28 September 2000

Nature 407, 465 - 466 (2000) © Macmillan Publishers Ltd.

DAVID J. LOW

David J. Low is in the Department of Civil and Offshore Engineering, Heriot-Watt University, Riccarton Campus, Edinburgh EH14 4AS, UK.
e-mail: d.j.low@hw.ac.uk

When we are at a major sporting event or travelling on public transport, our safety and comfort depend crucially on our fellow crowd members and on the design and operation of the facility we are in. So it is unnerving to realize that the modelling currently used to design and operate these venues has more in common with the design of water-pipe networks than anything with a human dimension. On page 487 of this issue¹, Helbing, Farkas and Vicsek present a dramatically different and potentially far more realistic modelling approach.

The movement of large numbers of people is important in many situations, such as the evacuation of a building in an emergency. In large crowds there is a risk of injury, and even loss of life, owing to the enormous forces that can be exerted on a single individual by the surrounding throng. The pressures that build up can bend steel barriers or push down brick walls. The consequences of crushing, trampling and panic in crowds are well known^{2, 3}, and a proper understanding of how groups of people move is vital if we are to minimize risks in these situations.

The traditional approach to predicting the motion of large crowds of pedestrians models the crowd as if it were a continuous homogeneous mass that behaves like a fluid flowing along corridors. The predicted flow rate indicates how quickly the crowd will move. However, this traditional approach assumes that the crowd is made up of identical, unthinking elements. A fluid particle cannot experience fear or pain, cannot have a preferred direction of motion, cannot make decisions, and cannot stumble or fall. The diverse behaviour of individual crowd members can drastically change the way in which the crowd as a whole behaves. Injuries to crowd members are related less to average pressure within the crowd than to point pressures at individual localities, and an injured pedestrian can fall and become an obstacle to the movement of others.

The new approach requires a recognition that the crowd is made up of individuals who possess the ability to think and react to events around them. One of the most dramatic cases in which human behaviour influences events is in a panic situation. Helbing et al. address this particular problem with a computer model of pedestrian behaviour that includes realistic reactions to crushing, panic and reduced visibility. They also simulate the tendency of people to do what others do and 'follow the crowd', but also allow for individuals to adopt personal strategies. Helbing et al. demonstrate that, because of their increased speed, panicking individuals will block up an exit that they could pass through safely at normal walking speed. They also show that a widening in a corridor actually slows down the movement of pedestrians, rather than allowing them to move faster, as one would assume. This surprising result is explained by those pedestrians who might have tried to move away from or overtake each other having to squeeze back into the mainstream flow at the end of the widening.

Modelling a crowd composed of discrete individuals rather than a continuous fluid clearly brings added complications. Helbing et al. model 'non-fluid' crowd properties, such as the 'faster-is-slower' phenomenon in which people in a rush end up going slower. They also investigate the best evacuation strategy for people in a smoke-filled room (Fig. 1). Such information can then be used to work out low-risk designs for the width of corridors, the number and position of doors, and the size of areas where people may gather. But these types of study can also provide us with a wider range of possible solutions to crowd problems. The crowd composed of individual people can respond to information directed towards them, to help them choose the most appropriate direction to take or the most appropriate exit to use.

Figure 1 How crowd behaviour affects escape from a smoke-filled room. High resolution image and legend (41k)

In the past, one of the main barriers to adopting this approach was the enormous number of calculations that are required to solve separate equations of motion for each crowd member. Modern computing power has dramatically changed that situation. Indeed, individual-centred approaches are now widely used in the modelling of road traffic networks^{4, 5}, which also used to be dominated by fluid-flow models. Similar individual-centred traffic models⁶ have produced excellent results and have led to effective new traffic management strategies. There has been extremely strong financial motivation to produce such improved traffic models. Traffic management strategies and road-building projects cost enormous sums of money, as do the delays caused by road congestion, and improved traffic modelling techniques can produce considerable savings. But the potential benefit of improved pedestrian models is even more valuable — a reduction in personal injury.

The model presented by Helbing et al. is just one of many possible models. To decide whether a particular model is an accurate description of real life, or to determine which model is the 'best' for the situation under consideration, requires real data to compare with each model's predictions. But such data are scarce or non-existent and may be extremely difficult to collect. With any type of mathematical modelling we always have to be careful to distinguish between 'real life' and our attempt to model it. Failing to recognize this difference can have serious consequences. But provided we are aware of when it is appropriate to use a particular model, it can provide valuable information to guide the planning process, for construction and for dealing with emergencies. Perhaps perfect safety is unattainable, but improved models of crowd dynamics can help to increase our safety in crowded situations.

References

1.	Helbing, D., Farkas, I.& Vicsek, T. Nature 407, 487-490 (2000).
2.	Taylor, P. The Hillsborough Stadium Disaster, 15 April 1989. Final Report (Home Office, HMSO, London, 1990).
3.	Johnson, N. R. Social Prob. 34, 362-373 (1987).
4.	Addison, P. S. & Low, D. J. Chaos 8, 791-799 (1998).
5.	Low, D. J. & Addison, P. S. Nonlin. Dynam. 16, 127-151 (1998).
6.	Duncan, G. Paramics-MP Final Report (Edinburgh Parallel Computing Centre, Univ. Edinburgh, 1994).