A mathematical model for moving bottlenecks in road traffic

January 19, 2011

Serious traffic gridlocks, like the jam on Beijing's national expressway a few months ago which brought vehicles to a halt for days, are a real-world issue needing attention. Unfortunately, such standstills are not uncommon in Beijing, or in other cities around the world.

Such incidents motivate the analysis of traffic to minimize similar events and provide insight into road design and construction, such as where to install and toll booths, how many lanes to build, and where to construct an overpass or a tunnel. The goals of these analyses are to relieve congestion in high traffic areas, reduce the risk of accidents, and manage safety and security of motorists.

Not surprisingly, vehicular has been tackled by mathematicians, engineers and physicists alike. Mathematical approaches to study traffic are usually based on the speed, density and flow of vehicles on a given roadway. In a paper published this month in the SIAM Journal on , authors Corrado Lattanzio, Amelio Maurizi and Benedetto Piccoli propose a of vehicular traffic based on the study of a moving bottleneck caused by a slow-moving vehicle within the flow of cars. The effect of moving bottlenecks on flow of traffic is an important factor in evaluating travel times and traveling paths for commuters.

Many different mathematical models have been proposed to study traffic, including models that use second-order equations for mass and momentum, multipopulation models that factor in the varying characteristics of different kinds of vehicles, and dynamic models that consider traffic flows.

Most of the models so far proposed, however, solve the problem of a single vehicle independently of the entire traffic flow, and so are not completely coupled. An example is a PDE-ODE model that used a partial differential equation to model the flow of traffic while using an ordinary differential equation to determine the position of a single vehicle. Since both could be solved independently, the system did not take into account the influence of the single car on the entire traffic flow.

The paper by Lattanzio et al provides a fully coupled, multi-scale model in which the microscopic position of a single car is taken together with the macroscopic car density on the road. In this micro-macro model, the dynamics of a moving bottleneck caused by a slow-moving vehicle on a street are used to study the effects of disruptions on the flow of traffic. Mathematically, the problem is solved using the fractional step method. In successive time steps, a PDE is first solved for the density of traffic and then the ODE is solved for the position of the slow-moving vehicle.

By solving the bottleneck problem in a coupled fashion, better transportation designs can be made in anticipation of such inevitable traffic congestion.

Explore further: If all drivers were polite, they would get where they're going faster

More information: Moving Bottlenecks in Car Traffic Flow: A PDE-ODE Coupled Model, Corrado Lattanzio, Amelio Maurizi, and Benedetto Piccoli
SIAM Journal on Mathematical Analysis, 43 (2011), pp 50-67. Pub date: January 4, 2011

Related Stories

MIT takes aim at ‘phantom’ traffic jams

June 9, 2009

(PhysOrg.com) -- 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.

Strung along -- easing holiday traffic pain

April 2, 2010

This Easter, motorists will experience the familiar frustration of being stuck on a motorway in a stop-start traffic jam that eventually disperses with no apparent cause.

Two new studies suggest ways of improving traffic flow

September 21, 2010

(PhysOrg.com) -- Two studies have just been published that may help improve traffic flows. The first, presented as a Santa Fe Institute working paper for September, concluded that if traffic lights responded to measured traffic ...

Smart traffic lights reduce fuel usage and lower emissions

October 27, 2010

(PhysOrg.com) -- Denso Corp. has designed the next version of 'the smart traffic light system'. By using messaging between vehicles and the traffic-light controller, better decisions about when to change signaling will help ...

Recommended for you

From a very old skeleton, new insights on ancient migrations

October 9, 2015

Three years ago, a group of researchers found a cave in Ethiopia with a secret: it held the 4,500-year-old remains of a man, with his head resting on a rock pillow, his hands folded under his face, and stone flake tools surrounding ...

Who you gonna trust? How power affects our faith in others

October 6, 2015

One of the ongoing themes of the current presidential campaign is that Americans are becoming increasingly distrustful of those who walk the corridors of power – Exhibit A being the Republican presidential primary, in which ...

Ancient genome from Africa sequenced for the first time

October 8, 2015

The first ancient human genome from Africa to be sequenced has revealed that a wave of migration back into Africa from Western Eurasia around 3,000 years ago was up to twice as significant as previously thought, and affected ...

Mexican site yields new details of sacrifice of Spaniards

October 9, 2015

It was one of the worst defeats in one of history's most dramatic conquests: Only a year after Hernan Cortes landed in Mexico, hundreds of people in a Spanish-led convey were captured, sacrificed and apparently eaten.


Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.