More and more people take part in marathons these days – over 30,000 people will run the London Marathon this weekend, for instance. But it’s not just the 26 miles and 385 yards that could be a daunting prospect. “I have to admit to being completely frustrated by the congestion and for 18-19 miles was just dodging people and being held up,” one participant grumbled after the 2012 London Marathon. “I had to overtake a lot of people and ended up with bruised forearms from all the elbows,” said another.
How do such crowding problems arise, and could they be reduced? Some researchers believe that we can find the answers through a more familiar system in which jams appear – road traffic flow. Martin Treiber, of the Technical University of Dresden in Germany, has previously developed models for traffic flow, and now he has reported modifications that capture the essential details of sporting events such as marathons.
One of the first attempts to model traffic flow was made in the 1950s by James Lighthill and his collaborator Gerard Whitham of Manchester University. They considered the traffic as a kind of liquid flowing down a pipe, and looked at how the flow changes as the fluid gets denser. At first the flow rate increases as the density increases, since you simply get more stuff through in the same period of time. But if the density becomes too high, there’s a risk of blockages or jams, and the flow rate plummets.