Over a lunch I recently attended at the Applied Physics Laboratory at Johns Hopkins, the talk turned briefly to the difficulty of modeling human behavior in large-scale evacuations of people in cars, as occurred during some of the recent hurricanes. “What happens when the driver turns around and sees a big black cloud in the sky?” as one person put it.

Of course, modeling routine traffic behavior presents myriad challenges of its own, which is probably why it is still such a robust activity. As Dirk Helbing notes in his article, “Traffic and related self-driving many-particle systems,” in Reviews of Modern Physics, “Altogether, researchers from engineering, mathematics, operations research, and physics have probably suggested more than 100 different traffic models, which cannot all be covered by this review.” (the article, by the way, is 75 pages long).

Some of these consider traffic flow as a kind of fluid behavior, some have looked at the behavior of “car following,” how one driver is “attracted” and “repulsed” by the person in front of them (which then laid the challenge of how to model a single driver, with no one ahead of him), others have delved into “cellular automata.” Some have tried to break driver behavior down into a complex range of attributes. But as Philip Ball notes in his excellent book Critical Mass, “the more complex the model, the harder it becomes to know what outcomes are in any sense ‘fundamental’ aspects of traffic flow, and which follow from the details of the rules.”

So while large-scale models can with some success predict, say, the formation of traffic jams, there’s an inherent amount of built-in “noise,” e.g., human behavior. For example, I have a bit of an aversion to driving right next to someone. If I’m cruising along at a comfortable speed, but then notice a car in the neighboring lane is unnervingly keeping the same speed, I will accelerate or decelerate, to have my own pocket of space. Are all drivers like this? If not, how many? How do you model something like that?

Helbing suggests a few other sorts of potential problems. If a driver in one lane puts on their blinker as if to change, how does this effect drivers in neighboring lanes? (in New York, this often invites drivers in that lane to speed up, while the person wanting to change lanes gradually slows, slowing drivers in his lane, causing a weird see-saw between two lanes). Or drivers may keep a ‘headway’ that is shorter than they would truly like, to prevent other drivers from entering the gap. Or drivers may react to trucks differently than they do cars. The list goes on.

Or to take another example, a recent paper, “The butterfly effect: imbalances in lane change accommodation time and lasting disturbances, by Benjamin Coifman, Chao Wang, and Yiguang Xuan, (presented at a traffic flow symposium), looks at a seemingly simple process — changing lanes — and notes a curious property that has not been fully addressed in previous models. Briefly, the paper notes that drivers will respond differently when a vehicle ahead of them changes to another lane, versus when the vehicle has changed to their lane from another. In both cases, there will be some reaction, or “perturbation.” But the study, looking at probe vehicle data, suggests that “the response time to an exiting vehicle is longer than the response time to an entering vehicle.” Why? The authors suggest that when a vehicle enters, the following driver’s response is mandatory, but when a driver ahead exits out of the lane, it is at the discretion of the following driver how quickly they want to “close the gap” and return to some desired following distance. “On average,” they write, “the new lane completely accommodates the vehicle before the ‘hole’ the vehicle left behind in the old lane is filled.” (it also takes less time to brake than to accelerate). This seems minor, but of course each driver’s decision has an effect on every following driver, and it’s why something like a lane change can create “disturbances” within a traffic queue that were beyond the comprehension of previous models.

This all reminds me of a discussion I had with a hydrologist at the U.S. Army Corps of Engineers research complex in Vicksburg, Mississippi, a few years before Hurricane Katrina. He was talking about the epistemological challenges of modeling the behavior of things like rivers (perhaps even more complicated than highways), and building, in response, adequate measures in the forms of levees and the like.

“This is probably where we spend most of our day, every day, trying to determine what truth is,” he told me, as we stood near a scale-model replica of a river. “Truth consists of what’s physically happening in the field. Of course you can’t measure that either. We go out there and measure that, but there’s so much uncertainty in our measurements, that if you match that with a calculation, you could could be off. Where is truth? That’s the first thing. The next thing we discuss a lot is: How good is good enough? How good is good enough to make an engineering decision to build something? What is real? How good is good enough towards whatever is real? You don’t even know what the river conditions are. You don’t even know what the flow rate — there’s a stream coming in over here and one over here, and you don’t know what it does, so you might measure it; you can measure any spot really well but it’s changing all the time.

Just go out there and look over the overlook the river. You see upwellings. You see big eddys. It’s not steady by an stretch of the imagination. So if you sample for a long time, and get an answer that’s 3 feet per second, that’s not really truth. It’s varying all about that. That’s true if you sat there for an hour and took an average. But it’s changing, this way and that way. You don’t want to calculate something to calculate it, but you do want to make a decision. We do pour concrete. Somebody’s gotta decide where to pour. We have to make calls. There’s some tough calls. We’re not academics, this if flood protection, people’s lives are at stake. You make a conservative call, but you can’t afford to be so conservative that you’re not doing engineering. Those are the things that keep you awake at night.”

As valuable as modeling can be, it seems unlikely that we can ever really be certain about the behavior of large, complex systems, whether traffic, rivers, or the financial markets, which increasingly turned to sophisticated models that, in the end, could only tell their masters how an idealized market — indeed perhaps one without humans — would perform.

This entry was posted on Friday, January 30th, 2009 at 2:10 pm and is filed under Etc., Risk, Traffic Engineering, Traffic Wonkery, Uncategorized. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.