Tag Archives: speed limits

Mathematicians Take Aim At ‘Phantom’ Traffic Jams: New Model Could Help Design Better Roads

Traffic jam in Los Angeles. (Credit: iStockphoto)

Countless hours are lost in traffic jams every year. Most frustrating of all are those jams with no apparent cause — no accident, no stalled vehicle, no lanes closed for construction.

Such phantom jams can form when there is a heavy volume of cars on the road. In that high density of traffic, small disturbances (a driver hitting the brake too hard, or getting too close to another car) can quickly become amplified into a full-blown, self-sustaining traffic jam.

A team of MIT mathematicians has developed a model that describes how and under what conditions such jams form, which could help road designers minimize the odds of their formation. The researchers reported their findings May 26 in the online edition of Physical Review E.

Key to the new study is the realization that the mathematics of such jams, which the researchers call “jamitons,” are strikingly similar to the equations that describe detonation waves produced by explosions, says Aslan Kasimov, lecturer in MIT’s Department of Mathematics. That discovery enabled the team to solve traffic jam equations that were first theorized in the 1950s.

The equations, similar to those used to describe fluid mechanics, model traffic jams as a self-sustaining wave. Variables such as traffic speed and traffic density are used to calculate the conditions under which a jamiton will form and how fast it will spread.

Once such a jam is formed, it’s almost impossible to break up — drivers just have to wait it out, says Morris Flynn, lead author of the paper. However, the model could help engineers design roads with enough capacity to keep traffic density low enough to minimize the occurrence of such jams, says Flynn, a former MIT math instructor now at the University of Alberta.

The model can also help determine safe speed limits and identify stretches of road where high densities of traffic — hot spots for accidents — are likely to form.

Flynn and Kasimov worked with MIT math instructors Jean-Christophe Nave and Benjamin Seibold and professor of applied mathematics Rodolfo Rosales on this study.

The team tackled the problem last year after a group of Japanese researchers experimentally demonstrated the formation of jamitons on a circular roadway. Drivers were told to travel 30 kilometers per hour and maintain a constant distance from other cars. Very quickly, disturbances appeared and a phantom jam formed. The denser the traffic, the faster the jams formed.

“We wanted to describe this using a mathematical model similar to that of fluid flow,” said Kasimov, whose main research focus is detonation waves. He and his co-authors found that, like detonation waves, jamitons have a “sonic point,” which separates the traffic flow into upstream and downstream components. Much like the event horizon of a black hole, the sonic point precludes communication between these distinct components so that, for example, information about free-flowing conditions just beyond the front of the jam can’t reach drivers behind the sonic point. As a result, drivers stuck in dense traffic may have no idea that the jam has no external cause, such as an accident or other bottleneck. Correspondingly, they don’t appreciate that traffic conditions are soon to improve and drive accordingly.

“You’re stuck in traffic until all of the sudden it just clears,” says Morris.

In future studies, the team plans to look more detailed aspects of jamiton formation, including how the number of lanes affects the phantom traffic jams.

The research was funded by the U.S. Air Force Office of Scientific Research, the National Science Foundation and the (Canadian) Natural Science and Engineering Research Council.

Journal reference:

M. R. Flynn, A. R. Kasimov, J.-C. Nave, R. R. Rosales, and B. Seibold. Self-sustained nonlinear waves in traffic flow. Physical Review E, 2009; 79 (5): 056113 DOI

(source : sciencedaily)


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Calls for ‘speed-limiting’ cars

Speed-limiting devices should be fitted to cars on a voluntary basis to help save lives and cut carbon emissions, according to a new report.

The government’s transport advisers claim the technology would cut road accidents with injuries by 29%.

The device automatically slows a car down to within the limit for the road on which it is being driven.

But campaign group Safe Speed warns against its use, saying it encourages drivers to enter a “zombie mode”.

Ministers are planning to help councils draw up digital maps with details of the legal speed on every road.

The speed-limiting devices will then use satellite positioning to check a vehicle’s location and when its speed exceeds the limit, power will be reduced and the brakes applied if necessary.

The Commission for Integrated Transport and the Motorists’ Forum, which both advise the government, are calling on ministers to promote a wide introduction of the system.

Education ‘important’

John Lewis, from the Motorists’ Forum, told BBC Breakfast he believed the devices would help drivers obey limits and therefore keep their licences.

“But we believe that the system should be a voluntary system, that the drivers decide if they have fitted to their car or not, and that they decide if they want to over-ride the speed limit – that should be their choice,” he said.

There would also be a positive impact on emissions and fuel consumption, he added.

Jon York, fleet manager for British Gas, whose vans are already limited to 70mph, told BBC Radio 5 Live the system had reduced road incidents for the company.

But he said the introduction of technology had to be combined with safety education.

“It does aid road safety, it does reduce incidents, but it is part of a wide-ranging number of initiatives within British Gas and one of those is driver training because you have to change people’s behaviour.”

Overtaking worries

But Claire Armstrong, from the road safety campaign group Safe Speed, said that the devices could be dangerous.

She said truck drivers using speed-limiting devices had been shown to “go into fatigue mode or zombie mode” and stopped paying attention to the road.

“That makes it highly dangerous in those scenarios. So you’ve taken the responsibility away from the driver and that is not [good] for road safety.”

Derek Charters, from the Motor Industry Research Association, has extensively tested speed-limiting technology.

He believes that if all cars were fitted with the system, safety would be improved, and that vehicles without it present a greater danger.

“The last thing you need is one car to be overtaking and then pull back in, in front of the cars in front, because that braking event will then cause everybody to start to slow down, which will then compress the traffic, which then causes an incident,” he said.

Motoring journalist Quentin Willson said he also believed taking away driver control was a “really, really bad thing”.

“Remotely policing the roads from satellites in the sky – I would worry about it an awful lot.”


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Many Motorists Don’t See Need To Heed Speed Limits

ScienceDaily (Nov. 8, 2008) — Research suggests U.S. motorists are growing increasingly cynical about the relevance of speed limits, and a new study indicates many motorists are more likely to think they can drive safely while speeding as long as they won’t get caught.

“So the faster you think you can go before getting a ticket, the more likely you are to think safety’s not compromised at higher speeds,” said Fred Mannering, a professor of civil engineering at Purdue University.

Mannering used a series of mathematical equations in “multinomial logit models” to calculate probabilities based on data from a survey of 988 motorists in Tippecanoe County, Ind., where Purdue is located.

Findings generally agree with other data taken in recent years.

“For whatever reason, respect for speed limits seems to have deteriorated,” Mannering said. “A 2002 survey indicated two-thirds of all drivers reported they exceeded the posted speed limit, and roughly one-third reported driving 10 mph faster than most other vehicles. These figures are even more disturbing when you consider that they’re self-reported and likely to be understating the degree of speeding problems.”

The Indiana survey participants were asked: “At what point do you feel speeding becomes a threat to the personal safety of you and your family?” The motorists were given three choices: 5 mph, 10 mph or 20 mph over the speed limit.

The survey was taken before and after a 2004 media campaign launched in the county stressing the dangers of speeding that included radio and newspaper messages.

Using survey data, Mannering applied a series of mathematical equations in a model to estimate the probabilities of speed and safety viewpoints for drivers in various categories.

Findings are detailed in a research paper appearing in the journal Transportation Research Part F: Traffic Psychology and Behavior, available both online and in an upcoming print edition of the journal.

“The intent of the study was to statistically assess drivers’ perception of the relationship between speed limits and safety,” Mannering said. “In recent decades it has become more common for speed limits to be set for political reasons rather than for safety reasons. Consequently, the motoring public seems to have increasingly begun questioning the rationality of speed limits. This is evident in observed speed data that show the majority of drivers routinely exceed posted speed limits.”

Of the 988 drivers in the survey, 21 percent thought it was safe to drive up to 5 mph over the speed limit, 43 percent thought it was safe to drive up to 10 mph over and 36 percent thought it was safe to drive up to 20 mph over the speed limit.

“The new findings show that the speed enforcement is critical to motorists’ safety perceptions,” Mannering said. “Let’s say you think enforcement is getting lax and the speed at which you think you will get a ticket goes up from 7 mph over the speed limit to 10 mph over the speed limit. If that happens, our statistical results indicate that you would be 27 percent more likely to think you can safely drive up to 20 mph over the speed limit.”

The research showed the media campaign relating to the dangers of speeding had no statistically significant impact on drivers’ views on speeding and safety.

Other findings showed that women who have never been stopped for speeding are 68 percent more likely to think that it’s only safe to drive 5 mph over the speed limit compared to all men and other women who have been stopped for speeding. Both men and women drivers who have been stopped for speeding in the last year are about 25 percent more likely to believe that it is safe to drive up to 20 mph over the speed limit than those who have not.

“This is probably because people who habitually speed are not significantly deterred by being stopped for speeding,” Mannering said. “They might become slightly more conservative, but it doesn’t slow them down to the level of people who are inherently more conservative.”

The findings also showed that people get progressively more conservative about speeding as they age. A 25 year-old driver is 75 percent more likely to think it is safe to drive up to 20 mph over the speed limit than a 50 year-old driver.

Adapted from materials provided by Purdue University.

Source : sciencedaily.com

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