Congested emergency evacuation of a population using a finite automata approach
Highlights
► Congestion effects were included in a simulation model for pedestrian dynamics. ► Computational experiments show that the evacuation simulations are more realistic. ► Adjusting the simulated data to an extreme value distribution indicates a close similarity.
Introduction
Emergency traffic computational models have drawn much attention from researchers in several areas, mainly because of the widespread availability of inexpensive and powerful computers needed to successfully address the sophistication of these models and also because of the obvious practical applications in many real-life situations. Usually, the metric used to assess the quality of a practical scenario is evacuation time (Zarboutis and Marmaras, 2007). Estimating evacuation time involves situations in which people must evacuate an environment in the shortest time possible because of natural or man-made emergency events such as hurricanes, floods, wildfires, and chemical spills.
The models that have been developed in the past to study evacuation problems use a variety of different methods, including Monte Carlo simulations (Kirchner and Schadschneider, 2002a, Smith et al., 2009, Guo and Tang, 2012), queueing (Stepanov and Smith, 2009), network theory (Cruz et al., 2005, Zheng and Liu, 2010), and hydraulic analogy (Hughes, 2002, Tian et al., 2009, Jiang et al., 2010, Li et al., 2012), being the latter very powerful and convenient for analyzing density waves in traffic flow.
Simulations can be considered in either a macroscopic or a microscopy way. Examples of the microscopy way include the multi-agent cellular automata method (Hamagami and Hirata, 2003, Song et al., 2006, Rinaldi et al., 2007), which is the focus of this paper. Among the main advantages of the automata approach we could mention the ease of use and understanding, the possibility of simulating virtually any real environment, with and without obstacles, without the need of including complex mathematical equations (say, e.g., as for the hydrodynamical models), and the possibility of real-time visualization in the plan of the environment under study. In comparison to the hydrodynamical models, however, the main drawback is the difficulty to directly relate speed and density as a continuous function.
The main objective of this paper is to propose a new simulation model to analyze the traffic of people under emergency situations based on Schadschneider’s (2002) model. The importance of this study arises from the importance of determining the best options or strategies for escape when site sheltering is not a preferred option, such as when infrastructure is damaged by hurricanes, floods, and fire.
The rest of this paper is organized as follows. In Section 2, we provide an overview of cellular automaton models, present some recent publications in the area, and introduce the proposed model. Some experiments that were performed are described and discussed in Section 3. Finally, in Section 4, we close the paper by summarizing our findings and discussing topics for future research in the area.
Section snippets
Overview
Modeling the space floor by means of cellular automata is convenient especially because of the ease with which this approach models the location of doors, corridors, and barriers, which may be crucial in an emergency evacuation. Traffic flow usually occurs in an environment (such as rooms, corridors, and stairs) in which there is only a limited amount of space available. Each individual occupies a certain area in that space, and therefore, the movement of people depends on the existence of
Results and discussion
The two models Eqs. (1), (3) were encoded in C++; the software is available directly from the web1 or from the authors upon request for educational and research purposes. In the simulations performed in this paper, we assign Q = 0.99 to represent a slow reduction of the trail effect. This value is usually arbitrary; further analysis of this issue should be undertaken in future studies. Note that matrix M (i.e., M1 or M2) must be rearranged during the
Conclusions and final remarks
This paper discusses improvements in a multi-grid model for pedestrian dynamics based on bionics-inspired cellular automata. The newly-added feature is useful to model congestion effects, which include a well-known reduction in the average pedestrian walking speed and an increase in the number of people in an environment (for recent studies that also explore congestion, see van Woensel and Cruz, 2009, Cruz et al., 2010a, Cruz et al., 2010b). A program was encoded and made available for research
Acknowledgments
This research is supported by CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico; Grants 201046/1994-6, 301809/1996-8, 307702/2004-9, 472066/2004-8, 304944/2007-6, 561259/2008-9, 553019/2009-0, 550207/2010-4, 501532/2010-2, 303388/2010-2), by CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior; Grant BEX-0522/07-4), by FAPEMIG (Fundação de Amparo à Pesquisa do Estado de Minas Gerais, grants CEX-289/98, CEX-855/98, TEC-875/07, CEX-PPM-00401/08, CEX-PPM-00390-10,
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