Simulation of a pediatric hospital in evacuation considering groups

https://doi.org/10.1016/j.simpat.2020.102150Get rights and content

Highlights

  • An extended CA model is established to simulate evacuation of groups with children.

  • The family group always stay together but the shape of the group is changeable.

  • Overlapping and speeding up drastically reduce evacuation time of groups.

  • Parents are suggested to cradle young children in arms as much as possible.

Abstract

Pedestrians will form groups in both normal and emergency sometimes. Members of these groups usually have certain social relations. We study emergency evacuation of pedestrians in a pediatric hospital in this paper. Pedestrians there have their own particularities. First of all, all patients are children. Secondly, the patients usually have no ability to see a doctor alone. They are always accompanied by their families. Thirdly, children of different ages move at different speeds, which is heterogeneous. Fourthly, pedestrians usually move in family units. Family units and independent pedestrians are also heterogeneous. According to our actual observations, pedestrians are mostly composed of three-person groups, two-person groups and independent ones. Each group usually has one leader and the rest are followers. We use an extended cellular automata model considering groups to study such evacuation. The rule of both overlapping and speeding up are set in the model to realize the change from heterogeneous to homogeneous from the view of speed. The local density field and its range R are introduced. The field can lead pedestrians move to the area with low density. The range R=4 is optimal because of the family relation. The priority order is added to avoid conflicts. Groups with child have priority over independent pedestrians. The cohesive distance between leader and follower ensures members of the group always stay together, but the shape of the group is changeable in simulations. The evacuation time, waiting time and path of each pedestrian are analyzed. The simulation verifies the phenomenon that pedestrians behind tend to follow the front. The rules together release more free space to drastically reduce evacuation time and waiting time of groups, but independent pedestrians are not influenced greatly.

Introduction

Research on crowded people mainly focuses on public places such as subway stations [1], [2], shopping malls [3], [4] and schools [5]. Hospitals are also typical crowded public place in China, especially pediatric hospitals. There are more than 15 million newborns every year according to statistics. The number of children aged 0 to 14 years is about 230 million. The proportion of sick children in the total sick population in China has increased gradually in recent years [6]. The number of pediatricians per thousand children only reaches 0.69 from the perspective of resource allocation. It is still lagging behind the allocation standard of 0.85∼1.30 pediatricians per thousand population in developed countries such as the United States, Canada and Japan [7]. As a result, pediatric hospitals are always overwhelmed. Major medical resources are concentrated in big cities in China, such as Beijing and Shanghai. Sick children in these pediatric hospitals not only come from this city due to the high medical standards and advanced medical facilities, but also from the surrounding ones. A Grade III Level A pediatric hospital in Shanghai receives more than 5000 outpatient visits every day [8], [9].

Evacuees are heterogeneous in pediatric hospitals. Not only are there differences in behavior and speed between adults and children, but also between individuals and families. The family groups have some special characteristics. Firstly, all patients are children and they have no independent ability to see a doctor. Sick children are accompanied by their family members when they go to the hospital. Secondly, family move as a unit during medical treatment. They will eventually reunite even if there is a brief separation. For example, parents leave to get the medicine. Thirdly, children under age 4 are usually cradled by their parent. Cradling these children will not greatly affect the speed of the parent because of their low weight. Fourthly, children aged 4 to 8 years are led by their parents. The speed of the whole family group with child aged 4 to 8 years is relatively slow because the parents need to match themselves with their child. For example, there will be waiting or even backtracking to ensure that the children will not be separated. The cohesiveness of the group is very strong. Finally, each family group actually tends to hold one member as the leader, such as the father, while others are followers.

There are some studies about homogeneous evacuees considering groups. It can be observed that pedestrians will form groups in both normal and emergency [10], [11], [12]. Data on celebrating a football victory indicated that the majority of participants were with one or more friends. In other words, they were in groups. The phenomenon of group-level was paid more attention to the conceptualization of crowd behavior [10]. Mehdi Moussaïd et al. [11] analyzed the movement of approximately 1500 pedestrian groups under natural condition. The social interactions among group members generated typical group walking patterns that influenced crowd dynamics. Group members tended to walk side by side. They would form a line perpendicular to the walking direction at low density. The linear walking formation bent forward and formed a V-shape when the density was high. Bonneaud et al. [12] introduced a study of small crowds walking towards a common goal. It was proposed to make the link between individual behavior and crowd dynamics. Participants formed a cohesive group and did not merely treat one another as obstacles. The phenomenon of the kin behavior often occurred during evacuation. The model presented by Yang et al. [13] was applied to simulate the evacuation with respect to the kin behavior. Many interesting phenomena during real evacuation, such as incoherence, jamming, gathering, backtracking and waiting, were simulated. It was found preliminarily that the proper kin behavior was beneficial to improve the evacuation efficiency. Li-Li et al. [14] proposed an extended floor field CA model to describe the walking behavior of pedestrian groups. The model represented the movement of pedestrian groups realistically. The walking behavior of groups had an important impact on the dynamics of pedestrian flow. It had some negative effects, especially when the group density was high. Large groups (such as tourists or hiking groups) would split up typically [11]. Group members only thought about pedestrians around them when they were too far apart to communicate. Therefore, clusters of 2 to 4 people would appear within the group.

Some scholars have also studied the evacuation of heterogeneous evacuees considering groups. Heterogeneity was reflected in speed difference or group sizes. You et al. [15] proposed a novel methodology for calculating movement profit based on CA model. Small groups had six different forms in terms of size. The simulation results showed that the evacuation efficiency of different forms of small groups was very different. The work of Lu et al. [16] was calibrated with a few field experiments of crowd evacuation conducted in a university building. The floor field CA model was based on the leader-follower behavioral rule. The crowds in field experiments were heterogeneous. Both group sizes and the speeds were different. The total crowd evacuation time increased significantly with the presence of pedestrian groups in the crowd. The model presented by Crociani et al. [17] could improve not only the ability to generate overall aggregated dynamics, but also the precision in the microscopic group dynamics. It paid attention to the shape of two-person groups. Ma et al. [18] studied the crowd dynamic on different social relations and the impacts of small groups in emergency evacuation. Three experiments were conducted in an 11-story office building. Different types of pedestrians had different behaviors and speeds in the experiments. Small group behavior had a positive effect on crowd dynamics when evacuees understood and cooperated with one another. Conversely, there were negative effects. The work of Drury et al. [19] opened the way for considering the principles of SCT as an alternative explanatory framework. The social identity framework had been able to provide explanations of small group processes and group productivity. The emphasis on social bonds rightly stressed the prevalence of solidaristic behavior.

Overlapping often occurs in groups, especially in emergency evacuation. Crociani et al. [17] described the mechanism of overlapping. The model allowed two pedestrians to temporarily occupy the same cell at the same step in high density case. Overlapping was allowed only in the case of counter-flow situations. In order to model the spatial behavior of pedestrian movement, both simple and structured groups were mentioned. Overlapping between agents of the same group was not allowed in simulations. Bandini et al. [20] proposed an extended CA model based on agent. The model allowed pedestrians to overlap transiently with a small probability. Two pedestrians (a maximum of) were allowed to stay in the same cell at each step. The rationale was the fact that pedestrians tended to rotate their bodies to pass in tight spaces, especially in high densities.

Some scholars have conducted experiments to study the evacuation behavior of groups. James [21] analyzed group data in a field project. The distribution of different sizes of group was fitted with Poisson model. The relationships governing the combinations of individuals were relatively stable. Zhang et al. [22] studied the evacuation of students in a classroom. Some typical characteristics of evacuation, such as variable speed and formation of groups, were found by studying the video record. Haghani et al. [23] performed experiments with various group sizes. Group size had a significant impact on pre-action and decision time. Subjects showed a behavior opposite to herding in making exit decisions, which was similar with that of individuals. In order to investigate the impact of social groups on evacuations, Cornelia von Krüchten et al. [24] performed an empirical study with pupils. Several evacuations with groups of different sizes and different interactions were carried out. The analysis showed that evacuation time for large groups might decrease due to self-ordering effects. Social groups were approximated as ellipses oriented along their moving direction.

The pedestrian groups were all composed of healthy people in most studies. The members within those groups were regarded as homogeneous whether they are friends or family members. The crowd is obviously heterogeneous in pediatric hospitals. Both behaviors and speeds of different types of pedestrians are different. The evacuees consist of many family groups. Family groups contains sick children. Some of the children such as ones under age 4 are always be cradled by the adults. Some of the children such as ones aged 4 to 8 years move slowly in normal. However, they will be cradled in arms in emergency. Thus overlapping occurs during the evacuation. This study focuses on the evacuation of family groups with sick children. All independent pedestrians are simply assumed to walk at the same speed. Parents with cradled younger children can struggle to reach the same speed as independent pedestrians in emergency. Older children over age 8 can also reach the speed of independent pedestrians with the urging force of parents. When overlapping occurs, the speed of the group will change. The whole will change from heterogeneous to homogeneous from the aspect of speed.

The rest of this paper is organized as follows. The second section introduces the model and transition probability. The third section introduces the rules. Case study and analysis of simulation results are performed in Section 4. The last section gives conclusion and suggestions for future works.

Section snippets

Basic model

In this study, an extended CA model that considers groups is established to simulate the evacuation of a pediatric hospital. The model is built on a two-dimensional space, which is divided into square grids. The cell size is 0.5 m × 0.5 m [25].

Most of the pedestrians move in family groups through our practical observations in a pediatric hospital. These pedestrians include three-person groups, two-person groups and independent ones. G-2 and G-3 refer to the two-person group and the three-person

Rules

This paper studies the mechanism of overlapping. Overlapping here means that parents cradle children aged 4 to 8 years because of their low height and light weight in emergency. Groups with children move slowly, but they will speed up during an emergency evacuation. Groups change from heterogeneous to homogeneous by speeding up. The way to achieve the simulations is to add both overlapping and speeding rules.

The affiliated pediatric hospital of Fudan University

The affiliated pediatric hospital of Fudan University is one of the top 10 pediatric hospitals in China. The comprehensive hospital has 13 pediatric sub-specialties. The daily outpatient visits can reach 6000∼7000. The pediatric hospital receives at least 15,000 visitors a day because pediatric patients are always accompanied by their parents. The composition of population is complex. The outpatient building has three floors. Most people are waiting outside the clinics on the second and third

Simulation results and discussion

The total evacuation time is the time from the beginning of evacuation to the last pedestrian leaving the hall. As the number of simulation steps increases, the number of remaining pedestrians are shown in Fig. 14(a). The red curve shows the change in emergency, while the blue one refers to the normal. The average evacuation time of different types of pedestrians is shown in the Fig. 14(b).

The average evacuation time of different types of pedestrians is shown in Table 7. The total average

Conclusion

The evacuation simulations of a pediatric hospital are studied based on an extended CA model in this paper. Groups are taken into account in our model because family unit is the biggest characteristic. There are groups of different sizes and shapes. The size of some groups is changeable due to the overlapping rule. The shape of groups is also changeable because followers always closely follow their leaders. The cohesive distance ensures group members always stay together. The rules of

Acknowledgements

This work is supported by the National Natural Science Foundation of China (71771149 and 71831008).

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