Granular Floor Plan Representation for Evacuation Modeling

Abstract

In this paper we describe the architecture of a simple evacuation model which is based on a graph representation of the scene. Such graphs are typically constructed using Medial Axis Transform (MAT) or Straight Medial Axis Transform (S-MAT) transformations, the former being a part of the Voronoi diagram (Dirichlet tessellation) of the floor plan. In our work we construct such graphs for floor plans using Voronoi diagram along with the dual Delaunay triangulation of a set of points approximating the scene. Information supplied by Delaunay triangulation complements the graph in two ways: it determines capacities of some paths associated with edges, and provides a bijection between graph vertices and a set of regions forming a partition of the floor plan. We call the representation granular for this reason.

In our earlier work we discussed a simplified model coupling a partial behavioral model (accounting for typical pre-movement times) and a traffic model. In this expanded paper, we provide a clearer exposition of the representation of fire scene and briefly discuss the applicability of network flow models (e.g. the Ford-Fulkerson method or the push-relabel method) in our setting.

This work was partially supported by the Polish National Centre for Research and Development (NCBiR) – grant O ROB/0010/03/001 under Defence and Security Programmes and Projects: “Modern engineering tools for decision support for commanders of the State Fire Service of Poland during Fire&Rescue operations in buildings”, and by the Polish Na tional Science Centre grants DEC-2011/01/B/ST6/03867 and DEC-2012/05/B/ST6/03215.