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A Crowd Evacuation System in Emergency Situation Based on Dynamics Model Qianya Lin, Qingge Ji, and Shimin Gong Department of Computer Science, Sun Yat-Sen University, Guangzhou, 510275, P.R.C. [email protected]

Abstract. This paper presents a system for crowd evacuation in emergency situation based on dynamics model to offer a base platform for further researches. Starting with the implementation of base functions, our focus is on the stability and expandable of the platform to offer new functions easily according to our needs latter. To improve the independence of the module, the function into layers and dividing the data are separated into blocks. To reach efficient system implementation, the 3D building is translated into a 2D graphics by turning the map into a group of nodes. Furthermore, the element called node plug is used to enhance the expansibility of the system. Experiments are carried out to analyze the crowd’s evacuation efficiency in a given building. The impact caused by mass behavior, the structure of the building and the number of people inside are also construed qualitatively in the experiments.

1

Introduction

As a branch of virtual reality, crowd animation is becoming more and more important and challenging. It is widely applied in city planning, building design and entertainment industry and so on, and involves a great many fields, such as physics, psychology, sociology, physiology, computer graphics, and computer network, etc.. The key point of researches focuses on how to simulate a lot of complicated and changeful human behaviors, activities and situations by a computer. The goal of this paper is to build up a platform for the research of the mutual influences between crowded individuals in emergency. Moreover, the influence on the crowd by the emergency extent and the environment is another emphasis of our research. To reduce the complexity, we use Helbing’s dynamic model[1] to analyze the behaviors of individuals and crowd. The paper is organized as follows. Section 2 covers related work in the field of crowd animation. Section 3 shows the rough characters of this system to give a clear impression to readers. Section 4 describes the details about the system. In section 5, experiments and results are presented to support the system. Conclusions and future work are presented in section 6. H. Zha et al. (Eds.): VSMM 2006, LNCS 4270, pp. 269–280, 2006. c Springer-Verlag Berlin Heidelberg 2006

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2 2.1

Q. Lin, Q. Ji, and S. Gong

Related Work General Studies of Crowd Animation

Crowd animation mainly includes crowd visualization, modeling of crowd behavior and crowd simulation, modeling of crowd behavior is the emphasis of this paper. The research of crowd animation in prophase adopts rule-based schemes. Reynolds[2] is one of the pioneer researchers that proposed crowd animation. His distributed behavior model simulated the behaviors such as flocks of birds, schools of fishes and controlled their behavior with three principal rules. Tu and Terzopoulos[3] studied simulating the behavior of artificial lives and present the model of artificial fishes with interaction, synthetic visions and exhibited realistic behaviors. Reynolds[4] strided a step forward by implementing some steering behaviors such as seek, pursuit and obstacle avoidance on his original model, that can provide fairly complex behaviors by combining the simple one together. Layered model appears to reduce the complexity, in which agent is endowed with different degrees of autonomy, social relationship and emotional state. Perlin and Goldberg[5]’s Improv system uses a blackboard for the actors to communicate with each other. They introduced a layered behavior model to break down the complex behaviors into simpler scripts and actions. Franco et al.[6] proposed a 2D-grid with a four-layered structure platform to simulate crowds in the city that each layer is used to reflect a different aspect of an agent’s behavior so as to implement complex behaviors. Soteris et al.[7] used the top-down approach where the movement of the pedestrians is computed at a higher level, and the lower level deals with the detailed and realistic simulation to reduce the computing burden. Musse and Thalmann[8] presented the ViCrowd model to simulate crowds with different levels of autonomy. Based on this work, Musse, Thalmann and Kallmann[9] put forward a system which collected actors together if they share a common goal and controls them as one group. Bouvier et al.[10] used particle system to simulate human behaviors. Each agent is regarded as a particle, endued with a state and a feedback function to dominate its behavior and all agents’ behaviors constituted the whole system’s performance. Still[11] studied the crowd in a physical aspect and abstracted the model by watching real crowds in his PhD thesis. Helbing and his research group adopted particle system to study the crowd behavior in emergency situation based on social psychology and dynamics. Adriana et al.[12] went further that they added up individual’s characteristic and relational behavior to vivify the evacuation. We should notice that distinct from other research methods, particle theory looks on things in a general view that one of the individuals may not act correctly when the crowd performs vividly. Nowadays, many new ideas are turning up in the study. Vallamil et al.[13] brought out the new idea that defines the agent and group in parameterization. As an old technique, cellular automaton reignited because of its simplicity and expeditiousness. Blue and Adler[14] used cellular automata model to solve the crowd evacuation problem in emergency situation. Yang et al.[15] imported

A Crowd Evacuation System in Emergency Situation

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relational behaviors into the cellular automata model. There are countless ways to generate human-like behaviors, such as hydromechanical model and psychologic model etc. As people pay more and more attention to crowd animation, more and more original and effective ideas will be introduced to the study. 2.2

Behavior Simulation in Emergency Situation

The obstacles of behavior simulation can be summarized into two types: how to compose natural and gliding behavior and how to generate appropriate path planning. Crowd simulation in emergency situation usually concentrates on the latter, e.g., Hebling’s particle model mentioned above. Musse goes further based on Helbing’s research. Besides, Musse also brings out a random distributing behavior model to study the relations between autonomy and mass behaviors. Adler’s cellular automata model offers a new way for crowd simulating research. L.Z. Yang et al. imported relational behaviors into cellular automata model and reached the conclusion that mass behavior is not always harmful.

3

General View

A crowd animation system in emergency situation based on Helbing’s dynamic model is presented in this paper to offer a basic platform for the study of crowd evacuation behaviors and effects. In this sytem, the main focus is the basic functions for easily improving new functions according to our subsequent needs. Generally speaking, the Helbing’s dynamic model can be summed up as the following formula: a = mi

→ → → − d− vi v0 − vi (t) e0−− → −→ = mi i i fij + fiw = dt τi w

(1)

j(=i)

− → −→ Thefij and fiw in the formula are interpreted by the next two formulas: r

−d

ij ij − → → B t − fij = [Ai i + kg(rij − dij )] · − n→ ij + kg(rij − dij )vji tij

(2)

r −d

i iw −→ B → −→ −→ − n→ fiw = [Ai i + kg(ri − diw )] · − iw + kg(ri − diw )( vi · tiw )tiw

(3)

Fig.1 shows the general structure of the proposed system which is divided into two execution layers and two store modules. The higher layer is the operation layer, which is responsible for computing the whole crowd and agents’ states, escape direction and evacuation effect, while the lower layer is the description layer, assigned to render the local 3D scenes. Separating computing and scene rendering can enhance the efficiency, reduce coupling extent among modules and make sure that each module concentrates on its own mission. The data store modules supply various data to two layers. Different layers communicate by gaining data from the two store modules instead of calling each

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Fig. 1. General structure of the system

other. One of the characteristic of the system is separating the function into layers and dividing the data into blocks. In detailed design, based on Soteris et al.[7]’s ideas of dividing the areas, the 3D building is transferred into a 2D graphic by making the room, the porch and the stairs as a node. In addition, inspired by Sung et al.[16]’s pluggable architecture, the node plug is clipped to enhance the expansibility. In path planning and dynamical analysis, simple arithmetic based on Helbing’s dynamic model is put forward for pre-computing.

4

Crowd Animation System in Emergency Situation

As mentioned before, this system is divided into operation and description layer, moreover, the environment and agent database are added to separate data and computing. Fig. 2 shows the whole system structure. 4.1

Environment Database

Environment database includes the map and the node plug. Map. The map records the building’s size, the amount of floors, how the room is divided, the location of walls and doors and so on. In other words, map is the digital presentation of the building. Partitioning of Map. Each partitioning of the map is defined to be a node. If node A connects to node B with an exit, then there is directed edge from A to B. First, the building’s map information is read in from predefined external files. The compositions of the building, such as rooms, porches and stairs, are marked as nodes. A door that connects two areas is an exit, which suggests that there is a bidirectional edge between these two nodes. Stairs is a special node that bridges the nodes of different floors. Finally, a 3D building can be turned into a 2D oriented graph by partitioned into a number of nodes and edges(Fig. 3(a)). The nodes format is shown in Fig. 3(b).


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Fig. 2. Detail structure of the system

Types of Nodes. There are various types of nodes of which the figurative properties are quite different. Room and porch can be regarded as the same type since they are in one plane. Stairs whose collision arithmetic is also quite different, which is another kind of node, so is the tumble motion. The concept of ”Node plug” is advanced to encapsulate different properties into different node plugs. When a new node plug is added up, without modifying the whole structure, the expansibility and applicability of the system later can be enhanced. Fig. 3(c) shows the structure of a node plug as following. – Name: The identifier which distinguishes it from others. – Description Information: Optional parameters that describe this plug. – Attractive Coefficient: The attractive extent shows the higher the coefficient is, the more attractive this node is, and also the larger probability that people flow to it. Attractive coefficient gains a autonomous right to the user by adding user-defined node plug. – Dynamical Analysis Arithmetic: It means the arithmetic analyzing the force that an agent suffers. Further explanation will be presented in the coming section. – Motion Set: It is a set of motions belonging to some kind of node. When description layer is rendering the scene, it chooses appropriate motions from the motion set according to the individuals’ states. The motions vary from one kind of nodes to anther.

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Connecting Table. It records the connecting degree of the nodes using connecting coefficient. Connecting coefficient is a real number between 0 and 1 (θ ∈ [1, 0]) that stands for whether two nodes are linking or not. It’s the probability that people from node A flow to node B. If two nodes are block, θ = 0. When θ is higher, the probability so does agents from A move to B. Element in row m, line n is the probability that node m moves to node n. Given node A has four edges, linking to node B, C, D, E respectively, then in connecting table, it is depicted as follows(Fig. 3(d)). The connecting table is unidirectional. The connecting coefficient in row m, line n may not be equal to the one in row n, line m in that people incline to run out of a room towards to porch, but not run back to the room. The way to calculate the connecting coefficient will be shown in the next few sections.

(a) The example building

(c) The node plug

(b) The node map

(d) Connecting table

Fig. 3. Map and Node

4.2

Agent Database

Agent database stores each agent’s data. The information includes: – Agent ID: The unique identity of each agent. – Coordinates: The location of agent in the map, which has three dimensionalities (X, Y, Z). – Speed: The current speed, including its coefficient and direction, which also has three dimensionalities (X, Y, Z). – Node ID: The node ID that agent is in. Detailed information can be found out through node id.


– – – – –

4.3

275

Quality Diameter: Agent’s width of shoulder is looked on as the diameter. Alive State: It has two states (alive and dead). Default State: State that includes stand, move, tumble, injury and so on. Escape Time: A period of time that starts from the beginning of escape. If the agent escapes successfully, its escape time stop.

Operation Layer

Operation layer is responsible for computing and has four modules. Three of them are important and detailed in the following. Node Type Detecting Module. We’ll show the steps of Node Type Detecting Module. First, Node Type Detecting Module reads information from agent database, then find out the node through node id. Second, after detecting the node type, it informs dynamic analysis model to adopt corresponding acting and description layer to call corresponding motion set. Path Planning Module. Agent’s intention direction relies on some sub-factors. First, the more number of doors, the lower probability of passing through one of them. Second, people prefer to leave from exit most near them. Third, the user-define property, attractive coefficient, reflecting the popularity of the node, grant rights to user to adjust the path mildly. The connecting coefficient from room A to room B through door i is

θ =

1

1 Atrb × ndi × n d Atr a j=1 j

(4)

n is the total number of room A s exit. di is the distance from agent to door i. n b are attractive coefficients. j=1 dj stands for the total distance. Atra and Atr When Atrb > Atra , room B is more attractive. As nj=1 dj is the same for each exit in a room, we can simplify the formulation as follows: θ = di ·

Atrb Atra

(5)

In emergency situation, an interesting crowd behavior is called mass behavior. Agent is influenced by self-consciousness and crowd-consciousness. An urgent coefficient U is defined to be the emergency degree. U ∈ [0, 1]. U = 0 means that the individual is not influenced by others at all, while U = 1 shows that it’s totally controlled by the crowd. → Agent has its own direction − ei , but it is also influenced by agents nearby in the form of average direction. The final direction of the target agent is: → − → −t → ei + Ui · e0i (1 − Ui )− ei = → − → (1 − Ui )− ei + Ui · e0i

(6)

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Dynamic Analysis Module. Helbing’s dynamic model can be concluded in a formula: α = mi

→ → → − d− vi v 0 (t)− e 0i (t) − − vi (t) → −→ = mi i fij + fiw + dt τi w

(7)

j(=i)

Since Helbing’s model is only fit for a plane, his model can be addressed as the dynamic analysis algorithm of nodes like rooms or porch. 4.4

Description Layer

Description layer is composed of three modules. Data Process Module is engaged in data reading and processing. It reads the situation and map information from environment database, fetches agent’s states from agent database and does some preparation for rendering. Motion Set module consists of some motion models pre-tailored by 3D modeling tools while Scene Rendering Module fetches corresponding motion which is prepared by the motion set in order to render the 3D scene in real time.

5

Experiment Result

We have designed an evacuation scenario for application based on the above system framework. For simplicity and practice, Helbing’s model is adopted as the algorithm of our node plug, which suggests that our test only focuses on a building with one floor, regardless of stairs. 5.1

Initialization of the Parameters

Fig. 4 shows the building which is a dormitory with one floor. According to the work of Helbing, τi is 0.5s. Usually, the crowd’s expecting evacuation speed reaches vi0 = 5m/s, but in fact, an agent is unable to escape in such a high speed because of the limit of environment that based on Helbing’s observation, the speed comes to 0.6m/s in free state, 1m/s in common state, and in urgent state, it can only reach to 1.5m/s.

Fig. 4. The given building


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Similarly, the constant parameters is : Ai = 2 × 103 N Bi = 0.08m k = 1.2 × 105 kg/s2 κ = 2.4 × 105 kg/ms We suppose the average quality of an agent is 60kg. In order to be close to the reality, the radius ri is defined as ( ri ∈ [0.25m, 0.35m] ). 5.2

Experimental Results

Analysis of Evacuation Time. Fig. 5 shows the curve while escaping in different door width. We observe that 1.60m is the turning point of door width. When door is narrower than 1.6m, the time of escaping increases obviously, and when it’s wider than 1.60m, the influence to time by door width is not obvious. Fig. 6 shows the impact given by different number of people with urgent coefficient 0.4, and doors width 1.6m. Obviously, the more people, the longer time for evacuation. In the point of 30 or 80 people, evacuation time increases quickly along with the increasing of people. 80 is a notable point since when there’re more than 80 people, jam and block will occur to stop the leaving. Jam and Block. When there are too many agents and too narrow exits, fanlike jam will appear in the bottleneck of the exit as showed in Fig. 7. Similarly, the flow of people will be blocked in the bottleneck when there are too many agents and too narrow exits, therefore sometimes few agents can pass through and other times, nobody can leave, as showed in Fig. 8. When it occurs, the flow is blocked, the leaving curve is discrete. Mass Behavior. The mass behavior under the urgent coefficient is also observed. The more urgent the situation is, the weaker the agent’s self-consciousness, the stronger influenced by others and the clearer the mass behavior, assumed that agent is easily inflected by people that five meters around

Fig. 5. Door width influence to escape time

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Fig. 6. The influence by agent’s number

Fig. 7. The fanlike jam

Fig. 8. The block of flow

Fig. 9. Influence by urgent coefficient

it in the same room. Finally Fig. 9 is got according to different urgent cases. From Fig. 9, it is found that mass behavior is not always harmful and some extent of mass behavior will contribute to evacuation. There is a turning point in U = 0.5, indicating that when the crowd in a panic with a degree of 0.5, the


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efficiency of evacuation climb up to the peak. When the panic gets into more deeply and the mass behavior runs into more intensively, the escape efficiency falls more steeply. This conclusion matches L.Z. Yang and Helbing’s observation. But in Helbing’s results, the turning point occurs in 0.4, which is different from our analysis, due to the different of two experiment environments.

6

Conclusions and Future Work

This paper presents a simple and expandable crowd evacuation system in order to offer a platform for the study. For improving the independence of the modules, the function is separated into layers and the data is divided into blocks. For efficient implementation, the 3D building are translated into a 2D graphic by turning the map into a group of nodes. In addition, a new element called node plug is applied to enhance the expandability of the system. In the future work, more motions can be added into the motion set to enrich the performance of agent and make it act vividly. In regard to the great amount of calculation, new techniques can be introduced to improve the concurrency. We believe that as the development of virtual reality, crowd animation system based on dynamics model will become one of the most important assistant tools for analysis of building structure or crowd evacuation.

Acknowledgements We would like to express our thanks to Prof. Xiaola Lin at Sun Yat-Sen University for his kind suggestions on english writing and Dr. Xianyong Fang at Anhui Univeristy for many helpful discussions with him on this paper. This research is supported by National Science Foundation of P.R.China(grant No. 60473109) and Guangdong Province Natural Science Foundation of P.R.China (grant No. 04300602).

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