How variable speed limits can reduce traffic jams. WTF?

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How the Mathematics of Explosions Explains Phantom Traffic Jams

To prevent such ‘jamitons,’ LED variable-speed-limit signs help traffic move faster

Traffic in the U.S. has worsened steadily for decades.

By Josh Zumbrun, WSJ

June 10, 2022 5:30 am ET

You are zipping along the road when your GPS shows the road ahead turning yellow and then red: an accident, or construction maybe. When you get to the red spot the traffic slows to a halt, but there’s no accident or construction. Then for no apparent reason, traffic speeds up.

While such phantom traffic jams have always happened, you might have noticed more of them recently. The pandemic has scrambled when and where people drive. So even though people haven’t fully returned to the office, roadways are experiencing more traffic and traffic jams than ever.

You might have also noticed road planners’ response: Instead of a fixed speed limit of, say, 65 miles an hour, some roads have a speed limit displayed on an LED sign that fluctuates throughout the day.

“Imagine it’s really congested, but everyone is going close to the speed limit,” said Beverly Thompson Kuhn, a senior research engineer at the Texas A&M Transportation Institute. “It only takes one person to dart into the next lane, a small gap, and you get the shock wave. The vehicles behind them brake, harder than they anticipate. It starts to propagate back down the freeway.” She added: “The idea of variable speed limits is to try to get ahead of that.”

It’s not a coincidence that her go-to metaphor is a shock wave. The mathematics of explosions explains exactly how phantom traffic jams take shape, and why LED speed-limit signs can stop them.

Traffic engineers have long known about phantom traffic jams—so-called because while the congestion is very real, no cause is visible. In 2008, a Japanese team created one experimentally from extremely benign driving. The next year, a different team from the Massachusetts Institute of Technology and four other universities showed the jams behave in the same way as detonation waves produced by explosions.

This explosive traffic wave has a name: a jamiton (a combination of traffic jam and soliton, the term in physics for a traveling wave). The drivers that originate these typically have no idea what they’ve done. Someone comes upon a car driving a tad too slowly, can’t switch lanes, taps the brakes. The car behind them brakes faster. The early cars slowly reaccelerate and never realize that their tiny perturbation ignited a traffic explosion.

The waves do not dissipate. They can ripple slowly along the road for miles, triggering new mini waves (dubbed jamitinos).

“A single instability can trigger an infinitely growing sequence of jamitinos,” the MIT team wrote. “They can only vanish by strong smoothing effects (extremely cautious drivers) or a lowering of density (a widening road, vehicles exiting).”

Strong smoothing effects are exactly what variable speed limits provide. By slowing all cars gradually, they obviate the need for any single car to slow abruptly. This defeats the phantom traffic jam, prevents accidents—one 2018 study found an 18% reduction in crashes—and restores the flow of traffic.

Traffic in the U.S. has steadily worsened for decades, as populations and travel demand have grown faster than roadways. Before the pandemic, U.S. traffic was at its worst by many measures. In the 12 months before February 2020, Americans drove a record 3.3 trillion miles.

Detroit’s Lodge Freeway experimented with a variable speed limit as far back as the 1960s. The last decade’s surge in traffic sparked their proliferation. In 2018, the Pew Charitable Trusts estimated that 15 states had variable-speed-limit systems. As of this year, with traffic rebounding to nearly prepandemic levels, that number had risen to 22, according to the National Operations Center of Excellence, a partnership of transportation agencies.

Though overall driving is getting closer to normal, “When and where people are traveling is different,” said Bob Pishue, a transportation analyst at Inrix. The firm hoovers up billions of data points every day from connected vehicles, smartphones, fleet vehicles and other sources to help feed now-ubiquitous real-time traffic maps.

Its data shows, for example, that morning commutes have been slow to come back, but that there are more trips between noon and 4 p.m. in many places. People aren’t driving downtown as much, but are driving around town more.

“If you’re out in the afternoon, it’s as bad as it was pre-Covid, as bad as ever,” he said.

As variable speed limits have proliferated, they’ve been met with occasional skepticism, with many drivers not realizing the connection to the growing traffic burden. Some commentators worry the systems are elaborate speed traps. In many states, though, the lowered limits are, from a legal standpoint, advisory, meaning you won’t be ticketed for failing to obey one.

Others worry about the cost. (A transportation planner once observed that any transportation project other than a highway inevitably gets compared to an episode of “The Simpsons” called “Marge vs. the Monorail,” in which a con man suckers the town of Springfield into a monorail-to-nowhere boondoggle.)

Dr. Kuhn of Texas A&M says much of this skepticism is misplaced. LED speed-limit signs are far cheaper than a new lane of interstate. She concedes that the systems work best when individual drivers realize it’s in their collective self-interest to comply. By slowing every driver down a little bit to prevent a phantom traffic jam, everyone reaches destinations more quickly.

“If you control the arc of that speed, you can actually get more throughput,” she said. Or, in layman’s terms, “You go slower to get there faster.”