For event organizers, predicting the highly complex dynamics within large crowds can be an unenviable task. But new computer-modelling research, which treats people as decision-makers rather than passive particles, could help authorities to identify where crowds could become dangerous.
Crowds display a wide variety of behaviours that arise spontaneously from the collective motion of unconnected individuals. For example, people walking in opposite directions along a single passageway tend automatically to divide up into distinct lanes. Then, as the density of pedestrians increases, this smooth motion starts to break down, eventually leading to highly fluctuating motion. On occasion, extreme crowd turbulence has led to fatal crushes, such as the tragic accident at the Love Parade festival in Duisburg, Germany, last year, which left 21 people dead.
To try and understand these behaviours, scientists usually employ a physics-based approach. Pedestrians can be modelled as solid particles that experience an attractive force towards their destination and repulsive forces from other pedestrians and from walls. However, according to Mehdi Moussaïd of the CNRS research centre for animal cognition in Toulouse, France, such physics-based models have a number of shortcomings. These include the ever-increasing complexity of the interaction functions needed to satisfy new data on crowd behaviour, and the limitations imposed by only ever considering interactions between two particles at any one time.
Seeking out empty space
In the new approach, developed by Moussaïd, Guy Theraulaz, also at the CNRS centre in Toulouse, and Dirk Helbing of the Swiss Federal Institute of Technology in Zurich, pedestrians instead alter their motion deliberately, and do so on the basis of what they see. Individuals work out the relative position of surrounding obstacles as they walk and use this information to modify their movement according to two simple principles. The first of these is to walk in the direction that provides the most direct obstacle-free path to the destination, and the second is to walk at a speed that allows a certain minimum time to react to potential collisions. As Moussaïd puts it, “physics-based modelling represents the tendency to move away from others, while our cognitive model represents the tendency to seek out empty space”.
To see how well their model stood up to empirical data, the researchers first tested it against laboratory observations of how two individual pedestrians avoid one another. They found that the predictions and data were in good agreement, both for the case in which the two pedestrians were moving in opposite directions and when one was stationary. Next, they tested the model against collective phenomena, and found that it correctly predicted the spontaneous dividing up of opposing flows. They also found that as they increased the density of pedestrians in their model, the resulting decline in the average speed of walkers was in line with real-life observations, carried out in Toulouse.
Increasing the density still further, Moussaïd and colleagues found that the model predicted the distinctive transitions to more disordered behaviour – stop-and-go waves and then turbulence. But because at these high densities people are in close contact with their neighbours and can be pushed and pulled about against their will, the researchers added a purely physical interaction term to their equations that kicked in once the density was high enough. With this extra term in place, the model was able to predict the extent of crushing around bottlenecks in passageways and the resulting stress releases that, say the researchers, can produce “earthquake-like” movements of many individuals in multiple directions. In particular, the researchers found that their results agreed closely with images of crowd turbulence that happened to be captured by a surveillance camera during the 2006 hajj pilgrimage to Mecca.
Foreseeing bottlenecks
According to Moussaïd, the new model could have a number of practical uses. One might be in the layout of sites for mass events, with the model predicting which bottlenecks, such as those around entrances and exits, could prove the most dangerous. Also, using the model to analyse real-time footage of crowd movements could give organizers vital minutes to try and restore order before the situation deteriorates. The researchers also point out that the visual basis of their model makes it particularly well suited to studying how people can be evacuated when there is reduced visibility, as would be the case in a smoke-filled room.
László Barabasi of Northeastern University in the US believes that the Franco-Swiss researchers “offer a compelling argument” that combining physical and cognitive elements within a single model “is an excellent new avenue to both individual and crowd modelling”. He adds that it would be “particularly interesting to see if this paradigm can be extended to other aspects of human dynamics – from the timing of human interactions to large-scale travel patterns.”
The research has been published online on the website of the Proceedings of the National Academy of Sciences.
