Traffic

by Tom Vanderbilt

  Or take what Daganzo has called the Los Gatos effect, after an uphill stretch of highway in California. You may have experienced this: Drivers seem reluctant to abandon the passing lane and join the lane of trucks chugging uphill, even when they are being pressured by other drivers, and even when the other lane is not crowded. What’s going on? Drivers may not want to give up the fast lane for fear of having trouble returning to it. They may also be unsure whether the person behind truly wants to go faster or is just keeping a tight space to prevent someone else from passing. A tight “platoon” forms, but for how long? We all see these odd patterns. One of the idiosyncrasies I have noticed in traffic flow is something I call “passive-aggressive passing.” You’re in the passing lane when suddenly the driver behind you pressures you to move into the slower right-hand lane. After you have done so, they then move into your lane, in front of you, and slow down, thus forcing you to pass them.

  The basic parameters of how highways perform have been gradually hammered out. One of the key performance measures is volume, also called flow, or the number of vehicles that pass a buried sensor or some other fixed point on the highway. At four a.m., before rush hour, cars may be zipping along a highway at 75 miles per hour. The volume is measured at 1,700 cars moving past a point in one hour. As rush hour begins, the volume quite naturally begins to rise in an upward curve, reaching a theoretical maximum of 2,400 cars traveling at 55 miles per hour. System-wise, this is traffic nirvana. Then, as additional vehicles enter the highway, the curve begins to drop. Suddenly, the volume is back at 1,700. This time the cars are going 35 miles per hour. “So you have the two 1,700s,” Helou says. “Same volume, completely different situation.”

  Because traffic moves in time and space, measurements like volume can be deceiving, as can the highway itself. Solo drivers sitting in a highly congested lane may look to the HOV lane next to them and think that it’s empty—a psychological condition so prevalent it even has a name, “empty lane syndrome.” Many times it just seems empty because of the large headways between vehicles moving at much higher speeds. That lane may actually be achieving the same volume as the lane you are in, but the fact that the drivers might be going upward of 50 miles per hour faster creates an illusion that it’s being underused. Of course, neither of these positive or negative individual outcomes—the driver whisking along at 80 miles per hour or the people stuck at 20 miles per hour in the congested lanes—are what’s best for the entire system. The ideal highway will move the most cars, most efficiently, at a speed just about halfway.

  Even as rush hour kicks in and the speed-flow curve begins to drop, traffic can perk along at what has been called “synchronized flow,” heavy but steady. But as more vehicles pile onto the highway from on-ramps, the “density,” or the number of cars actually found in a one-mile stretch (as opposed to passing a single spot), begins to thicken. At a certain point, the critical density (the moment, you will recall from before, when the locusts began their coordinated march), the flow begins to break down. Bottlenecks, fixed or moving, squeeze the flow like a narrowing pipe. There are simply too many cars for the road’s capacity.

  Ramp metering aims to keep the highway’s “main-line flow” below the critical density by not letting the system be flooded with incoming on-ramp cars. “If you allow unimpeded access, then you have a platoon of vehicles that are entering the main line,” says Helou. This means not only more cars but more cars jockeying to merge. Studies have shown that this is neither predictable nor always cooperative. “That [merging] eventually breaks down the right lane,” she says. “This overflows to the next lane, because people try to merge left before they get to it. And then the people in the second lane try to merge to the next lane before they get to it, so you break down the whole freeway.” A line of cars waiting to exit an off-ramp can trigger this same chain reaction, one study showed, even when all the other lanes were flowing nowhere near critical density.

  If done properly, ramp metering, by keeping the system below the critical density, finds that sweet spot in which the most vehicles can move at the highest speed through a section of highway. Engineers call this “throughput maximization.”

  A simple way to see this in action involves rice. Take a liter of rice and pour it, all at once, through a funnel and into an empty beaker. Note how long it takes. Next, take the same rice and pour it not all at once but in a smooth, controlled flow, and time that process. Which liter of rice gets through more quickly? In a demonstration of this simple experiment by the Washington DOT, it took forty seconds for one liter of rice to pass through the funnel using the first method. The second method took twenty-seven seconds, nearly one-third less time. What seemed slower was actually faster.

  Rice has more to do with traffic than you might think. Many people use water analogies when talking about traffic, because it’s a great way to describe concepts like volume and capacity. One example, used by Benjamin Coifman, an engineering professor at Ohio State University who specializes in traffic, is to think of a bucket of water with an inch-wide hole in the bottom. If the inflow into the bucket is half an inch in diameter, no water will accumulate. Raise it to two inches, however, and the water rises, even though some water is still exiting. Whether we drive into a jam (or a jam drives into us) depends on whether the “water”—that is, the traffic trying to flow through a bottleneck—is draining or rising. “As a driver, the first thing you encounter is the end of the queue,” Coifman told me. “The first thing you encounter is wherever the water level happens to be that day.” The bucket metaphor also teaches us something else about traffic: No matter how much capacity there is in the rest of the bucket (or on the roads), the size of the hole (or the bottleneck) dictates what gets through.

  At places like bottlenecks, however, traffic acts less like water (it does not speed up as highway “channels” narrow, for one) and more like rice: Cars, like grains, are discrete objects that act in peculiar ways. Rice is what’s called a “granular media,” a solid that can act like a liquid. Sidney Nagel, a physicist at the University of Chicago and an expert in granular materials, uses the analogy of adding a bit of sugar to a spoon. Pour too much, and the pile collapses. The sugar flows like a liquid as it collapses, but it’s really a group of interacting objects that do not easily interact. “They do not attract one another,” says Nagel. “All they can do is scatter off one another.” Put a bunch of granular materials together, and it is not easy to predict how they will interact. This is why grain silos are the building type most prone to collapse, and it’s also why my box of Cascadian Farm Purely O’s cereal begins to bow outward at the bottom after several pours.

  Why does the rice jam up as you pour it into the funnel? The inflow of rice exceeds the capacity of the funnel opening. The system gets denser and denser. Particles spend more time touching one another. More rice touches more rice. The rice gets “hung up” from the friction of the funnel walls. Sound familiar? “That’s like cars on the highway,” says Nagel. “And when you get narrowing of traffic, then that becomes very much stuff trying to flow through the hopper.”

  Pouring less rice at a time—or moving fewer cars—keeps more space, and fewer interactions, between the grains. Things flow faster. As intuitive as the “slower is faster” idea is, it’s not always easy for a driver stuck in traffic to accept. In 1999, a state senator from Minnesota, claiming that ramp metering in the Twin Cities was doing more harm than good, launched a “Freedom to Drive” proposal that called for, among other things, shutting down the meters. The legislation died, but under another bill a ramp-meter “holiday” was declared. For two months the meters were turned off. Drivers could enter the highway at will, on so-called sane lanes, unfettered by troublesome red lights. And what happened? The system got worse. Speeds dropped, travel times went up. One study showed that certain highway sections had double the productivity with ramp meters than without. The meters went back on.

  The “slower is faster” idea shows up often in traffic. The classi
c example concerns roundabouts. Many people are under the mistaken impression that roundabouts cause congestion. But a properly designed roundabout can reduce delays by up to 65 percent over an intersection with traffic signals or stop signs. Sure, an individual driver who has a green light may fly through a signalized intersection much more quickly than through a roundabout. Roughly half the time, however, the light will not be green; and even if it is green there is often a rolling queue of vehicles just starting up from the previous red. Add to this such complications as left-turn arrows, which prevent the majority of drivers from moving, not to mention the “clearance phase,” that capacity-deadening moment when all lights must be red, to make sure everyone has cleared the intersection. Drivers do have to slow down as they approach a roundabout, but under typical traffic conditions they rarely have to stop.

  In the 1960s, experiments were made at the Holland Tunnel, one of the main arteries for traffic coming into and leaving New York City. When cars were allowed to enter the tunnel in the usual way, with no restrictions, the two-lane tunnel could handle 1,176 cars per hour, at an optimal speed of 19 miles per hour. But in a trial, the tunnel authorities capped the number of cars that could enter the tunnel every two minutes to 44. If that many cars got in before two minutes were up, a police officer made the next group of cars wait ten seconds at the tunnel entrance. The result? The tunnel now handled 1,320 vehicles per hour. (I will explain why shortly.)

  On streets with traffic signals, engineers set progressions with a certain speed in mind that will enable the driver to hit a line of constant greens. To drive faster than this only ensures that the driver will be forced to come to a stop at the next red light. Each stop requires deceleration and, more important, acceleration, which costs the driver in time and fuel. A queue of drivers stopped at a light is a gathering of “start-up lost time,” as engineers call it (in an appropriately forlorn echo of Proust). The first cars in a queue squander an average of two seconds each, two seconds that would not have been lost had the car sailed through at the “saturation-flow” rate. The first driver at a light that turns from red to green, because he must react to the change, make sure that the intersection is empty, and accelerate from a standstill, generates the most “lost time.” The light is green, but for a moment the intersection is empty. The second driver creates a bit less lost time, the third driver less still, and so on (assuming everyone is reacting as soon as they can, which is not a given). SUVs, because they are longer (on average, 14 percent longer than cars), and take longer to accelerate, can create up to 20 percent more lost time.

  Some of the start-up lost time could be “found” if drivers approached at a slower, more uniform speed that did not require them to come to a stop. (If they came too slowly, however, time would also be lost, as green signal time would be wasted on an empty intersection.) Much of the time being lost these days is “clearance lost time,” the time between signals when the intersection is momentarily empty. This is because traffic engineers are increasingly lengthening the “all-red phase,” meaning that when one direction gets the red, the competing direction has to wait nearly two seconds before getting a green. They do this because more people cannot seem to stop on red.

  Now picture a highway during stop-and-go traffic. Like those drivers stopped at the light, each time we stop and start in a jam we are generating lost time. Unsure of what the drivers ahead are doing, we move in an unsteady way. We are distracted for a moment and do not accelerate. Or we overreact to brake lights, stopping harder than we need to and losing more time. Drivers talking on cell phones may lose still more time through delayed reactions and slower speeds. The closer the vehicles are packed together, the more they affect one another. Everything becomes more unstable. “All of the excess ability for the system to take in any sort of disturbance is gone,” says Coifman. He uses the metaphor of five croquet balls. “If you put them a foot apart and tap one lightly, nothing happens to the other four. If you put them all up against one another and tap one lightly, the far one then moves out. When you get closer to capacity on the roadway, if there’s any one little tweak, it impacts a lot of the cars.”

  When the first in a group of closely spaced cars slows or stops, a “shock wave” is triggered that moves backward. The first car slows or stops, and the next one slows or stops a little farther back. This wave, whose speed usually seems to register at about 12 miles per hour, could theoretically go on for as long as there was a string of sufficiently dense traffic. Even a single car on a two-lane highway, by simply changing its speed with little rhyme or reason (as people so often seem to do, in what I like to call “speed-attention-deficit disorder”), can itself pump these waves back down a stream of following vehicles. Furthermore, even if that car’s average speed is fairly high, the fluctuations wreak progressive havoc. This was the secret behind the Holland Tunnel experiment: With cars limited to “platoons” of forty-four vehicles each, the shock waves that were triggered were confined to each group. The platoons were like croquet balls spaced apart.

  Many times we find ourselves stuck in traffic that seems to have no visible cause. Or we make it through a jam and begin to speed up, seeming to make progress, only to quickly drive into another jam. “Phantom jams,” these have been called, to the annoyance of some. “Phantom jams are in reality nonexistent,” thunders Michael Schreckenberg, a German physics professor at the University of Duisburg-Essen so noted for his traffic studies that he has acquired the epithet “jam professor” in the German media. There is always a reason for a jam, he says, even if it is not apparent. What seems to be a local disturbance might just be a wave pumped up from downstream in what is in reality a big, wide moving jam. It is wrong, says Schreckenberg, to simply call the whole thing stop-and-go traffic: “Stop-and-go is the dynamic within a jam.”

  We fall for the phantom-jam illusion because traffic happens in both time and space. You may be driving into a space where a jam has been. Or you may not be driving into a jam—instead, the jam might be driving into you. “In my bucket analogy,” says Coifman, “the driver would be a water molecule. If the water level’s rising, then the jam’s coming to us.” We are also driving into history—or, perhaps more accurately, we are being driven back into history. By the time we actually arrive where something triggered the shock wave, in all likelihood the event will be only a memory. It may have been an accident, now cleared. “The queue’s going to persist for a while as it’s dissipating,” says Coifman. “It’s that water sitting in the bucket. In this case you’ve enlarged the hole in the bucket, but it does not disappear instantaneously.”

  Or the hiccup in heavy traffic that passes through you might be the echo of someone who, forward in space and backward in time, did something as simple as change lanes. The car that changes lanes moves, eating up capacity in the new lane and causing the driver behind to slow; it also frees up capacity in the lane it has left, which triggers a bit of acceleration in that lane. These actions ripple backward in a kind of seesaw effect. This is why, if you pick one car in the neighboring lane as your benchmark, you will often find yourself passing that car and being passed by that car continuously. This is equilibrium asserting itself, the accordion of traffic flow stretching and compressing, the lingering chain reaction of everyone who thought they could get a better deal.

  Since it takes so long for traffic to resume flowing freely once it has plunged past the critical density, it would seem the best way to avoid the ill effects of a jam would be not to drive into it, or let it drive into you, in the first place. This is the thought that occurred one afternoon a few years ago to Bill Beatty, a self-described “amateur traffic physicist” who works in the physics laboratory at the University of Washington. Beatty was on State Highway 202, returning from a state fair. The road, a “little four-lane,” was thronged with traffic from the fair. The traffic was “completely periodic,” as he describes it. “You’d drive real fast and then almost get to sixty and then you’d slow down and come to a stop, for almost two minut
es,” he says.

  So Beatty decided to try an experiment: He would drive only 35 miles per hour. Rather than let the waves drive into him, he would “eat the waves,” or subdue the wildly varying oscillations of stop-and-go traffic. Instead of tailgating and constantly braking, he would try to drive at a uniform speed, leaving a large gap between himself and the car ahead. When he looked in his rearview mirror, he saw a revelation in the pattern of headlights: Those behind him looked to be in a regular pattern, while the other lane had clusters of clumped stop-and-go vehicles. He had “damped” the wave, leveled off the extremes. “It cuts off the mountains and puts them in the valley,” he says of his technique. “So instead of getting to drive at sixty miles per hour briefly, you’re forced to drive at thirty-five miles per hour. But you don’t have to stop, either.”

  Without analyzing the total traffic flow of the highway, it would be hard to know for sure what good Beatty’s experiment did. People may have just merged in front of him, pushing him back (if he wanted to keep the same following distance), while those behind him who thought he was going too slow may have jumped into the next lane, causing additional disturbance. But even if Beatty’s technique did little more than take a tightly congested traffic jam and stretch it backward, so that a car spent the same amount of time traveling a section of road, it would still save fuel and reduce the risk of rear-end accidents—two added benefits for the same price. Only how do you get everyone to cooperate? How do you prevent people, as so often seems to happen, from simply consuming the space you have left open? How, in essence, can we simulate ant-trail behavior on the highway?

  One way is the “variable speed limit” system now being used on any number of roads, from England’s M25 “controlled motorway” to sections of the German autobahn to the Western Ring Road in Melbourne, Australia. These systems link loop detectors in the road to changeable speed-limit signs. When the system notices that traffic has slowed, it sends an alert upstream. The approaching drivers are given a mandatory speed limit (enforced by license-plate cameras) that should, in theory, lessen the effects of a shock wave. Even though many drivers suspected it was the lowering of speeds to 40 kilometers per hour that was causing the congestion, a study of the M25 found that drivers spent less time in stop-and-go traffic, which not only helped lower the crash rate by 20 percent (itself good for traffic flow) but cut vehicle emissions by nearly 10 percent. As drivers adjusted to the system, their trip times declined. Again, slower can be faster.