  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.
