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A modified dynamic cellular automata model is proposed to simulate the evacuation of occupants from a room with obstacles. The model takes into account some factors that play an important role in an evacuation process, such as human emotions and crowd density around the exits. It also incorporates people’s ability to select a less congested exit route, a factor that is rarely investigated. The simulation and experimental results show that modifications to the exits provide reasonable improvement to evacuation time, after taking into account the fact that people will tend to select exit routes based on the distance to the exits and the crowd density around the exits. In addition, the model is applied to simulations of classroom and restaurant evacuation. Results obtained with the proposed model are compared with those of several existing models. The outcome of the comparison demonstrates that it performs better than existing models.

The use of cellular automata (CA) in modeling crowd movement has attracted considerable attention in transportation science. Since simulations of real-life evacuations are nearly impossible to conduct, different modeling methods have been used to develop simulations for studying human behavior during evacuation.

Research has shown that the complex behavior of pedestrians can be studied from a physical point of view [

Similarly, numerous models have been proposed to study these systems, such as those based on particle flows [

The majority of CA models divide the floor into rectangular cells and assign a weight to each cell for every time step. Weight assignment is based on the location and width of exits, human emotions, and the position of obstacles. There are two types of floor fields: static and dynamic fields. A static field does not change with time, even in the presence of pedestrians. Nishinari et al. [

Dynamic floor fields, on the other hand, change with time and with the presence of pedestrians. During weight assignment at each time step, certain parameters have to be considered, such as pedestrian behavior, distribution, and density in the exit area, as well as distance to the exits. Then, the movement of pedestrians is decided based on the rules of pedestrian interaction and the weight assigned to the cells. Most existing models make the assumption that pedestrians are uniformly distributed in a room; only a few models consider the distribution of pedestrians around the exit area or in a room without obstacles.

We propose a model in which the weight of cells at each time step is affected by crowd distribution. We use the metric of Varas et al. [

In this study, the proposed model is used to investigate the effect of obstacles on the evacuation process with the aim of creating a safer environment and reducing fatalities. The next section briefly describes the static field model for determining pedestrian premovement, Section

The static floor field consists of a room represented by a bidimensional grid with a cell size of 0.5 × 0.5 m^{2}, a typical pedestrian space in a crowded situation. The mean speed of pedestrians is assigned as 1.0 m/s for a normal situation, as reported in [

The model of Varas et al. [

Weight assignment is repeated until the value for every cell is calculated. In addition, the walls in the field are assigned very high weights to ensure pedestrians will never occupy them. During simulations, only the positions of occupants are updated at each time step while the floor-field values remain the same.

In addition, we set some intelligent local rules as introduced in [

As mentioned above, the weight of a cell depends on its location in relation to obstacles and the exits. Since the obstacle’s parameters are constant, the floor-field value of the obstacle is independent of time and set to be static (Figure

An 18 × 24 floor field with 40 pedestrians near the left side of exit A.

Values of the floor field in Figure

A dynamic floor field is established by considering pedestrian distribution in the evacuation process. Assuming there are

Therefore, we define the dynamic floor field in mathematical terms as

We incorporate the defined degree of impatience into this proposed model because research has shown that emotions such as impatience could affect pedestrians’ choice of evacuation route [

As the proposed model is dynamic, some of the pedestrians may change their choice of exit after a number of time steps, regardless of their current location. Figure

Values of the floor field in Figure

Snapshot of a simulation performed using the proposed model of the floor field in Figure

One of the most important problems in pedestrian evacuation study is where to place the exits for speedy evacuation. Many existing models do not consider crowd distribution in a room, assuming uniform distribution in a large room without obstacles. However, obstacles are an important factor to consider in determining the optimal exit location.

In this section, we report the results of a series of simulations performed for a room without obstacles to test and validate our proposed dynamic model against the findings of Daoliang et al. [

We test the model in a room divided into 14 × 18 cells with

Floor-field values generated using the proposed model for a room with a central exit in the left wall.

Figure

Snapshot of a simulation for the floor field in Figure

Relationship between exit width and evacuation time (in time steps) for the room in Figure

To further test and validate our model’s dynamic capability for multiple exits, we performed simulations with a room that has obstacles. Consider a classroom of 13 × 28 cells with 30 students, 10 tables, and two single-door exits (Figure

A room with 30 occupants and two single-door exits.

Snapshot of a simulation for the room in Figure

The proposed model includes various forces due to human behaviors, such as attraction, clogging, and repulsion. A plot of the relationship between the mean speed of occupants and evacuation time for classroom illustrated in Figure

Relationship between the mean speed of occupants and evacuation time for the room in Figure

Consider ^{2}), and the speed of occupants shows that, when speed exceeds 1.3 m/s, the effectiveness of evacuation decreases (Figure

Effectiveness of evacuation,

Consider a restaurant of 18 × 28 cells with 109 occupants and 18 tables, with the tables representing obstacles. Possible locations for the exits are labeled from 1 to 78 in Figure

A restaurant with 18 tables and 109 persons.

Floor-field values for the room in Figure

Evacuation time is calculated for different locations of the exits, with the obstacles being fixed and the 109 persons distributed in the room. For evaluation purposes, we consider two cases: (i) one double door or two single doors; (ii) one quadruple door or two double doors. Here, a single door is defined as an exit that allows one person to leave through it at one time, while a double door allows two persons to leave through it simultaneously (Figure

Types of exit doors.

Figure

Evacuation time (in time steps) for 112 persons in the restaurant shown in Figure

The effect of exit width with a door located at the center of the left wall in the presence of obstacles is then analyzed for the static, dynamic, and proposed models. As seen in Figure

Variation in evacuation time (in time steps) with increasing exit width in the restaurant shown in Figure

Restaurants commonly have quadruple doors, which are defined here as a door that lets four persons go through simultaneously. The results for double-door and quadruple-door exits are plotted in Figures

Evacuation time (in time steps) for different locations of one double-door exit in the restaurant shown in Figure

Evacuation time (in time steps) for different locations of one quadruple-door exit in the restaurant shown in Figure

The optimal evacuation times for a double-door and a quadruple-door exit are, respectively,

Next, we replace the double door with two single doors, and the quadruple door with two double doors. Figure

The restaurant from Figure

Comparing evacuation time (in time steps) for the static, dynamic, and proposed models for different types of doors.

Snapshot of a simulation with 112 persons in the floor field from Figure

In this paper, we use a modified dynamic CA model to simulate the evacuation process in the presence of obstacles. The design of the model takes into account the distribution of the crowd, the location of exits, and the position of obstacles at each time step in order to make an optimal decision in selecting the best evacuation exit. Simulations using the proposed model produce the following results. First, evacuation time is effectively reduced in the proposed model compared with existing static and dynamic models. Second, the optimal positions for exit doors that minimize evacuation time are at the center of both sides of the restaurant. Third, compared with both static and dynamic models, evacuation time in the proposed model is lower in all simulations that we performed in this study. Finally, when there is only one exit (whether single door, double door, or quadruple door), increasing the exit width only contributes to a minor reduction in evacuation time for the three models studied, which is consistent with most of the existing findings.

The proposed model can be improved further by considering obstacles such as tables as movable, since during an evacuation some people may move the tables to create a new walkway, which may lead to a smoother flow. For more realistic simulations, factors such as age, physical ability, psychological factors (e.g., emotions), and group formation should also be considered. For future work, some of these factors will be integrated into our model and applied to other types of spaces, such as halls, stadiums, and movie theaters.