A study of the evacuation behavior simulation to investigate the effect of concessions and obstacles

Kentaro Tani, Yoshinobu Maeda Graduate School of Science and Technology,

Niigata University 2-8050 Ikarashi, Nishi-ku, Niigata 950-2181, Japan

f10l002b@mail.cc.niigata-u.ac.jp (KT), maeda@eng.niigata-u.ac.jp (YM)

Nao Ito Department of Electronics and Computer Engineering,

Toyama National College of Technology 1-2 Ebie-neriya, Imizu, Toyama, 933-0293, Japan

ito.nao@nc-toyama.ac.jp

Abstract— It is difficult for all evacuees to behave the smooth evacuation, if they are panicked in occurring some disaster. Such a man-made disaster will increase the damage. Evacuees have to give good influence to the global evacuation behavior by means that they evacuate calmly without preceding personal benefit. So far, a lot of computer simulations, especially using the multi-agent system, or MAS, have tried to clarify the valuable knowledge for the smooth evacuation. We also have made the MAS model on the evacuation behavior. Especially, we have investigated the influence of the mutual concession of the agents on the global evacuation time, which was the time all agents in some space completely evacuated to the outside. As a result, the global evacuation time was minimized when the α, the probability of the concession, was in the range between 0.3 and 0.5. Also, the global evacuation time was decreased more by means of placing obstacles near the exit.

Keywords-component; MAS; Evacuation Behavior; Mutual Concession; Obstacle;

I. INTRODUCTION In Japan, we have a lot of natural disasters, such as

earthquakes, typhoons, cloudbursts, volcanic explosions. In particular, the damage of earthquakes is huge and almost all people experience earthquake hazards [1]. There are several damages occurred by the disaster, but generally, to evacuate swiftly has a possibility to reduce the damage. The death toll from the Great East Japan Earthquake climbed to 15,270, and more than 90% of deaths were caused by Tsunami [2]. This fact suggests that the swift evacuation should be needed to protect human lives from the damage. In order to inhibit the damage caused by such a disaster as much as possible, the smooth evacuation from the disaster is very important. However, it is difficult to examine how to reduce the evacuation time by means of the actual experiment using the human participants, because of psychological influence and the safety securing. Therefore, the computer simulation has been frequently available for the study of the evacuation behavior [3-13]. Multi-agent systems or the multi-agent simulation models (MAS) were adopted to investigate the evacuation phenomena. In the model, the autonomously behaving agents evacuate from the virtual-space (virtual room) to the exit.

We assumed that a lot of agents in the room simultaneously evacuate to the outside at the room through the small exit. If every agent adopts a strategy preceding an individual advantage prior to the whole evacuation, the agents will collide with and will scramble the exit each other. However, in such a case, the evacuation time which all the agents evacuate completely increases oppositely with the congestion of the bottleneck (social dilemma [14]). Actually, according to the famous study of Mintz, the total evacuation time of participants decreased by mutual concessions. In this paper we investigated, using MAS, how the concession affected on the evacuation time. Furthermore, we investigated how obstacles set near the exit affected on the evacuation time.

II. MULTI-AGENT MODEL In simulating, we used the two dimensions grid space in

which the agents who behave autonomously the evacuation behavior are arranged. Size of one cell is determined 60 cm by 60cm from the human body ellipse by J. J. Fruin [15]. All agents either evacuate to the exit if it can, move at random occasionally, or stop if it is crushed into the crowd. Such the agent’s behavior is simultaneously done at 1 turn. The agent stops on the spot, or moves to 4 neighbors which are the up, the bottom, the left, and the right. The agent cannot enter the cell the other agent has already existed, by the excluded-volume-effect. Therefore, the alternatives of the place the agent can move are only the cells where the other agent doesn't exist in the present turn. Basically the agent moves to the exit, and the agent who reached the exit is excluded from the simulation. When all agents reach the exit, the simulation ends.

A. Setting in the space In this study, we consider the square virtual room of N by N

grid space (N2 cells, where N=16), as shown in Fig. 1. Each agent is randomly placed to some cell at the initial state. Equal to or more than two agents cannot exist on the same cell. Each agent moves forward to the exit according to the decided moving rule. Each agent always recognizes the coordinates of the exit, (gx, gy).

2013 IEEE 6th International Workshop on Computational Intelligence and Applications July 13, 2013, Hiroshima, Japan

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Figure 1 Virtual room of 16 by 16. The black cell represents the exit.

B. Moving rule of the agent Let the present coordinates of agent i be (xi, yi). The agent is

classified into five state, "forward", "retreat ", "congestion ", "collision", and "wait", based on the pre-turn action of the agent, as follows:

i. In each agent, the movement rate wjk (j=-1, 0, 1; k=-1, 0, 1) is calculated using information of both the present and the exit coordinates. The wjk is represented as follows: 0 0 (1)

where (gx, gy) represents the coordinates of the exit. The movement rate wjk represents the ratio of moving toward the direction, as shown in Fig. 2. The larger the movement rate becomes, the higher the probability to move to the direction becomes. It is calculated whether the movement direction approaches the exit or not, by comparing the present coordinates with the exit coordinates. The movement rate of the movement direction is calculated by dividing the distance to the exit coordinates of the movement direction axis by total distance to the exit coordinates (Manhattan distance). For example, as shown in Fig. 3, when some agent i who was shown with the white circle goes down direction toward the exit which was shown with the black cell, the movement rate becomes 3 / (2+3) = 0.6 by using the x-axis directed distance “gx-xi=2” and the y-axis directed distance “gy-yi=3”. On the other hand, the movement rate of the movement direction which leaves away from the exit is zero.

ii. Each agent determines the action based on both the environment and the action caused in the last turn. The flowchart of the moving determination is shown in Fig.4. Each agent keeps the state in the last turn. When the last state is "collision", the agent stops at the place to concede a route to the other with the concession probability . Then, the state of the agent becomes "stop" in this turn. When without conceding, the agent selects the action by

means of checking around. When the vacant cell doesn't exist at the left, right, up and down, the agent cannot move and the state becomes "congestion". When the cells with having the positive values of wjk is vacant, the agent selects a cell as the destination from in these vacant ones. The movement probability pjk is calculated by using wjk

∑ …(2)

When the cells of the movement direction toward the exit aren't vacant and the cells of the movement direction which leaves away from the exit (wjk=0) are vacant, the agent selects a cell from these vacant cells with the same probability. In this case, there is a possibility staying the present cell.

iii. After selecting the actions of all agents, the overlap of the destinations is investigated, because equal to or more than two agents cannot exist at the same cell with the excluded-volume-effect. When the destinations overlaps, all the agents concerned stay at the present location and the state becomes "collision". On the other hand, when there is not an overlap of the destination, the state of the agent becomes "forward" in the case of approaching the exit, and vice versa, becomes "retreat".

iv. The present locations of all agents simultaneously place to the destinations. When the coordinates (xi, yi) of the agent is equal to the exit coordinates (gx, gy), the agent reaches a goal and is excluded from the simulation.

Figure 2 Movement rate wjk

Figure 3 Example of movement rate calculation

0 w0,-1 0

w-1,0 w0,0 w1,0

0 w0,1 0

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Figure 4 Flowchart of the moving decision

C. Obstacles In this model, obstacles are placed in the virtual room as

shown in Figs. 5 and 6. These obstacles are regarded as the cells which cannot go through. In this study, we investigate the effect on the evacuation time about two cases which one obstacle or four obstacles is/are placed diagonally in front of the exit (Figs. 5 and 6). Also, we compare these results with the case of not placing obstacles.

Figure 5 One obstacle is placed diagonally in front of the exit. The gray cell is the obstacle and the agent cannot go through this cell.

Figure 6 Four obstacles are placed diagonally in front of the exit.

III. METHOD AND RESULT We simulated three cases. One is in case of placing no

obstacle (control, or non-obstacle), another is in case of placing one obstacle (1-obstacle), and the last is in case of placing four obstacles (4-obstacle). We set at random the number of agents n = 230 which is about 90 % of all the cells. In the initial state, the virtual room is relatively packed with many agents. We changed the concession probability α from 0.05 to 0.95 every 0.05 and recorded the evacuation time. Each simulation is performed 50 times and we calculated the average evacuation time.

Figure 7 shows the relationship between the average evacuation time and the concession probability . The vertical and horizontal axes represent the average evacuation time and the concession probability α, respectively. Also, Figure 8 is a magnification of Fig. 7.

In Figs. 7 and 8, about three cases (control, 1-obstacle, and 4-obstacle), we can see that the average evacuation times were minimized at concession probability α = 0.4. Figure 8 is a magnification between 350 and 600 on the average evacuation time of Fig. 7. Also, when comparing every case, the average evacuation time is rapidest near α = 0.4 in the case of four obstacles.

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movement place overlaps?

Collision

Forward Retreat

Congestion

Does the vacant cell existin front?

Choose the movement place Choose the movement place

Wait

Does the vacant cell exist?

Last condition:Collision

hifts to the wait in probability

Last condition:Collision

Shifts to the wait in probability α

Does the vacant cell exist?

Does the vacant cell exist in front?

movement place overlaps?

movement place overlaps?

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Figure 7 Relationship between the average evacuation tiprobability α

Figure 8 Relationship between the average evacuation tiprobability α (magnification of Fig. 7)

IV. DISCUSSION In Figs. 7 and 8, the average evacuation

the control, the 1-obstacle and the 4-obstaclwhen the concession probability was arou10, 11, 12 and 13 show the relationships brates in the state of the agent, "forward", "retr"collision", and "wait", and the concessirespectively. In all, the cases of the control were compared. The vertical and horizontal average on the agents of the sum of each staof all states (average rate) and the concessrespectively. In Fig. 12, we unambiguously of "collision" is monotonically decreasing the concession probability α. Also, in Fig. 13rate of "wait" is monotonically increasing the concession probability α. When the mulittle (α is small), the evacuation time becommany agents collide with each other, and, owhen the mutual concession is observed mlarge), the evacuation time becomes surprisinmany agents concede their way mutually. Thsee the minimum of the evacuation timeHowever, it has not been clear that the evacuation time did not appear at α = 0.5.

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times of all cases, le were minimized und 0.4. Figures 9, between 5 average reat", "congestion", on probability α, and the 4-obstacle axes represent the

ate to the total sum sion probability α, know that the rate against increasing , we know that the against increasing

utual concession is mes large because on the other hand, many times (α is ngly large because herefore, we could e when α = 0.4.

minimum of the

Furthermore, we verified inevacuation time of the 4-obstaccases. In Figs. 11-13 (three graand "wait"), the changes of thsimilar with those of the controof "forward"), the changes of upper than that of the conaccelerated the evacuation. Opp"retreat"), the changes of the 4-than that of the control. To sretreat. We found that the obstathe exit, and, as such, must evverified the surprising effect of

Figure 9 Relationship between averagprobability α.

Figure 10 Relationship between averaprobability α.

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0.75 0.8

0.85 0.9

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-obstacle

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-obstacle

n Figs.7 and 8 that the average cle case is smaller than the other aphs of "congestion", "collision" he 4-obstacle case against α are ol. However, in Fig. 9 (the graph the 4-obstacle case against α is

ntrol. To set up the obstacle positely, in Fig. 10 (the graph of -obstacle case against α is lower set up the obstacle reduced the acle made agents put forward to vacuate quickly to the exit. We f obstacles in evacuating.

ge rate of “forward” and the concession

age rate of “retreat” and the concession

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Figure 11 Relationship between average rate of “concession probability α.

Figure 12 Relationship between average rate of “collisioprobability α.

Figure 13 Relationship between average rate of “waiprobability α.

V. CONCLUSION In this paper, using MAS on the evacuatio

investigated the effects of both the mutual coand the obstacle set near the exit. As a resultthat the evacuation time should be minimizconcession probability). In addition, we founset near the exit accelerated the evacuation.

Our results suggested that the cooperatioshould be important from the viewpoint oFurthermore, it was found that the obstacleresolved the bottleneck effect.

“congestion” and the

on” and the concession

it” and the concession

on phenomena, we oncession of agents t, it was suggested zed at α = 0.4 (α: nd that the obstacle

on with the others of the evacuation. e set near the exit

Our future works are as follfor the optimal evacuation, 2)minimized at the case that thabout 0.4.

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