Symmetry in behavior of complex social systems - discussion of models of crowd evacuation organized in agreement with symmetry conditions

TL;DR

This paper models crowd evacuation in stadiums using symmetry principles to improve simulation accuracy, comparing results with and without symmetry considerations, and introduces a new simulation program based on a modified Helbing model.

Contribution

It introduces a novel approach incorporating symmetry conditions into crowd evacuation models and presents a new simulation program based on a modified Helbing model.

Findings

Evacuation times are affected by symmetry considerations.

Average forces during evacuation are influenced by symmetry modeling.

Simulation results differ significantly when symmetry is included.

Abstract

The evacuation of football stadium scenarios are discussed as model realizing ordered states, described as movements of individuals according to fields of displacements, calculated correspondingly to given scenario. The symmetry of the evacuation space is taken into account in calculation of displacements field - the displacements related to every point of this space are presented in the coordinate frame in the best way adapted to given symmetry space group, which the set of basic vectors of irreducible representation of given group is. The speeds of individuals at every point in the presented model have the same quantity. As the results the times of evacuation and average forces acting on individuals during the evacuation are given. Both parameters are compared with the same parameters got without symmetry considerations. They are calculated in the simulation procedure. The new program (using modified Helbing model) has been elaborated and presented in this work for realization the simulation tasks the.