Simulations of Evacuation Using Small World Network
A stochastic cellular automaton(CA) model using Small World Network [5] has been proposed to simulate evacuation of persons from a room with plural exits. The number of persons escaping from each door is studied numerically in several kinds of rooms. Nume
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Introduction
Recently, behaviors of pedestrians have been extensively studied by physicists, and various models have been proposed to research collective effects, such as the spontaneous lane formation and the arching phenomena in front of an exit [14]. In this paper, we propose a stochastic cellular automaton(CA) model using Small World Network(SWN) [5] in order to simulate evacuation of persons from a room with plural exits. We consider the number of persons escaping from each door, and the total time of evacuation from the 'room. These values are quite important when we design and evaluate buildings. There is the law called "Building Standard Art" (BSA) in Japan, in which a simple method is proposed experimentally to estimate the above quantities. One of the main purpose of the calculations in the BSA is to check whether all the people in a building can evacute safely within the permissible time or not in case of a fire. We will compare numerical results of these quantities in our simulations with those calculated according to the BSA in detail.
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Calculations According to the BSA
The calculations in the BSA are based on a few experimental facts and a simple queue theory. There are many tables of formulae of calculations according to various types of buildings, such as office buildings and theaters. For example, the density of people in a typical office room is defined as O.25(person/m2 ) and M. Fukui et al. (eds.), Traffic and Granular Flow’01 © Springer-Verlag Berlin Heidelberg 2003
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N. Ohi, M. Ikai, and K. Nishinari
the flow rate escaping from a door per 1m width is 1.5(person/second·m). In the case of a room with plural exits, each person is assumed to use his nearest door in the BSA. Thus to obtain the number of people using each door, we first divide the floor of a room into subareas considering which door is the nearest one. The floor is discretized to a fine lattice and the distance from each cell to each door is all checked, then we select the door of the minimum distance at each cell. Finally we calculate the area of each part and divide the total number of people into each door according to their ratio. This division rule is one of the simplest ones, and is expected to be hold in average in the case of evacuation from a room. We have made a program of calculating the above division in an arbitrary kind of room by using the Dikstra method [6], and we will compare the division with direct simulations given in the next section.
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A CA Model Using SWN
The behavior of evacuating persons is complex in reality. There are continuous fluctuations of judging which direction to escape in case of a fire. We simulate these situations by using the combination of cellular automaton (CA) and the SWN. Originally, the SWN is proposed as intermediate networks between order (p = 0) and randomness (p = 1), where where p represents the randomness parameter [5]. We can quantify the structural properties of the SWN by a characteristic path length L(p) and clustering coefficient C(p). L(p) measures the typica
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