Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:

 

A mathematical model for moving bottlenecks in road traffic

20.01.2011
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 traffic lights 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 traffic flow 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 Mathematical Analysis, authors Corrado Lattanzio, Amelio Maurizi and Benedetto Piccoli propose a mathematical model 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.

Source:

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

Karthika Muthukumaraswamy | EurekAlert!
Further information:
http://www.siam.org

More articles from Studies and Analyses:

nachricht Smart Data Transformation – Surfing the Big Wave
02.12.2016 | Fraunhofer-Institut für Angewandte Informationstechnik FIT

nachricht Climate change could outpace EPA Lake Champlain protections
18.11.2016 | University of Vermont

All articles from Studies and Analyses >>>

The most recent press releases about innovation >>>

Die letzten 5 Focus-News des innovations-reports im Überblick:

Im Focus: Novel silicon etching technique crafts 3-D gradient refractive index micro-optics

A multi-institutional research collaboration has created a novel approach for fabricating three-dimensional micro-optics through the shape-defined formation of porous silicon (PSi), with broad impacts in integrated optoelectronics, imaging, and photovoltaics.

Working with colleagues at Stanford and The Dow Chemical Company, researchers at the University of Illinois at Urbana-Champaign fabricated 3-D birefringent...

Im Focus: Quantum Particles Form Droplets

In experiments with magnetic atoms conducted at extremely low temperatures, scientists have demonstrated a unique phase of matter: The atoms form a new type of quantum liquid or quantum droplet state. These so called quantum droplets may preserve their form in absence of external confinement because of quantum effects. The joint team of experimental physicists from Innsbruck and theoretical physicists from Hannover report on their findings in the journal Physical Review X.

“Our Quantum droplets are in the gas phase but they still drop like a rock,” explains experimental physicist Francesca Ferlaino when talking about the...

Im Focus: MADMAX: Max Planck Institute for Physics takes up axion research

The Max Planck Institute for Physics (MPP) is opening up a new research field. A workshop from November 21 - 22, 2016 will mark the start of activities for an innovative axion experiment. Axions are still only purely hypothetical particles. Their detection could solve two fundamental problems in particle physics: What dark matter consists of and why it has not yet been possible to directly observe a CP violation for the strong interaction.

The “MADMAX” project is the MPP’s commitment to axion research. Axions are so far only a theoretical prediction and are difficult to detect: on the one hand,...

Im Focus: Molecules change shape when wet

Broadband rotational spectroscopy unravels structural reshaping of isolated molecules in the gas phase to accommodate water

In two recent publications in the Journal of Chemical Physics and in the Journal of Physical Chemistry Letters, researchers around Melanie Schnell from the Max...

Im Focus: Fraunhofer ISE Develops Highly Compact, High Frequency DC/DC Converter for Aviation

The efficiency of power electronic systems is not solely dependent on electrical efficiency but also on weight, for example, in mobile systems. When the weight of relevant components and devices in airplanes, for instance, is reduced, fuel savings can be achieved and correspondingly greenhouse gas emissions decreased. New materials and components based on gallium nitride (GaN) can help to reduce weight and increase the efficiency. With these new materials, power electronic switches can be operated at higher switching frequency, resulting in higher power density and lower material costs.

Researchers at the Fraunhofer Institute for Solar Energy Systems ISE together with partners have investigated how these materials can be used to make power...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

Event News

ICTM Conference 2017: Production technology for turbomachine manufacturing of the future

16.11.2016 | Event News

Innovation Day Laser Technology – Laser Additive Manufacturing

01.11.2016 | Event News

#IC2S2: When Social Science meets Computer Science - GESIS will host the IC2S2 conference 2017

14.10.2016 | Event News

 
Latest News

UTSA study describes new minimally invasive device to treat cancer and other illnesses

02.12.2016 | Medical Engineering

Plasma-zapping process could yield trans fat-free soybean oil product

02.12.2016 | Agricultural and Forestry Science

What do Netflix, Google and planetary systems have in common?

02.12.2016 | Physics and Astronomy

VideoLinks
B2B-VideoLinks
More VideoLinks >>>