Control Engineering

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Could automated control help traffic move smoothly on superhighways?
October 29, 2007

I’m afraid not. I know a lot of very smart people are spending a lot of time and money trying to do it, but it won’t work. Don’t get me wrong, automated highways will likely reduce the accident rate by … a lot. It could also save a ton of energy and likely shorten average commute times on heavily used highways. But, the traffic will not flow more smoothly during heavy-use periods.

To understand why, we have to start with why traffic gets so messed up to begin with. Bear with me and we’ll get to the answer to your question at the end.

Traffic patterns are subject to instabilities called solitons, which are self-reinforcing solitary waves that appear in a number of energy-transport phenomena, such as light moving through an optical fiber, and patterns of automobile traffic moving on highways. While they are often triggered in traffic patterns by human behavior, they are not caused by it.

When the flow rate on a highway is less than about 900 cars per hour per lane (c/h/l), cars are spaced more than 4 seconds apart and move independently. You end up with a more-or-less Gaussian distribution of speeds centered somewhat above the posted speed limit.

Note that the number of cars physically on each mile of the highway (the density) has little to do with the flow rate in light traffic. The density is the number of cars per mile per lane (c/m/l). You multiply that by the speed (m/h) to get the flow rate. In light traffic, the two are independent.

As you push more vehicles onto the highway, the flow rate rises. Cars get closer, and drivers start taking other vehicles into account. This cooperation causes the dispersion (width of the Gaussian distribution) to drop, becoming very narrow as the flow rate approaches 1,800 c/h/l, which is the maximum capacity of any highway.

That limit is set by the average human reaction time of approximately 0.7 s. Exceeding that limit requires cars to be spaced so closely that drivers cannot react reliably to changes in time to avoid collisions.

At that point, you’re into catastrophe theory. We won’t go there today.

When the flow rate is constrained to 1,800 c/h/l, you can pack more cars on only by lowering the average speed. That is exactly why traffic slows nearly to a stop as you keep packing more cars onto the highway. Heavy traffic (900-1,800 c/h/l) is a regime where the local speed is inversely proportional to the local density.

Note that traffic can never completely stop. If it did, the flow rate would drop below the maximum limit, and start moving again. Instead, it must crawl along at the average speed of one car length per two seconds (about 7 mph).

To see how solitons appear in traffic, go back to the wide open highway with moderate traffic at about 900 c/h/l. A “wolf pack” is a soliton that moves at a speed slightly slower than the average vehicle speed within the pack, which is slower than the free-highway speed. Cars arrive at the back of the pack and slow down to a speed governed by the pack’s density. Cars at the pack’s front see clear highway ahead and accelerate to the free-highway speed. It’s as if cars “evaporate” off the pack’s front, only to be replaced by cars “condensing” onto the back.

In light traffic, when more cars enter the highway than leave, the flow rate rises because the density can rise without affecting the average speed. As the flow transitions to heavy traffic, however, any disturbance, such as cars merging onto the highway or changing lanes, gives rise to variations that grow into solitons. The stop-and-go pattern appears at maximum flow rate, when solitons propagate through traffic lanes, causing vehicle speeds to vary from zero to well over 7 mph in waves.

Nobody can do anything to make traffic move smoothly because solitons appear and grow whenever there are variations. It is not possible to avoid the variations because the patterns of highway use are essentially random.

Even making an entirely automated highway will not do the trick. Patterns of arrival of vehicles wanting to use the highway will still be random, and cars will still need to enter, exit, and change lanes. Automated highways might have a higher maximum flow rate due to a faster automated reaction time, but it is unlikely that the reaction time for a 3,000 lb electromechanical system can be reduced beyond a few hundred milliseconds. The maximum flow rate under such conditions would be larger—perhaps even a factor of two larger—but still quite finite. Whenever the flow rate approaches that maximum, solitons will appear and flow will be disrupted.

For more about on related topics, read:
AIMing for Automated Vehicles: Look into the world of driverless vehicle building, see some of the things that Paul Grayson sees, and puzzle over the problems of making vehicles driverless.

Posted by Charlie Masi on October 29, 2007 | Comments (1)