highway, as is now done on some congested  freeways; rather, it may be necessary to time each car's entry precisely  to coincide with a transient drop in density along the main road, thus  aiming to smooth out the fluctuations that can trigger a phase shift.  There may even be situations in which widening roads or "metering"  on-ramp flow could backfire, making flow breakdowns more likely.  Preventing flow breakdowns in a nonlinear, chaotic world could  ultimately require realizing an Orwellian idea that has been suggested  from time to time: directly controlling the speed and spacing of  individual cars along a highway with central computers and sensors that  communicate with each car's engine and brake controls.

         

        To say that not all American traffic engineers like these discoveries in  chaos theory and their implications for traffic is an understatement.  Banks acknowledges that there has been a strong, almost visceral,  reaction against the Germans' conclusion, because of its assault on  rational determinism and common sense, and also on what might be termed  culture-of-science grounds. "Scientists and engineers are human  beings,"he says, "and the first reaction is, These guys are not only  physicists -- they also have a knack for getting themselves in the  press. So right away there's an envy factor: Who do these guys think  they are?" It doesn't help that the German theoreticians' papers are  very difficult to understand. "They're written in such a way that those  of us who aren't physicists never know if it's their English, or whether  they're using physics jargon, or whether they just don't make sense,"  Banks says.

         

        The Americans also question how well the Germans' theoretical results  relate to traffic in the real world. All mathematical models involve  assumptions, and just because a model re-creates certain real-world  phenomena doesn't mean it accurately reflects reality in toto; there is  always the possibility that the weird properties of the equations are  artifacts of the model itself and its assumptions. The Germans' theory  "is one plausible description," says Carroll Messer, a research engineer  at Texas A&M University , using words that are obviously chosen  carefully, "but that's not saying it's been verified." Indeed, some  American researchers have questioned whether elaborate chaos-theory  interpretations are needed at all, since at least some of the traffic  phenomena the Germans' theories predict seem to be much like things that  have been appearing in the traffic-engineering literature under other  names for years, and these have straightforward cause-and-effect  explanations. Banks published a paper in 1999 pointing out that data  from monitors that record how many cars pass a fixed point -- the sort  of data the Germans obtained from Dutch and German highways, which they  say verify their predictions -- often fail to capture the complete  picture of what is happening on the road. He suggests that the behavior  of drivers may in fact offer a simpler explanation for the phase shifts  and other nonlinear features of the Germans' theoretical models. A  sudden slowdown in traffic may have less to do with chaos theory and  self-organizing phenomena of systems than with driver psychology.  Synchronized flow, for example, has appeared in American traffic  literature for decades, under the name "speed sympathy," and Banks says  it often happens as traffic gets heavier simply because of the way  individual drivers react to changing conditions. As the passing lane  gets more crowded, aggressive drivers move to other lanes to try to  pass, which also tends to homogenize the speed between lanes. Another  leveling force is that when a driver in a fast lane brakes a bit to  maintain a safe distance, the shock wave travels back much more rapidly  than it would in other lanes, because each following driver has to react  more quickly. So as a road becomes congested, the faster-moving traffic  is the first to slow down.

         

        Thus many American traffic engineers insist that when breakdowns in flow  occur for no apparent reason, it is only because no one has looked hard  enough to find the reason, which could be anything from a bad stretch of  pavement to a deer running across the road. Much work is now under way  on both sides of the Atlantic on a "theory of bottlenecks" that may help  to settle the matter.

         

        Even if traffic engineers manage to slay the mathematical bogeyman that  theoretical physics and chaos theory have unleashed, another bogeyman  may be lurking nearby. It turns out that the properties collectively  exhibited by large numbers of cars moving over a network of roadways  have many mathematical features in common with the behavior of other  things that flow over networks, such as data carried by telephone lines  and the Internet. The mathematics of networks is a well-studied topic in  communications research, and a recent paper draws on this body of theory  to establish an interesting paradox about the flow of vehicular traffic:  adding a new road segment to an existing network of roadways can under  certain circumstances reduce the car-carrying capacity of the network as  a whole. The safest advice for budding engineers may be, If you want  determinacy, stick to something simple -- like rockets or atomic bombs.

         

        Stephen Budiansky is a correspondent for The Atlantic. Illustration by Maris Bishofs.

         

        Copyright © 2000 by The Atlantic Monthly Company. All rights reserved. The Atlantic Monthly; December 2000; The Physics of Gridlock - 00.12;  Volume 286, No. 6; page 20-24.

         

         

         

         Links to related material on other Web sites.

         

        Institute of Transportation Engineers Home Page "ITE members are traffic engineers, transportation planners and other  professionals who are responsible for meeting society's needs for safe  and efficient surface transportation through planning, designing,  implementing, operating and maintaining systems worldwide." The site  offers technical information, conference and event listings, publication  notices, discussion listservs, and job listings.

         

        Computer Models for Traffic Flow "This applet demonstrates the simulation of traffic flow by several  computer models, some of them cellular automata, some based on partial  differential equations or differential-difference equations." Posted by  a physicist at Otto-von-Guericke University , Magdeburg , Germany .

         

        "Further on down the road," by Philip Ball, Nature, (1998) "You thought you were just a poor, down-trodden commuter. Little did you  know that you are in fact taking part in an experiment on the physics of  self-organization."

         


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