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State-of-the-Art

One of the largest areas where crowd behaviors have been modeled is the domain of safety science and architecture with the dominant application of crowd evacuation simulators. Such systems model movements of a large number of people in usually closed and well-defined spaces like inner areas of buildings [TM95a, BBM05], subways [Har00], ships [KMKWS00], or airplanes [OGLF98]. Their goal is to help designers to understand the relation between the organization of space and human behavior [OM93]. The most common use of evacuation simulators is the modeling of crowd behavior in case of forced evacuation from a confined environment due to some threat like fire or smoke. In such a situation, a number of people have to evacuate the given area, usually through a relatively small number of fixed exits. Simulations are trying to help answer questions like: Can the area be evacuated within a prescribed time? Where do the holdups in the flow of people occur? Where are the likely areas for a crowd surge to produce unacceptable crushing pressure [Rob99]? The most common modeling approach in this area is the use of cellular automata serving both as a representation of individuals and as a representation of the environment. Simulex [TM95a, TM95b] is a computer model simulating the escape movement of persons through large, geometrically complex building spaces defined by 2D floor plans and connecting staircases. Each individual has attributes such as position, body size, angle of orientation, and walking speed. Various algorithms as distance mapping, way finding, overtaking, route deviation, and adjustment of individual speeds due to proximity of crowd members are used to compute egress simulation, where individual building occupants walk toward and through the exits. G. Still developed a collection of programs named Legion for simulation and analysis of the crowd dynamics in evacuation from constrained and complex environments like stadiums [Sti00]. Dynamics of crowd motion is modeled by mobile cellular automata. Every person in the crowd is treated as an individual, calculating its position by scanning its local environment and choosing an appropriate action. Helbing et al. [HM95, HFV00, WH03] proposed a model based on physics and sociopsychological forces in order to describe the human crowd behavior in panic situations. The model is set up by a particle system where each particle i of mass mi D. Thalmann, S.R. Musse, Crowd Simulation, DOI 10.1007/978-1-4471-4450-2_2, © Springer-Verlag London 2013

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has a predefined speed vi0 , i.e., the desired velocity, in a certain direction e0i to which it tends to adapt its instantaneous velocity vi within a certain time interval τ (for 1st term of Eq. (2.1)). Simultaneously, the particles try to keep a velocity-dependent distance from other entities j and walls w controlled by interaction forces fij and fiw (second and third terms of Eq. (2.1)), respectively. The change of velocity with time t is given by the dynamical equation:  v 0 e0 − vi (t)