Inflow Process: A Counterpart of Evacuation

Abstract

We propose a new concept,“inflow process” of pedestrians as a counterpart of an evacuation process. In the inflow process, pedestrians enter a limited area without hurrying. This type of pedestrian motion can be observed in our daily life, e.g. in elevators, trains, etc. From experimental observation, we found intriguing behaviors, including pedestrians’ preference for boundaries, collective orientation, etc. Besides, the inflow process has contrastive aspects to evacuation process. For this reason the process is important for the pedestrian dynamics field.

Appendix: Voronoi Diagram

In this appendix we present the definition of a Voronoi diagram [18]. For a given area X and points P ₁, P ₂, ⋯ , P _n  ∈ X, a Voronoi domain for each P _i (1 ≤ i ≤ n) is defined as

$$\displaystyle{ V (P_{i}) =\{ P \in X\vert d(P,P_{i}) \leq d(P,P_{j}),j\neq i\}, }$$

(1)

where d(⋅ , ⋅ ) is a distance between two points. Namely, V (P _i ) is a set of points whose distance to P _i is smaller than to other points P _j (j ≠ i). A set of V (P _i ) defines a Voronoi diagram for X and P _i (1 ≤ i ≤ n). This Voronoi diagram has been used to calculate the area used by one pedestrian [19]. In the inflow process, since the final spacial distribution of pedestrians is of great interest, the diagram is a powerful tool for evaluating it.