A mathematical model for moving bottlenecks in road traffic

Jan 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: Researchers help Boston Marathon organizers plan for 2014 race

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

Smart traffic lights reduce fuel usage and lower emissions

Oct 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 ...

Strung along -- easing holiday traffic pain

Apr 02, 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.

MIT takes aim at ‘phantom’ traffic jams

Jun 09, 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.

Two new studies suggest ways of improving traffic flow

Sep 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 ...

Recommended for you

Egypt archaeologists find ancient writer's tomb

Apr 19, 2014

Egypt's minister of antiquities says a team of Spanish archaeologists has discovered two tombs in the southern part of the country, one of them belonging to a writer and containing a trove of artifacts including reed pens ...

Study finds law dramatically curbing need for speed

Apr 18, 2014

Almost seven years have passed since Ontario's street-racing legislation hit the books and, according to one Western researcher, it has succeeded in putting the brakes on the number of convictions and, more importantly, injuries ...

User comments : 0

More news stories

Egypt archaeologists find ancient writer's tomb

Egypt's minister of antiquities says a team of Spanish archaeologists has discovered two tombs in the southern part of the country, one of them belonging to a writer and containing a trove of artifacts including reed pens ...

Making graphene in your kitchen

Graphene has been touted as a wonder material—the world's thinnest substance, but super-strong. Now scientists say it is so easy to make you could produce some in your kitchen.