Comparative Evaluation of the Fast Marching Method and the Fast Evacuation Method for Heterogeneous Media

ABSTRACT

The evacuation problem is usually addressed by assuming homogeneous media where pedestrians move freely in the presence of several exits and obstacles. From a more general perspective, this work considers heterogeneous media in which the velocity of pedestrians depends on their location. We use cellular automata with a floor field that indicates promising movements to pedestrians and, in this context, we extend two competitive evacuation methods in order for them to be applied to heterogeneous media: the Fast Marching Method and the Fast Evacuation Method. Furthermore, we evaluate the performance that these two methods exhibit over different simulated scenarios characterized by the presence of heterogeneous media. The resulting winning method in terms of evacuation effectiveness is greatly influenced by the particular problem being simulated.

Notes

1. Specifically (see for example (Schadschneider 2002)), it is usual to consider in the literature that every cell is 40 cm × 40 cm (typical space occupied by a pedestrian in a dense crowd) and a single pedestrian (not interacting with others) moves at a velocity of one cell per time step. Since the empirical average velocity of a pedestrian is about 1.3 m/s, this gives an estimated time step of 0.3 s.

2. In this work, the Moore neighborhood is considered for the movement of pedestrians.