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August 24, 2016

Infrequently Asked Questions: Why do traffic jams seem to start and stop for no reason?

Anyone who's been stuck in traffic on the Schuylkill Expressway knows the drill: accelerate, brake, let out a deep sigh, repeat. 

Traffic seemingly comes and goes without any obvious reason for the holdup. One second, you're hoping to rev up to a snail's pace; the next, you're Vin Diesel in "The Fast and the Furious." Wondering why this happens, we reached out to Benjamin Seibold, associate professor of mathematics at Temple University, who's used numerical models to analyze the cause of "phantom jams." 

How is it that traffic jams seem to start and stop for no apparent reason?

First, it has to be pointed out that most traffic jams do have a clear reason [to exist]. Large-scale congestion basically occurs when demand, or the number of drivers wanting to use the roadway, exceeds the capacity of the roadway. And/or it is caused by a physical bottleneck: a traffic accident, a construction site, etc.

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However, there are also jamming phenomena, so-called 'phantom traffic jams,' that arise without a discernible cause. You suddenly have to break, because the car ahead of you brakes, and thus you force the car behind you to brake, and so on. Then you look around, and you see no potential cause of this slowdown.

These phantom jams, and the traffic waves that they cause, are dynamic features that result from the collective driving behavior of all drivers on the road. They arise when traffic density is high, but traffic is still flowing. Rather than a slow but steady flow of vehicles, drivers are forced to constantly brake and accelerate. The resulting unsteady driving increases fuel consumption and accident risk.

Your research seems to suggest it’s all about the little things on the highway — a tap on the brake can suddenly cause the whole highway to jam up. How’s that possible?

Research on the analysis of mathematical traffic models, traffic simulations, as well as controlled experiments has shown that phantom traffic jams arise when uniform traffic flow is unstable. This can be understood as follows: There are constantly small perturbations occurring in traffic flow: road imperfections, engine hiccups, small moments of driver inattention, etc. When the traffic density is low, uniform flow — where everybody travels with roughly the same speed — is stable. I.e., these small perturbations decay and the uniform flow persists. In contrast, when the traffic density is high, small perturbations amplify and drive the flow away from a nice uniform profile. Instead, traffic flow becomes unsteady and dominated by traffic waves, i.e., constant braking and accelerating. 

The key lesson that can be learned from the fact that phantom jams arise from instabilities is that unsteady flow patterns, such as traffic waves, can arise even if all drivers behave in exactly the same way and fully predictably. They can arise from the collective driving behavior, and they need not be caused by a single individual driver.

Can you explain in layman’s terms what you mean by 'waves'? I saw 'solitons' and 'jamitons' thrown in there as well. 

To an individual driver, a traffic wave is a single sudden slowdown, followed by an acceleration. However, if you stand next to the roadway and watch traffic waves, you will see a wave of brake lights that travels backward along the road. These waves can be quite persistent and travel backward along the road for miles. A great example in the Philadelphia area is the Schuylkill Expressway — I-76 — toward Valley Forge during afternoon hours. Traffic waves are frequently triggered near the Conshohocken Curve and can travel upstream as far as Manayunk.

Those traffic waves are sometimes called 'jamitons.' This is a play on the term 'soliton,' which denotes nonlinear waves in physics. The study of traffic models reveals that traffic waves are, in fact, nonlinear waves. Even more, they follow very similar equations and dynamics as detonation waves in equations that describe combustion and explosions.

Anything to add? What can people take away from this?

With an understanding of the causes of the dynamics of phantom jams, the key question is: What could one do to prevent or get rid of these undesirable traffic waves? After all, these traffic waves can arise from the collective behavior of all drivers on the roadway and are not necessarily caused by individual drivers. One possible approach is to change the way people drive — how much headway they leave, how rapidly they accelerate, how preventive they drive, etc. However, the connections between individual driving behavior and the emergent large-scale phenomena, such as traffic waves, are complicated. So changing how people drive is a difficult endeavor. 

Another possibility is to prevent traffic flow from becoming too dense so that it never reaches the regime in which phantom jams arise. This is one of the motivations behind ramp metering, where traffic lights at on-ramps limit the influx of vehicles onto a highway. The problem is that on-ramps have only limited storage capacity for vehicles, so the potential of ramp metering is limited. Moreover, highway traffic-control infrastructure, such as ramp meters and adaptive speed limit signs, is quite costly.

Any additional, related research you’re working on?

One alternative approach that my collaborators and I are currently working on is to devise strategies on how autonomous — that is, self-driving — vehicles could be used to regularize traffic flow. While the scenario of all vehicles on the road being self-driving is still a distant future, a situation in which a few vehicles on the highway will be autonomous, or semi-autonomous, is on our immediate horizon. Those vehicles will enter — in fact, have entered in some states — our roadways anyway. Our research attempts to go beyond the question how an autonomous vehicle can operate safely and efficiently on its own — a task that in itself is highly challenging. We study how autonomous vehicles can be used to a greater benefit by pushing a system consisting of many human drivers from an unsteady regime back into a nice and uniform flow regime, without the human drivers having to modify their own driving style.

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