Computer Simulations of Pedestrian Dynamics and Trail Formation
  A simulation model for the dynamic behaviour of pedestrian crowds is mathematically formulated in terms of a social force model, that means, pedestrians behave in a way as if they would be subject to an acceleration force and to repulsive forces describing the reaction to borders and other pedestrians. The computational simulations presented yield many realistic results that can be compared with video films of pedestrian crowds. Especially, they show the self-organization of collective behavioural patterns.   By assuming that pedestrians tend to choose routes that are frequently taken the above model can be extended to an active walker model of trail formation. The topological structure of the evolving trail network will depend on the disadvantage of building new trails and the durability of existing trails. Computer simulations of trail formation indicate to be a valuable tool for designing systems of ways which satisfy the needs of pedestrians best. An example is given for a non-directed trail network. 
D. Helbing, P. Molnar, and F. Schweitzer