Mathematics Professor Unwraps the Science of Crowd Dynamics

Rutgers-Camden mathematics professor Benedetto Piccoli analyzes crowd dynamics in his new book.

Rutgers-Camden mathematics professor Benedetto Piccoli analyzes crowd dynamics in his new book.

During the holiday shopping season, malls seem to be as crowded as busy city streets. It’s a pedestrian traffic jam from store to store as people try to navigate the pathways that will lead them to the perfect holiday gift, and maybe even a bargain.

Trying to get around or through droves of people isn’t just a science perfected by savvy shoppers. A new book by a Rutgers University–Camden mathematics professor analyzes crowd dynamics and the reasons people choose the paths they take.

“Pedestrian dynamics is really a broad area studied from many different perspectives, from the human gait to crowd behavior,” says Benedetto Piccoli, the Joseph and Loretta Lopez Chair of Mathematics and director of Rutgers–Camden’s Center for Computational and Integrative Biology.

Piccoli’s book, Multiscale Modeling of Pedestrian Dynamics (Springer, 2014), brings together two disciplines when analyzing crowd dynamics: psychology, which studies the cognitive processes behind the action of walking; and mathematics, which attempts to quantify the laws that govern the way crowds of people move or interact.

“The main idea of the book is to create a mathematical framework in which you can essentially integrate the two approaches and give rise to more efficient crowd behavior models,” Piccoli says. “We wanted to make the jump forward in this research area to produce reliable data and mix ideas from many different fields.”

Piccoli says most of the complex trends exhibited by crowds are due to an intrinsic interplay between individual and collective behaviors.

“When you walk you can decide your pace, when to accelerate or decelerate, the angle you take, and a mixture of other factors that lead to your decisions,” he says. Generally, pedestrians will choose to take the route that expends the least amount of energy.

Benedetto Piccoli

Benedetto Piccoli

Another factor is based on the side of the road that people drive. More often than not, Americans will walk on the right because they drive on the right side of the road. People from countries in which they drive on the left side of the road will walk on the left. Staying to one side or the other is the key to walking among pedestrians in a mall or a sports arena, where crowds of people are the norm.

Piccoli says people stay to the right or left to allow others to move more efficiently in opposing directions. Instead of negotiating around oncoming people, a person can simply follow the person in front of them. This self-organizing behavior is automatic among large groups of people; a reflex that allows pedestrians to avoid collisions with others.

“In reality, every walking pedestrian continuously makes choices on now to navigate the environment and the cognitive process behind that is far from trivial,” Piccoli says.

The Rutgers–Camden scholar recently performed an experiment on the Rutgers–Camden campus by placing a traffic cone in an outdoor area that typically has a lot of pedestrian traffic. It was placed in such a way that staying to the left of the cone would be the most direct path around it.

In one observation, Piccoli and his students simply watched how people navigated around the obstacle. In another instance, they asked the pedestrians if they could watch them walk, but did not mention the cone as part of the experiment. In the third scenario, the researchers pointed out the cone.

“The people we simply observed almost always stayed to the left of the cone,” Piccoli says. “In the second scenario, results were split. When we told them about the cone, they almost always stayed to the right. This is an example of how complex the decision making process can be.”

Taking the shortest route and the “proper” route aren’t the only ways pedestrians get from one point to another, especially when traveling in a crowd of people.

“Pedestrians will try to walk so that they are aligned with their final destination even if there is a short cut to take, especially in an environment that is a little unfamiliar,” Piccoli says. “In a known environment, you’re developing a structured strategy for getting to your destination, but in unknown environments, people are less likely to stray from the path.”

Piccoli says studying vehicular traffic shares some of the same components as crowd dynamics, but there are other factors at play such as city infrastructure, traffic signals, how cars are engineered, and the driver. He has been awarded a $239,971 grant from the National Science Foundation to study how autonomous vehicles could improve vehicular traffic flow.

An expert in control systems and systems biology, Piccoli earned his bachelor’s degree from the University of Padua in Italy and his master’s and doctoral degrees from the International School for Advanced Studies in Italy.

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