Discretisation effects and the influence of walking speed in cellular   automata models for pedestrian dynamics
  We study discretisation effects in cellular automata models for pedestrian dynamics by reducing the cell size. Then a particle occupies more than one cell which leads to subtle effects in the dynamics, e.g. non-local conflict situations. Results from computer simulations of the floor field model are compared with empirical findings. Furthermore the influence of increasing the maximal walking speed $v_{{\rm max}}$ is investigated by increasing the interaction range beyond nearest neighbour interactions. The extension of the model to $v_{{\rm max}}>1$ turns out to be a severe challenge which can be solved in different ways. Four major variants are discussed that take into account different dynamical aspects. The variation of $v_{{\rm max}}$ has strong influence on the shape of the flow-density relation. We show that walking speeds $v_{{\rm max}}>1$ lead to results which are in very good agreement with empirical data. 
Ansgar Kirchner, Hubert Kluepfel, Katsuhiro Nishinari, Andreas   Schadschneider, and Michael Schreckenberg