Methods of physics and modern computer science have been used successfully for the investigation of vehicular traffic problems for a long time [@chowd; @dhrev; @nagatani]. Also pedestrian dynamics has attracted some attention in recent years [@PedeEvak] and many interesting collective effects and self-organisation phenomena have been observed (for an overview see [@dhrev; @nagatani; @PedeEvak; @HePED]).

One topic which has not been studied intensively up to now (see, however, [@panic]) is the relevance of local conflicts in pedestrian traffic. A conflict indicates a situation in which two or more people try to enter the same space in one timestep. Obviously this is a real two-dimensional effect which has no counterpart in (directed) one-dimensional vehicular traffic. These conflicts are local phenomena which can have a strong influence on global quantities like evacuation times and flows in the presence of bottlenecks. Typical examples where conflicts become important are situations with clogging and stucking encountered in crowds of panicing pedestrians, e.g. near intersections and bottlenecks. In real life this often leads to very dangerous situations and injuries or even fatalities during evacuations. From a physics point of view these phenomena are related to flow properties of granular materials [@granul0; @gran_1; @gran_2; @gran_3; @granul1; @granul2; 