To model crowd disasters, though, they had to consider involuntary as well as voluntary behaviors. What the pedestrian can see remains important, but sometimes the push and pull of the crowd can be even more so. “When the crowd becomes high-density, the simple model isn’t enough,” says Theraulaz. “You have to take into account the rules of physical contact.”
Adding a physical-force component to the vision-based model allowed the study authors to predict pedestrian behavior in different types of overcrowding situations, such as a bottleneck around a blocked exit or a pileup that forms behind a fallen pedestrian.
When the study authors applied their modified model to a real-world bottleneck disaster, they were able to predict the location of the highest-risk areas and map out how pedestrian collisions would spread once the situation became critical. “This is the most dangerous type of case,” says Helbing. “You can do video analysis afterward, but even then it’s hard to see exactly what’s going on, because people are hardly moving.”
One of the biggest advantages of the vision-based model is its versatility, says Michael Batty, an urban planning researcher at University College London, who studies crowd modeling. “It’s relevant to a whole range of pedestrian situations, and that’s what makes it more testable,” he says. The study authors suggest that the model could also be used to analyze crowd disasters in low-visibility cases, such as fires, and could help improve the design of crowd-navigating robots.