Optimised crowd and traffic management: QED!
On the occasion of the European Mobility Week (16-22 September 2012), cities are encouraged to take initiatives to promote a sustainable urban mobility. Noise and air pollution have become sources of concern in many urban areas. Major European cities have to take crowd and traffic management ever more seriously - as populations grow and infrastructure has to cope with rising demand and increased traffic congestion.
©Grantee's picture: INRIA
Wouldn’t life be easier if planners could look at a traffic solution and say, “This is the best possible approach”, with real certainty? That is what Dr Paola Goatin, of France’s Institut National de Recherche en Informatique et en Automatique (INRIA), who was awarded a Starting grant from the European Research Council in 2010, hopes to achieve.
“Pedestrian and traffic-flow modelling are societal issues,” explains Dr Goatin, “but currently, they tend to be modelled using a ‘microscopic’ approach, simulating the trajectory of each vehicle and individual.” This has several drawbacks: the number of parameters needed to model every vehicle or pedestrian leads to huge demands on computing resources; and this approach is more suitable for simulating traffic, rather than for quantifying effects or optimising results.
Dr Goatin’s TRAM3 research project is developing a ‘macroscopic’ approach which could change this by using models derived from fluid-dynamics that treat traffic in similar ways to waves. “We can get a view of the whole flow and density of the traffic, instead of how individual vehicles interact,” she says. By treating traffic and crowds as a fluid, their behaviour can be described using just a few equations, with the parameters obtained from real-world data.
While macroscopic models have been used in traffic management before, they have difficulties in handling some realistic scenarios. “Usually we want to find the minimum travel time under a particular arrangement,” Dr Goatin continues, “but the mathematical solutions display discontinuities, such as moving traffic arriving at the back of a static queue, and this makes it impossible to apply standard minimisation techniques.”
In other words, the classical mathematical tools cannot be used directly to produce mathematical proof of which traffic arrangements are best for many real-world cases, and simulations can only help planners observe the behaviour of a few vehicles. In addition, there has been much less work on pedestrians and crowd management.
“We have specific situations we would like our models to be able to reproduce,” says Dr Goatin, “such as a crowd exiting a door in a room with columns.” One of the biggest problems to solve is how to describe both the distribution of this crowd and the various velocities and directions of their movement.
“Our final goal is to harness our new methodology to produce optimisation results for real-world problems,” says Dr Goatin. “For example, we want to be able to prove mathematically the optimum position of the columns in order to maximise the crowd’s flow through exit doors.
“We are collaborating with UC Berkeley in the US for empirical traffic data,” she continues, “and are using video analysis of crowds in the Paris Metro provided by another research group at INRIA.”
After only two years into the project, the team have already published several papers, and have preliminary predictive results using INRIA’s computer model. “We have chosen to invest a lot of time on this particular platform as it has a lot of flexibility and good prospects for handling optimisation problems,” she explains. “Now we can move on to validation”.
“I first started work on traffic analysis in 2004,” says Dr Goatin, “as it combines the beauty of pure mathematics with producing practical solutions to real problems for the public.” As the project continues, she hopes this research will lead to reliable predictions and optimised approaches for handling traffic queues, emergency exits and other real-world applications.
For further information
Dr Paola Goatin’s TRAM3 project web page: http://www-sop.inria.fr/members/Paola.Goatin/tram3.html
Project details on CORDIS: http://cordis.europa.eu/projects/rcn/95809_en.html
• C. Chalons, P. Goatin and N. Seguin, “General constrained conservation laws. Application to pedestrian flow modeling”, submitted.
• N. El-Khatib, P. Goatin and M.D. Rosini, “On entropy weak solutions of Hughes' model for pedestrian motion”, Z. Angew. Math. Phys., to appear.
• M. Garavello and P. Goatin, “The Cauchy problem at a node with buffer”, Discrete Contin. Dyn. Syst. Ser. A 32(6) (2012), 1915-1938.
• M. Garavello and P. Goatin, “The Aw-Rascle traffic model with locally constrained flow”, J. Math. Anal. Appl. 378(2) (2011), 634-648.
• R.M. Colombo, P. Goatin and M.D. Rosini, “On the modeling and management of traffic”, ESAIM: M2AN 45 (2011), 853-872.