A granular dynamic method for modelling the egress pattern at an exit

In recent years, in many countries around the world there have been many disasters caused by crushing in dense crowds. For example, the 1992 Lan Kwai Fong disaster in Hong Kong [20 people crushed to death], 1996 Guatemala City disaster [84 deaths in a football stadium], 2000 Denmark Music Festival [8 deaths in a stampeding crowd], 2001 Johannesberg disaster [43 deaths in Ellis Park stadium], 2001 Lubumbashi of Congo [14 deaths in a football stadium], 2001 Ghana disaster [126 deaths at a football match], 2001 Aracaju of Brazil [4 deaths in a prize giving event], 2001 Akashi of Japan [10 deaths in a Firework display], 2001 Sofia of Bulgaria [7 deaths in a disco], 2002 Goma of Congo [4 deaths at a concert], 2003 Chicago [21 deaths in a Club Fire] and 2004 Miyun, Beijing [37 deaths in a stampeding crowd across a bridge]. This indicates that when large number of people gathering together, the crowd movement, especially under emergency situations, may be hazardous and that congestion may substantially restrict the crowd's movement. A granular dynamic method is proposed in this article to model the egress pattern of evacuees in a densely populated enclosed space. The method models individual movement patterns in that the inter-personal forces acting on each person have been considered by adopting a contracted boundary approach. The out-flow rate of exits of various sizes is studied and modelled by a simple equation.