Spatial games and memory effects on crowd evacuation behavior with Cellular Automata
Introduction
When we are part of a large moving crowd inside a building or a room, our safety and comfort depend strongly both from the behavior of the fellow crowd members and the design of the facility we are in. In situations where the crowd needs to evacuate the facility immediately, the process often leads to conflict when seeking a better position, especially around the exits. Former research of crowd dynamics during emergency evacuations has been based both on macroscopic and microscopic models. Macroscopic models face the crowd as a homogeneous mass that has certain characteristics. Such models, just to name a few, are the Regression models [1], the Route Choice models [2], the Queuing models [3], the Gas kinetics [4] and the Flow-based models [5]. On the other hand, the microscopic dynamics models seem more realistic, as the simulated crowd is composed from discrete individuals. These models include both continuous and discrete space models, while the most common categories are the Social Force models [6], [7], the CA models [8], [9], the Rule-based models [10] and the Agents-based models [11].
The Cellular Automata (CA) model offers a computational intelligent technique which approaches the evacuation simulation from the perspective of artificial intelligence. According to the CA models, both time and space are discrete, while the principal of the CA gives us the opportunity to create a parameterized model, as detailed as possible, focusing on specific individual behaviors under certain conditions. In addition, Game Theory is used to solve conflict problems among the crowd, as an acknowledged tool for interpreting human behavior and decision making. Despite this fact, very few studies have been conducted to explore crowd conflict behaviors during emergency evacuation with Game Theory [12], [13], [14], [15], [16], [17], [18], [19].
In this paper, we developed a CA evacuation model which investigates conflicts among individuals in the evacuation process by using a spatial game. This model provides us with the ability to predefine almost every evacuation parameter, such as the size of the evacuated area, the emergency and risk scale, the crowd density inside the room, the crowd different behaviors, the individuals’ velocity, etc. Thus, this model incorporates both topological features and features that describe the crowd formation and manners. It should be reminded that every individual constitutes a different entity, which has distinguished characteristics but still can interact with the others. This feature enhances the realism of the model, giving us the capability to study various phenomena under different panic circumstances. Moreover, although previous studies [13] have introduced the scheme of CA crowd behavior combined with game theory, or discrete modeling like Gas Lattice scheme enriched with game theory [15] or snowdrift game theories [14], to simulate crowd behavior, the presented study can be considered enhanced in many different ways. More specifically, taking into account Moore neighborhood instead of von Neumann [13], [14], [16], [17], the ability of the proposed model to better illustrate the movement of people inside the room in more physical way is apparent and state their preferable next position according to a desired direction, considering the position of the exit. Furthermore, the outcome of the proposed game, namely Chicken Game's, not only sets who of the players will move to the desired position, but also affects the players’ behavior and thus choice of possible strategy in subsequent conflicts. Thus, compared to the aforementioned studies [12], [13], [14], [16], [17], [18], [19], one's behavior is not an acquired feature but is affected by many parameters, which are both initial and current distance from the exit, along with the level of emergency, and the outcome of previous games; and can change during the evacuation. In other words, the proposed model outmatches previous evacuation models which utilize short term memory characteristics, adopting a fully dynamic behavior for the under study crowd taking advantage of the long memory CA based approach as a prominent feature of the people that instinctively affects their behavior. Finally, compared to the aforementioned confrontations, another novel feature of the proposed model towards realistic modeling of crowd is the incorporation of more than one velocities for the moving agents and how the ratio of different velocities in a heterogeneous crowd affect the evacuation process. This difference in velocities does not affect the introduced mechanism of the considered game played between individuals in a conflict. The slow individuals deal with the drawback that they do not participate in a conflict as often as a faster individual. The advantage is a model that approaches a more realistic situation providing us with much more interesting results. Finally, the efficacy and the robustness of the proposed CA model has been proven in both qualitative and quantitative ways, with the help of fundamental diagrams of flow, speed and density, compared with real life data as reported in literature.
In the remainder of this paper, Section 2 describes the contribution of Game Theory in the model when conflicts occur among evacuees. In Section 3, the selected CA modeling approach for crowd evacuation is briefly analyzed in its fundamental characteristics while Section 4 outlines the proposed CA model and its parameters and features, as well as the spatial game developed and how the payoffs affect the individuals involved and consequently the evacuation evolution. The corresponding simulations with various parameter settings, the metrics diagrams and the data results obtained from the simulations are presented in Section 5. Finally, in Section 6 conclusions regarding this model are made and some suggestions for future work are proposed.
Section snippets
Game Theory
Game Theory constitutes “the study of mathematical models of conflict and cooperation between intelligent rational decision-makers” [20]. It has been a known scientific field since 1928, when physicist and mathematician John von Neumann proved his minimax theorem. He then extended his research upon games and published the results in his 1944 book, Theory of Games & Economic Behavior along with Oskar Morgenstern [21]. A few years later, another mathematician, John F. Nash, whose contribution to
Cellular Automata
Cellular Automata (CA) are computational discrete models of physical systems, where space and time are discrete and interactions are local. A CA consists of a finite number of dimensions, usually two dimensional, lattice of n × n cells.
Apart from Pascal's triangle, which is considered to be the first cellular structure, the original concept was discovered in the 1940s by Stanislaw Ulam and John von Neumann [25]. Despite the studies among the next decades, it was 1970s that the CA got a
The proposed CA model
In this study, we propose an evacuation model, based on CA and coupled with a special game in situations of crowd collisions. To be more specific, the physical space in which the evacuation takes place, is being simulated with a two dimensional CA lattice of n × n cells, while the exit point is being represented by specific number of cells, which corresponds to exit door width equal to the length of the under study exit. Each of the CA cells is considered either empty or occupied by an
Simulation results
We developed a simulation environment using MATLAB, in order to couple the CA evacuation model with the evacuation game. In the following we describe the results of the simulations. In order to better present the underlying mechanism of the proposed overall model, in Fig. 2(a) a snapshot of a simulation, in which the people evacuating the room have the same velocity, is depicted. In this ground truth example, there are no individuals that are slower than the others. This homogeneity in velocity
Conclusions
In this work we introduced a CA based evacuation model, where the evacuees are participants to a spatial game when collisions take place. Thus we have a heterogeneous population inside the room, where every individual can choose either the polite or the competitive strategy, according to his experience and/or other parameters, such as the walking distance from the exit and the hazards of the situation, in order to exit the room as quick as possible, with a memory mechanism that was developed in
Martha M. Mitsopoulou received her Diploma in Electrical and Computer Engineering in April 2014 from Democritus University of Thrace (DUTh), Greece, followed by her M.Sc. from the same University on June 2017. During her studies she was an active member of IEEE Student Branch of Thrace and a member of the Organizing Committee of the 5th Panhellenic Electrical and Computer Engineering Students Conference. Her research interests lie in the areas of cellular automata, real-time models and
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2021, Physica A: Statistical Mechanics and its ApplicationsCitation Excerpt :The most famous continuous model is the social force model which was proposed by Helbing et al. [15], this model successfully reproduces crowd self-organization phenomenon. The classical discrete model includes the cellular automata model [16–19], the lattice gas model [20–22], and the agent-based model [10,23]. As the extension of the classical CA model, the floor field cellular automata model(FFCA) keeps the advantages of the classical CA model, such as high computational efficiency, simplicity, etc.
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Martha M. Mitsopoulou received her Diploma in Electrical and Computer Engineering in April 2014 from Democritus University of Thrace (DUTh), Greece, followed by her M.Sc. from the same University on June 2017. During her studies she was an active member of IEEE Student Branch of Thrace and a member of the Organizing Committee of the 5th Panhellenic Electrical and Computer Engineering Students Conference. Her research interests lie in the areas of cellular automata, real-time models and algorithmic game theory.
Nikolaos I. Dourvas received his Diploma and his M.Sc. degree in Electrical and Computer Engineering from the Democritus University of Thrace (DUTh) in Xanthi, Greece in 2013 and 2015, respectively. He is now working as a Ph.D. candidate at the same department. His main interests are cellular automata, modeling of large scale systems, design and integration of novel and emergent micro-nano-bio devices and systems, unconventional and parallel computing, modeling and simulation and bio-inspired algorithms. He is member of IEEE.
Georgios Ch. Sirakoulis received his Ph.D. degree in Electrical and Computer Engineering from Department of Electrical and Computer Engineering (ECE) in the Democritus University of Thrace (DUTh), Greece, in 2001, where he is serving as Full Professor while he is also Visiting Research Professor in University of West England. He has published more than a hundred papers in leading international journals, more than 140 papers in international conference proceedings and 14 guest-editorials. He is co-editor of 7 books as well as co-author of 20 book chapters. He is Associate Editor in “Journal of Cellular Automata”, “International Journal of Parallel, Emergent and Distributed Systems”, “International Journal of Unconventional Computing”, “IEEE Trans. on Nanotechnology”, “Microelectronics Journal”, “Integration, the VLSI Journal”, “Parallel Processing Letters”, etc. His research emphasis is on Complex and Smart Electronic Systems, Cellular Automata Theory & Applications, Future and Emergent Nano-Electronic devices, circuits, models and architectures, beyond CMOS computing devices and circuits, Memristors, Bioelectronics and Bioengineering, Unconventional computing, High performance Computing, FPGAs, Modelling and Simulation.
Katsuhiro Nishinari received his Ph.D. degree in aerospace engineering from The University of Tokyo, Japan, in 1995. He is currently a professor at the Research Center for Advanced Science and Technology (RCAST), The University of Tokyo, Japan, and the director of the crowd management research society. He is a member of the Japan Society for Industrial and Applied Mathematics, and an editor, Journal of Cellular Automata. He has published more than a hundred research papers in leading international journals, and wrote several books concerning traffic jam and applied mathematics. He has won awards for his work including “The 23th Scientific Publication Award in Japan by the book “Jamology” (in Japanese)” (2007), and NISTEP Award 2013 from National Institute of Science and Technology Policy. His research interests are “Jamology”, i.e. interdisciplinary research on transportation and jamming phenomena (vehicular traffic, pedestrian motion, queue network and supply chain, etc.), Cellular Automata, Soliton theory and its Applications and Network system, Non-linear Dynamics.