We investigate the role of conflicts in pedestrian traffic, i.e., situations where two or more people try to enter the same space. Therefore a recently introduced cellular automaton model for pedestrian dynamics is extended by a friction parameter $\mu .$ This parameter controls the probability that the movement of all particles involved in a conflict is denied at one time step. It is shown that these conflicts are not an undesirable artifact of the parallel update scheme, but are important for a correct description of the dynamics. The friction parameter $\mu$ can be interpreted as a kind of an internal local pressure between the pedestrians which becomes important in regions of high density, occurring, e.g., in panic situations. We present simulations of the evacuation of a large room with one door. It is found that friction has not only quantitative effects, but can also lead to qualitative changes, e.g., of the dependence of the evacuation time on the system parameters. We also observe similarities to the flow of granular materials, e.g., arching effects.

We investigate a probabilistic cellular automaton model which has been introduced recently. This model describes single-lane traffic flow on a ring and generalizes the asymmetric exclusion process models. We study the equilibrium properties and calculate the so-called fundamental diagrams (flow versus density) for parallel dynamics. This is done numerically by computer simulations of the model and by means of an improved mean-field approximation which takes into account short-range correlations. For cars with a maximum velocity of 1, the simplest nontrivial approximation gives the exact result. For higher velocities, the analytical results, obtained by iterated application of the approximation scheme, are in excellent agreement with the numerical simulations.

A spatially continuous force-based model for simulating pedestrian dynamics is introduced which includes an elliptical volume exclusion of pedestrians. We discuss the phenomena of oscillations and overlapping which occur for certain choices of the forces. The main intention of this work is the quantitative description of pedestrian movement in several geometries. Measurements of the fundamental diagram in narrow and wide corridors are performed. The results of the proposed model show good agreement with empirical data obtained in controlled experiments.