To Tame Traffic, Go With The Flow

Wednesday, October 27th, 2010

I thought this was old news, but a recent Santa Fe Institute working paper demonstrates that traffic lights that measure traffic inflow and outflow and communicate with their nearest-neighbor lights can smooth traffic and achieve the green wave:

When that happens, no drivers have to wait very long and sections of road don’t become so filled with cars that there’s no room for entering vehicles when the light does go green.

To achieve this rare bliss, traffic lights usually are controlled from the top down, operating on an “optimal” cycle that maximizes the flow of traffic expected for particular times of day, such as rush hour. But even for a typical time on a typical day, there’s so much variability in the number of cars at each light and the direction each car takes leaving an intersection that roads can fill up. Combine this condition with overzealous drivers, and intersections easily become gridlocked. Equally frustrating is the opposite extreme, where a driver sits at a red light for minutes even though there’s no car in sight to take advantage of the intersecting green.

“It is actually not optimal control, because that average situation never occurs,” says complex-systems scientist Dirk Helbing of the Swiss Federal Institute of Technology Zurich, a coauthor of the new study. “Because of the large variability in the number of cars behind each red light, it means that although we have an optimal scheme, it’s optimal for a situation that does not occur.”

Helbing and his colleague Stefan Lämmer from the Dresden University of Technology in Germany decided to scrap the top-down approach and start at the bottom. They noted that when crowds of people are trying to move through a narrow space, such as through a door connecting two hallways, there’s a natural oscillation: A mass of people from one side will move through the door while the other people wait, then suddenly the flow switches direction.

“It looks like maybe there’s a traffic light, but there’s not. It’s actually the buildup of pressure on the side where people have to wait that eventually turns the flow direction,” says Helbing. “We thought we could maybe apply the same principle to intersections, that is, the traffic flow controls the traffic light rather than the other way around.”

Their arrangement puts two sensors at each intersection: One measures incoming flow and one measures outgoing flow. Lights are coordinated with every neighboring light, such that one light alerts the next, “Hey, heavy load coming through.”

That short-term anticipation gives lights at the next intersection enough time to prepare for the incoming platoon of vehicles, says Helbing. The whole point is to avoid stopping an incoming platoon. “It works surprisingly well,” he says. Gaps between platoons are opportunities to serve flows in other directions, and this local coordination naturally spreads throughout the system.

“It’s a paradoxical effect that occurs in complex systems,” says Helbing. “Surprisingly, delay processes can improve the system altogether. It is a slower-is-faster effect. You can increase the throughput — speed up the whole system — if you delay single processes within the system at the right time, for the right amount of time.”

The researchers ran a simulation of their approach in the city center of Dresden. The area has 13 traffic light–controlled intersections, 68 pedestrian crossings, a train station that serves more than 13,000 passengers on an average day and seven bus and tram lines that cross the network every 10 minutes in opposite directions. The flexible self-control approach reduced time stuck waiting in traffic by 56 percent for trams and buses, 9 percent for cars and trucks, and 36 percent for pedestrians crossing intersections. Dresden is now close to implementing the new system, says Helbing, and Zurich is also considering the approach.


  1. Great example of a Theory of Constraints Drum-Buffer-Rope application. The 56% reduction in average queue times is typical.

    In this case the rope is the communications between traffic signals, the buffer is the “right amount of time” used as the delay and the drum is the rate at which the road can safely handle the traffic demand.

    Put another way, the traditional traffic management approach is similar to Lean Manufacturing’s balanced production lines, only with the balance keyed to the clock time to meet average demand. Unfortunately, due to all kinds of variables including accidents, weather, driver behavior and statistical variation, a bottleneck (traffic jam) can easily occur. This bottleneck can occur anywhere so it cannot be managed in advance and the system cannot recover until the load decreases.

    Accidents, weather, etc. still affect the new traffic system in the posting but the system’s simple intelligence can restore maximum throughput far more quickly.

  2. Isegoria says:

    That’s interesting, Michael, because I was thinking just the opposite: a system of local optima is not an optimal system at all. Is it still drum-buffer-rope if every traffic light is a drum? Or would a canonical drum-buffer-rope traffic system tie all the lights to the nearby tunnel or bridge?

  3. Hi, great blog. I love your “filter” and take on the world.

    The article doesn’t go into the details but does say that “Lights are coordinated with every neighboring light, such that one light alerts the next, Hey, heavy load coming through.

    From that statement I’m inferring that the drum is not any one light or even every light. The system may not be that smart at all, but it certainly could be tied to a natural bottleneck as you suggest and use that as the drum, or the drum could be non-physical, as is the time of a strategic resource in project management. This might look like optimizing throughput in a section or to some “safe maximum” rate.

    My guess is that by connecting the in and out sensors of a series of lights together that they’ve created an implicit drum. Bohm meets Goldratt!

    Another possibly interesting system might use something similar to a TOC inventory dollar days calculation — incorporating time spent in some road section before a tunnel or bridge and the toll charge for that vehicle. Public transportation and commuter vehicles that might not pay tolls could have a higher pseudo-toll for this calculation, enabling road managers and planners an easy mechanism for lane assignments, signal gating, and such, depending upon their goals (such as getting private cars in and out of suburbia or encouraging mass transit.)

  4. Isegoria says:

    Thanks for the kind words, Michael. If you’re not the “Herbie” on any of your current projects, you might peruse the archives — or, at the very least, the Theory of Constraints category.

    Anyway, the reason I balked a bit at the drum-buffer-rope label is that most descriptions emphasize a single constraint as the drum, in contrast to the situation in a balanced production line, where the current constraint bounces around less predictably — which is how I see the traffic situation.

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