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In order to effectively depict the group evacuation behavior in the complicated three-dimensional space, a novel pedestrian flow model is proposed with three-dimensional cellular automata. In this model the calculation methods of floor field and fire gain are elaborated at first, and the transition gain of target position at the next moment is defined. Then, in consideration of pedestrian intimacy and velocity change, the group evacuation strategy and evolution rules are given. Finally, the experiments were conducted with the simulation platform to study the relationships of evacuation time, pedestrian density, average system velocity, and smoke spreading velocity. The results had shown that large-scale group evacuation should be avoided, and in case of large pedestrian density, the shortest route of evacuation strategy would extend system evacuation time.

As the density of urban population increases rapidly, the sudden disaster in the complicated environment may bring about serious consequences, so the study focus of the pedestrian flow is how to provide effective evacuation strategy [

Moreover, the pedestrians’ intimacy often leads to group evacuation. Based on A* algorithm, the evacuation efficiency of different-scale group was studied by Ji and Gao [

Meanwhile, pedestrians’ velocity of walking upward or downward the stairway is clearly different from their velocity of walking horizontally, which has great effect on the evacuation efficiency. Kretz et al. [

As shown in Figure

The three-dimensional Moore structure.

Cellular structure

Position schematic diagram

In this formula,

Meanwhile, different from the two-dimensional cellular automata Moore structure, the parameter

In the two-dimensional platform, the calculation methods of “floor field” have been put forward in many studies [

Three-dimensional space.

The floor field.

Usually, after the fire breaks out, the spreading velocity of smoke has major impact on evacuation. For the sake of depicting the problems clearly, the influence of smoke on the cellular

In this formula,

According to the findings of [

As influenced by intimacy and conformity mentality, under emergency and in the complicated environment, pedestrians tend to evacuate in herding. Therefore, in this thesis, the effect of group behavior on the evacuation efficiency is studied. Assume group

In this formula,

Then, the member

The model adopts parallel update mechanism, and the pedestrians meet the following rules from moment of

At the initial moment, the groups are initialized based on intimacy; the members of group calculate the transition gain

According to (

When many pedestrians compete for one target position at the same time, one of the pedestrians is chosen randomly by the system with equal probability to move to the target position, and the other pedestrians stay still.

The pedestrians would evacuate out of the system at moment of

When all pedestrians finish evacuating, the simulation is completed.

Based on the three-dimensional automata model above, the experiment platform is established to study the performance of group evacuation when the fire breaks out. The complicated three-dimensional evacuation space is considered as shown in Figure

The evacuation process.

By combining the above initial state and experimental results, the discussion of performance is made. In order to reduce the impact of the initial experiment status or waiting probability on the statistical indicators, the average value of thirty runtime value is taken for every indicator. In Figure

The relationship between system evacuation time

The relationship between system evacuation time

Meanwhile, the relationship between system evacuation time

The relationship between system evacuation time

Finally, the relationship between system evacuation time

The relationship between system evacuation time

In order to depict the group evacuation behavior and evacuation efficiency when fire breaks out in the complicated three-dimensional environment, a novel evacuation model is established based on the three-dimensional cellular automata. The calculation methods of floor field and fire gain are given in the model, in which the transition gain of the target position at the next moment is defined, and pedestrians will move to the position which is the minimum gain. Meanwhile, based on pedestrians’ intimacy and velocity change, the group evacuation strategy is elaborated. At last, the established experiment platform is used for simulation; the results show that

The authors declare that there is no conflict of interests regarding the publication of this paper. They also would like to thank the reviewers for their valuable comments on the paper.

This research was supported by the National Natural Science Foundation of China (Grant no. 61304187), the Program for New Century Excellent Talents in University of China (Grant no. NCET-12-0764), the Scientific Research Fund of Sichuan Provincial Science and Technology Department (Grants nos. 2014JY0111, 2013GZ0016), the Scientific Research Foundation of the Education Department of Sichuan Province of China (Grant no. 13ZA0296, 13ZB0052), and the Funds of Chengdu Normal University of China (Grants nos. CS13ZD01, YJRC2012-6).