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Would highway automation work for a highway designated for automated cars only?
December 17, 2007

This question came from Frank Grassi, who provided no additional identifying information. He continued: “First realize that the car like any machine is a combination of the static and dynamic. In this case the dynamic being the automobile has advanced to an unimaginable degree of perfection and uses the most advanced technologies. The laggard is the highway. This is the half that if mass production and standardization of its construction were to be improved, unimaginable progress could be achieved. What I am proposing is doing for the other half what Henry Ford did for the manufacturing and assembly of the other.”

The automated highway concept has been around for quite a while. The earliest reference I’ve found for something resembling an automated highway appeared in Robert Heinlein’s 1941 science fiction novel Methuselah’s Children (originally serialized in Astounding Science-Fiction magazine). The hero’s love interest “set the control combination for North Shore” then “settled back for a little nap” from which “she woke just before the signal from the car which would have called her.”

Since then, both positive and negative aspects of the automated highway concept have been sorted through by many authors, and the negative aspects figure heavily in Alex Proyas’ 2004 motion picture I, Robot, which was based on a set of stories by Isaac Asimov first published in 1950. Science fiction authors generally seem to agree that travel by automated cars on automated highways is both safe and boring until something goes wrong, at which time it becomes deadly.

All of the above is beside the point of Frank’s question, to which the short answer is “yes.” In fact, it is easy to make the case that only automated vehicles should ever be allowed on automated highways. The Intelligent Transportation System concept, as I understand it, would require every vehicle to pass a rigorous inspection at the entry to an automated highway.

Nobody disputes that automated highways will work. Certainly they will work in theory, and we are now closing in on a time when they can be made to work in practice. What nobody can now say is whether they can be made to work without violating Scheiber’s Law: “Just because you can, doesn’t mean you should!”

The way I read Frank’s question is: assuming for the moment that the ITS can clear Scheiber’s Law (meaning that if you build it they will come), could automated control help traffic move smoothly on them? The answer is “no.” Automated highways will work, but they will not carry significantly more traffic and will not move significantly more smoothly.

I stated this in my 10/29/07 “Ask Charlie” answer, but didn’t go into it too deeply. Apparently, I need to, so here goes….

Traffic-flow mathematics works the same way whether the vehicles are operated by human drivers having limited perception of the overall pattern, or computers with perfect knowledge of the traffic pattern at present. Whether anyone will ever devise a computer that can see the future starts with the metaphysical question of what exactly is the “future.” For the purposes of this blog, we’ll just assume that the ITS is run by a computer that has perfect of knowledge of everything in its purview, which includes everything between its entrances and exits.

In August of 1997, the National Automated Highway System Consortium (NAHSC) conducted a live demonstration showing, among other things, a platoon of eight vehicles driving in formation on a 7.6 mile segment of I-15 outside San Diego, CA at highway speed (60-65 mph). Automated vehicles demonstrated close-following formation, passing, and other maneuvers while carrying passengers, but having no human-driver input. By all accounts, everything worked perfectly.

That’s all well and good, but now imagine a 75-mile stretch of four-lane highway filled end-to-end and side-to-side with vehicles separated by, say, three feet bumper-to-bumper and traveling at a more realistic commuter-speed of 70 mph. Except for the following distance, this is a scenario not unlike what plays out every morning during rush hour on I-128 outside Boston, MA, and many other commuter highways. I’ve specified the short following distance because it is the feature that observers of the 1997 demonstration typically cite as most impressive.

Now, assume an additional 20-foot-long vehicle wants to enter the highway at a point, say, 15 miles from the start. The omniscient computer must make a hole 23 feet (276 in) long for it.

The computer has various methods to do so. For example, it might slow all 3,443 vehicles occupying the right-hand lane back 15 miles to the starting point long enough to make the 23-foot gap needed without violating the 3 foot intervehicle spacing.

Or, it might accelerate cars ahead of the gap it was opening and slow some cars behind. If, for example, it involved 24 cars in the maneuver, it would have to take one foot from each inter-vehicle space, shortening it to two feet. It could, on the other hand, take only 2.76 inches from each space, but that would force it to involve 101 vehicles in the maneuver.

Now, assume a second vehicle wants to enter the traffic stream. This causes a second disruption to the smooth flow of traffic. Since we’ve got 70 miles of roadway, we could easily have 10 vehicles entering simultaneously. All of a sudden, that 2.76 inches balloons out to most of the three-foot space being taken away for a whole lot of cars!

And, you have exactly the same problem when you need to have cars change lanes. While this is not impossible—indeed it wouldn’t be a terribly difficult calculation problem for even a medium-size computer—it most definitely would disrupt smooth traffic flow. Imagine, you would be riding in an automated car that changes speeds randomly for no apparent reason. How pleasant would that be?

The solution to this problem is to add back the two-second gap between vehicles that I recommended in my 10/29 entry.

Impossibility rears its ugly head when you ask vehicles to slow down, however. Let’s say that we have two of those four lanes of traffic funnel down into a cloverleaf intersection for a sporting event.

In the 10/29 entry I asserted that the traffic flow rate—the number of vehicles passing a point in a given time interval—must be the same everywhere. This rule is a consequence of conservation of matter.

The high-school wording for the Law of Conservation of Matter usually starts by specifying “a closed system.” There is also a version for open systems. Engineers learn it in the form of Kirchoff’s Circuit Laws. There’s one law for current and another for voltage.

In fact, both Kirchoff’s Laws are special cases of a more general law governing any conserved quantity in an open system. In words, it goes something like this: “What goes in must come out, or stay there.” The version for current comes from conservation of charge. The voltage version comes from conservation of energy.

Cars on a highway are a conserved quantity, too. On a highway at maximum capacity, the “stay there” option is not possible. What goes in must come out because there’s nowhere to put excess in between.

With Kirchoff’s Laws in mind, let’s try to take those two lanes of traffic off the highway onto the cloverleaf intersection. Conservation of vehicles requires that when you squeeze two lanes on the highway down to one lane on the ramp, the speed must double. Since the vehicles are already moving at 70 mph, funneling onto the cloverleaf forces them to move at 140 mph around the curve. Try that in Mom’s SUV!

To allow Mom’s SUV to negotiate the cloverleaf at a still-pulse-raising 40 mph, you’d have to slow traffic on the highway to 20 mph. Of course, that’s exactly what happens today with un-automated vehicles on un-automated highways. If you thought the traffic snarl was because of human drivers, think again. It’s conservation of matter, baby.

Again, the solution is to use the two-seconds-between-vehicles rule. It changes traffic density in response to changes in average vehicle speed while keeping flow rate constant. Things still slow down, but now there’s somewhere to put the extra cars.

The point is that, as far as traffic smoothness and highway capacity are concerned, using automated vehicles on automated highways buys you practically nothing.

Does this mean highway automation is worthless? No! It just doesn’t smooth traffic or increase highway capacity.

What highway automation can do is clear out the drivers sleeping at the wheel, gawking at construction sites, and those applying makeup while closing real-estate deals on their cellphones. It could end worries about looking in your rear-view mirror to see a tailgater eating ice cream while steering with his knees. It also takes care of the folks hogging the high-speed lane by pacing the 18-wheeler in the right lane on a two-lane road. It would also end the screeching stops when you suddenly come upon the traffic jam at a construction site—the computer would have known about it and planned better.

Highway automation can do a lot for us and to us. When deciding whether it’s something we want to do, we should have clearly in mind what it’s capable of and what it is not.

For more about automated vehicles, visit Paul Grayson’s blog “AIMing for Automated Vehicles” at the Control Engineering Website.

Posted by Charlie Masi on December 17, 2007 | Comments (2)