  For the modelling of pedestrian dynamics we treat persons as self-driven
objects moving in a continuous space. On the basis of a modified social force
model we qualitatively analyze the influence of various approaches for the
interaction between the pedestrians on the resulting velocity-density relation.
To focus on the role of the required space and remote force we choose a
one-dimensional model for this investigation. For those densities, where in two
dimensions also passing is no longer possible and the mean value of the
velocity depends primarily on the interaction, we obtain the following result:
If the model increases the required space of a person with increasing current
velocity, the reproduction of the typical form of the fundamental diagram is
possible. Furthermore we demonstrate the influence of the remote force on the
velocity-density relation.
