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 blocking and for 18-19 miles was just keeping away from 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. 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 jams, and the flow rate drops sharply. Treiber's model of a marathon uses this same principle that the flow rate first increases and then decreases as the density of runners increases, thanks to an sudden switch from free to crowded flow. He assumes that there is a range of different preferred speeds for different runners, which each maintains throughout the race. With just these factors, Treiber can calculate the flow rate of runners, knowing the "carrying capacity" at each point on the route. This allows Treiber to figure out how blocking might depend on the race conditions - for example, for different starting procedures. Some marathons start by letting all the runners set off at once (which means those at the back have to wait until those in front have moved forward). Others assign runners to various groups according to ability, and let them start in a series of waves. Treiber has applied the model to the annual Rennsteig half-marathon in central Germany, which attracts around 6,000 participants. The traditional route had to be changed in 2013, because the police were no longer willing to close a road to ensure that runners could cross safely. It could pass either over a 60m wooden bridge or through a tunnel. Treiber used his model to predict the likely blocking caused in the various options. The model predicted that a mass start would risk an overload of runners if the bridge were to be used. Only by moving the starting point further back from the bridge could the danger be avoided - and even then, if some of the numbers assumed in the model were only slightly inaccurate, there was still a risk of jams at the bridge. On the other hand, no dangerous blocking seemed likely for the tunnel route. The run organizers consulted Treiber's team, and eventually chose this option. What is the worst thing while running a marathon?
The long distance. Too many participants. The dangerous blocking. Serious injuries in forearms.