Eliminating unexplained traffic jams

A sample run of Horn’s simulator (complete with brake lights). The system starts out in a stable state, but backups begin about 30 seconds in, even though all the cars are executing algorithms typical of current adaptive-cruise-control systems. The bilateral-control algorithm is switched on at the one-minute mark. Courtesy of Berthold Horn

If integrated into adaptive cruise-control systems, a new algorithm could mitigate the type of freeway backup that seems to occur for no reason.

Everybody’s experienced it: a miserable backup on the freeway, which you think must be caused by an accident or construction, but which at some point thins out for no apparent reason.

Such “traffic flow instabilities” have been a subject of scientific study since the 1930s, but although there are a half-dozen different ways to mathematically model them, little has been done to prevent them.

At this month’s IEEE Conference on Intelligent Transport Systems, Berthold Horn, a professor in MIT’s Department of Electrical Engineering and Computer Science, presented a new algorithm for alleviating traffic flow instabilities, which he believes could be implemented by a variation of the adaptive cruise-control systems that are an option on many of today’s high-end cars.

A car with adaptive cruise control uses sensors, such as radar or laser rangefinders, to monitor the speed and distance of the car in front of it. That way, the driver doesn’t have to turn the cruise control off when traffic gets backed up: The car will automatically slow when it needs to and return to its programmed speed when possible.

Counterintuitively, a car equipped with Horn’s system would also use sensor information about the distance and velocity of the car behind it. A car that stays roughly halfway between those in front of it and behind it won’t have to slow down as precipitously if the car in front of it brakes; but it will also be less likely to pass on any unavoidable disruptions to the car behind it. Since the system looks in both directions at once, Horn describes it as “bilateral control.”

Traffic flow instabilities arise, Horn explains, because variations in velocity are magnified as they pass through a lane of traffic. “Suppose that you introduce a perturbation by just braking really hard for a moment, then that will propagate upstream and increase in amplitude as it goes away from you,” Horn says. “It’s kind of a chaotic system. It has positive feedback, and some little perturbation can get it going.”

Doing the math

Horn hit upon the notion of bilateral control after suffering through his own share of inexplicable backups on Massachusetts’ Interstate 93. Since he’s a computer scientist, he built a computer simulation to test it out.

The simulation seemed to bear out his intuition, but to publish, he needed mathematical proof. After a few false starts, he found that bilateral control could be modeled using something called the damped-wave equation, which describes how oscillations, such as waves propagating through a heavy fluid, die out over distance. Once he had a mathematical description of his dynamic system, he used techniques standard in control theory — in particular, the Lyapunov function — to demonstrate that his algorithm could stabilize it.

Horn’s proof accounts for several variables that govern real-life traffic flow, among them drivers’ reaction times, their desired speed, and their eagerness to reach that speed — how rapidly they accelerate when they see gaps opening in front of them. Horn found that the literature on traffic flow instabilities had proposed a range of values for all those variables, and within those ranges, his algorithm works very efficiently. But in fact, for any plausible set of values, the algorithm still works: All that varies is how rapidly it can smooth out disruptions.

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