A Reformed Lattice Gas Model and Its Application in the Simulation of Evacuation in Hospital Fire 1
Weili Zhang1， Zhengyu Yao1
Institute of Systems Engineering, Southeast University, Nanjing, 210096, China Email:
[email protected]
Abstract - In order to provide the rescuing decisionmaker with the optimal evacuation plan when hospital fire happens, so as to improve the rescuing capability, the evacuation process is divided into two sections which include rescue and evacuation. Taking factors of fire to in-patient department into account, combine the swarm behavior in fish school algorithm with Agent-based technology, a reformed lattice gas model is established. Ultimately with the help of simulation software Anylogic, on the basis of reformed lattice gas model the paper simulates the pedestrian evacuation and chase down a plan to solve during rescue. The simulation result indicated that the reformed lattice gas model can simulate the scene of evacuation in hospital fire realistically. Keywords - pedestrian evacuation; lattice gas model;
simulation I. INTRODUCTION In recent years, fire has happened frequently, killing numerous people. On Jan 22, 2004, fire happened in the warehouse of the in-patient department of the commercial workers’ hospital in Wuhan, causing 7 deaths, 11 seriously injured and 147 thousand RMB in direct losses. On Dec 15, 2005, extraordinarily serious fire happened in the Liaoyuan Centre hospital, causing 37 deaths, 95 seriously injured and 8.21 million RMB in direct losses. There are no detailed studies on evacuation in hospital currently. In order to help the hospital to improve emergency management, the paper simulates the evacuation in in-patient department of the hospital when fire happens. Some recent papers have made deep studies on crowd evacuation. Helbing al. proposed Social Force Model [1-3]. Masakuni [4] (2000) used Lattice Gas Model to study crowd evacuation in open-end intersection. Tajim Y [5] (2002) and Nagatani [6-9] apply Lattice Gas Model, regard agent behaviors as movable particle and study the characteristics of agents through probability statistics method. Reynolds [10] adopted focusing system to simulate the group behavior of humanity, birds and fish. He used three rules (collision preventation, velocity matching and centre focus) which were of digressive priority to control the group behaviors. In China, Fang Zheng and Lu Siuming proposed network model [11]; Xu GAO proposed intelligent agent model [12]; PAN Zhong proposed geometrical model [13]. They managed to simulate the crowd evacuation and applied to actual cases [14-15]. Considering the particularity of the people in hospital, the paper combines separated individuals and cluster
978-1-4244-8503-1/10/$26.00 ©2010 IEEE
groups to simulate the evacuation in hospital. Firstly, we define the lattice gas as the foundation of model, for it can reduce the amount of calculation remarkably. Secondly, we add Intelligent Agent Technology to lattice gas model. Although Social Force Model (proposed by Helbing [1-3]) and Network Model (proposed by Fang and Lu) have made certain progress in this field, all these models have their limitations because all the agents in their model are of the same characteristics, aiming to evacuate the crowd in the shortest time. But numerous patients who have different characteristics exist in the hospital. We have to build a hybrid model with both rescue and evacuation instead of evacuation only. We must optimize the integral process of rescue and guarantee crowd evacuation under condition of successful rescue. So we add swarm intelligence to the study and add bionic research of fish school to the model [16-17]. We replace the original agents in fish school with agents in hospital. For instance, fish’s movement to the bait is replaced with staffs’ movement to serious patients. The details will be elaborated in the model below. Taking all the factors above into consideration, we build the model in the following steps: firstly, set the rules of conduct for the agents according to the fish school theory and agents’ characteristics. Secondly, in accordance with the rules of conduct, build the concrete lattice gas model based on intelligent agent technology. Then, use Anylogic to simulate and calculate all the models that have been built, research in population in the model along with time variation rule under different circumstances and analyze the most prominent block in the rescue process. Finally, we make further study the order of evacuation and the location of sickroom and find the optimum solution to disperse more people in shorter time. Thereby, the hospital would be able to evacuate the crowd more efficiently and effectively and we also build theoretical basis for making emergency management proposal and ward distribution. II. THE MODEL A. Problem description and assumptions According to the research of Tong Ren Hospital, fig.1 shows the ichnography of a universal layer in this hospital. Details are as follows: L=27m, W=15m, l=8m, w=3m. Each floor has 10 rooms that each one contains 2 patients respectively. The layer is also equipped with toilets, drug reserves, the medical station, duty room and staff lounge. During
1543
Proceedings of the 2010 IEEE IEEM
P (i , j ) (i, j ) N
working hours there are 34 people in this floor, including 28 patients and 6 staffs.
: Position of serious patients;
P(i, j ) : The center position of all the serious patients; P(i0 , j0 ) : Position of current staffs; Dw1 : Current staff to center position of all the serious patients; Di (i n) : Directions of agents around Research object; Dw 2 : Opposite direction of Di ;
M : Number of agents within the scope of collision; Dw3 : Average direction from current objective to agents Fig. 1.Sketch map of the wards
within the scope of collision;
Swarm intelligence is emerge intelligence stems from nature swarm ecosystem [16-17]. Through research on the natural fish, the paper chooses the pedestrian as the objective of the research. Combining the special circumstances of the hospital with the fish group behavior algorithms reformed lattice gas model consists of world, agents and the behavioral rules. World stands for the hospital. The agents include 3 kinds of people agents, patient agent, kin agent and staff agent. Fig.2 shows the relationship among these agents.
Dw 4 : Direction from current agents to exit;
ai : An agent; l ( x, y ) : Position of ai ;
vi
: Rate of ai ; ( vi 0)
Di : Weight of dominant direction of ai ; Ds : Weight of dominant direction of world [i ][ j ] 1 ; D p : Weight of dominant direction of world [i ][ j ] 2 ;
s : Level of understanding of the hospital’ structure;
: Reasonable degree of ai ; D ' : Weight of dominant direction considering s and .
Fig.2. relationship framework of agents
Available from the above analysis, the model is set up under following assumptions: 1) Simulation only for single-layer, which means only considering plane evacuation and all agents are rational man. 2) Except for the 3 agents above, there is nobody in the hospital. Patients and kin stay in the ward, meanwhile staffs stay in the office. 3) Slight patients can walk with the help of their kin. Every serious patient needs two staffs’ assistance before starting evacuation. B. Model formulating The Reformed Lattice Gas Model is presented in this section. a) Parameter and variable explanation The following notations have been used in the present mathematical model. world [i ][ j ] : The coordinate representing the position of a point on the layer; world [i][ j ] 0 means there is nobody on this point; world [i][ j ] 1 stands for slight patients and kin; world [i][ j ] 2 represents serious patients; world [i ][ j ] 3 represents workers. Different coordinate matches different behavioral rules.
1544
b) Updating rules The paper improves on original lattice gas model, based on the special circumstances of the hospital. Step.1: A specified arrangement used in ordering according to the coordinate above. Step.2: After receiving a fire alarm, if the lattice around him is unobstructed, world [i][ j ] 1 leave the ward to the corridor, and world [i][ j ] 3 walk towards world [i ][ j ] 2 . This stage is a two-tier model of rescue and evacuation. Step.3: When the rescue process finished the model change into evacuation stage. Step.4: In accordance with the serial number, we update the model. As long as agents reach the exit stairs the model will eliminate the subject from the system. c) Behavioral rules of staffs 1. Staffs first aid world [i][ j ] 2 , to help them with the evacuation. The center location of serious patients is average weight within observation of current agent. (Fig.3 (a)) (1) P(i, j ) (i, j ) N , D arctan j0 j P (i , j ) w1
N
i0 i
2. During rescue stage, staffs move towards opposite direction of agents around him. (Fig.3 (b)) Di (i n ) (2) D w2
n
3. When the distance between the two agents less than minimum collision distance, they should avoid collision. (Fig.3 (c))
Proceedings of the 2010 IEEE IEEM
Dw3
arctan
j0 j i0 i
M
(a)
(3)
(( i , j ) M )
(b)
circumstances surrounding the lattice with the equation (4-12), namely to identify the direction of maximum movement probability direction. Calculated in accordance with the above updating rules until all staffs reaching the serious patients, the rescue process is completed. Fig.5 (b) shows agents’ Di in evacuation process, in which the purpose of staffs is leaving(to leave) this layer with serious patients. The algorithm is as same as rescue process, but Dw1 defines current agent to the center
(c)
Fig.3. behavioral rules of workers
position of the entire pedestrian. Update this model iteratively until the entire agents getting the exit and are removed from this system.
d) Mathematical basic model Based on the lattice gas model, changing swarm intelligence technology of natural fish, the paper builds a reformed lattice gas model. Fig.4 shows a simple lattice gas model, pedestrian can move forward, left and right move, not backward. The size of each lattice is 0.4 m 0.4m [5].
(a) rescue (b) evacuation Fig.5. Determine the direction of Dw
Fig.4 pedestrian’s movement state diagram
Pedestrian movement in all directions is a certain probability, the pedestrian will eventually move to the greatest probability, updated in the adjacent lattice in the direction. 1 D 1 D 1 D (4) P D ;P D ;P x
3
y
3
y
3
1 D 1 D Px D ; Py 0; P y 2 2
(5)
1 D 1 D ; Py D ; P y 0 2 2
(6)
Px D
Px 0 ; P y D
1 D 1 D ; P y 2 2
(7)
P x 1; P y 0 ; P y 0
(8)
Px 0; Py 1; P y 0
(9)
P x 0 ; P y 0 ; P
y
1
(10)
Each agent is defined as: a i {li , v i , D i , s , } D ' (D s)
(11) (12)
e) Evacuation model of world [i ][ j ] 3 Fig.5 (a) shows agents’ Di in rescue process, in which the purpose of staffs is close to world [i][ j ] 2 . Because staffs are familiar with the structure of hospital and have received fire training, their s and are relatively higher than others. (13) Dw 1Dw1 2Dw2 3Dw3(1 2 3 1) If the calculated direction and x, y direction in any one parallel and the adjacent lattice in Dw are available, agent moves in this direction. Otherwise we calculate D ' according to equation (12), then combining the
1545
f) Evacuation model of world [i ][ j ] 1& 2 After receiving the fire instructions, slight patients and their families leave the hospital without waiting for the rescue staffs, while the serious patients can must lie in bed waiting for the arrival of staffs. Two kinds of agent follow the similar behavior rules: firstly, current agent move towards the center of the crowd which takes the average coordinates of each location; secondly, current agent’s movement direction and the average moving direction of the crowd are the same; thirdly, when the distance between the two agents less than minimum collision distance, they should avoid collision; fourthly, agent wants to reach the exit at the shortest time. Because this model is only an evacuation process, the algorithm is similar with the latter part of world [i ][ j ] 3 . However, world [i][ j ] 2 cannot leave the ward until staffs come to assist, while world [i][ j ] 1 start evacuation at the beginning. III. SIMULATIONS A. Principle and process According to the actual characteristics of crowd evacuation in hospital, we choose Pedestrian Library of Anylogic as simulating tool. Considering the real situation in in-patient department, we classify the agents into four categories: slight patient, serious patient, kin, and staffs. Moreover, we also set three different speeds: V1 (for slight patients and kin), V2 (for staffs in recue process), and V3 (for serious patients and staffs in evacuation process). Through investigation in hospital, we set the numerical value for each speed according to the scale. The result is presented in Table 1.
Proceedings of the 2010 IEEE IEEM
TABLE I The Speed of Simulation Models
Then we use Anylogic to simulate the reformed Lattice Gas Model. Fig 6 shows flow chart of the simulation. Fig.8. Population in the model changes along with time lapse without optimization
C. Solutions and comparison studies To solve the problem mentioned, we propose three solutions and then find out the best one by simulation. Solution 1: When slight patients and kin move to the lift, the staffs have to move to serious patients’ room in the opposite direction. And this increases the possibility of block. We consider changing the location of serious patients’ room and make staffs who have to move in the opposite direction as less as possible. We try to make serious patients in the closest room to the staffs’ office (Fig.9.). Thus we try to shorten the time for staffs to move to serious patients’ room and also reduce the possibility of block. Fig.6. flow chart of the simulation
B. Results analysis After following these steps, we find that staffs who are rescuing serious patients would be seriously blocked by slight patients and kin (Fig.7.). This situation reduces the capability and efficiency of evacuation. In the simulation, the total time for evacuation is 4.57 min (Fig.8.). In order to verify that the situation above is universal, we do the simulation for 100 times. Through observation, we find that staffs are blocked for 76 times. The rate is as high as 76%. As a consequence, we think that this situation is very common in the model. Although it doesn’t take long to evacuate the slight patient, the time for second half section is apparently excessively long (Fig.8.). This is the result of block in the evacuation and the model cannot be integral optimum. So, we will propose constructive solutions in the next part.
Fig.9. relocation of the serious patients’ room
After optimization, the total time is 4.04 min and much less block happens in the rescue (Fig.10.).
Fig.10. Population in the model changes along with time lapse under solution 1
Solution 2: Solution 1 tries to change staffs’ movement to reduce block, now we try to change the movement of slight patients and patients’ kin. We set a rule that slight patients and kin have to wait until all the staffs have pass the corridor. Apparently, this solution can avoid block in the rescue thoroughly. No block would exist in this situation. The total time is 3.10 min (Fig.11 (a)).
Fig.7. hampered the rescue process
1546
Proceedings of the 2010 IEEE IEEM
REFERENCES
Solution 3: The two solutions above both have their advantages and the third solution is to combine their advantages. That means set the rule in solution 2 and in the meantime change the location of serious patients’ room. As a result, the total time is 3.10min (Fig.11 (b)).
[1] Helbing D. Social force model for pedestrian dynamics [J]. Phys. Rev. E. 1972, 24:353. [2] Helbing D, Molnar P. Social force model for pedestrian dynamics [J]. Physical Review E, 1995, 51(5):4282-4286. [3] Helbing D, Hostikka S, Keski-Rahkonen O. A proposal for the goals and new techniques of modeling pedestrian evacuation in fires [C]. In: The 8th IAFSS Symposium, Beijing, 2005: 557-567. [4] Masakuni Muramatsu, Takashi Nagatani. Jamming transition in pedestrian counter flow [J]. Physica A, 1999, 267:487-498. [5] Tajima Y, Takimoto K. Scaling of pedestrian channel flow with a bottleneck [J].Physica A, 2001, 294：257-286. [6] Nagatani T.Jamming transition in the traffic-flow model with 2-level crossings [J]. Phys Rev E, 1993, 48:3290-3294. [7] Yusuke Tajima, Takashi Nagatani. Clogging transition of pedestrian flow in T-shaped channel [J]. Physica A, 2002, 303:239-250. [8] Muramatsu M, Nagatani T. Jamming transition in Twodimensional Pedestrian traffic [J]. Physica A, 2000, 275:281-288. [9] Muramatsu M, Nagatani T. Jamming transition of pedestrian traffic at a crossing with open boundaries [J].Physica A, 2000, 286:377-386. [10] Reynolds C. Flocks herds and schools a distributed behavioral model [J]. Computer Graphics, 1987, 21 (4):25 – 34. [11] Fang Zheng, Lu Siuming. A Spatial Grid Model for Emergency Evacuation from Building [J]. China Safety Science Journal, 2001, 11(4):10～13. [12] Xu Gao.Simulation Model for Crowd Evacuation Based on Agent Technology [J]. Journal of Southwest Jiaotong University, 2003, 38(3):301～303. [13] Pan Zhong, Wang Changbo, Xie Buying. Simulation of Evacuation Based on Continuous Geometry Model [J] Journal of System Simulation, 2006, 18：233～236. [14] Wen Limin, Chen Baozhi. Study on the Model of Emergency Evacuation in Case of Major Accident [J]. China Safety Science Journal, 1999, 9(6):69～42. [15] Li Fujing, Fang Weining. Simulation of Passenger Evacuation under Emergency in Maglev Train [J]. China Safety Science Journal, 2005, 15(8):17～20. [16] VillamilM B, Musse S R, de Oliveira L P L. A model for generating and animating group s of virtual agents[R]. Irsee, Germany: IVA, 2003. [17] Yang Yongjuan. Realization of Fish-swimming Simulation System with Java [J]. Journal of Anhui University of Science and Technology(Natural Science), 2006, 26(4): 67-71. [18] Zhao Jian, Zeng Jianchao. Modeling and Simulation of the Swarm Behavior in Fish School [J]. Journal of Taiyuan University of Science and Technology, 2009, 30 (1):31-35.
(a) change evacuation order (b) relocation and change order Fig.11. Population in the model changes along with time lapse under different solution
In summary, changing the location of sickroom and order of crowd evacuation can shorten the time to as less as 3.10 min instead of 4.57 min in the initial situation. No block would ever exist. Solution 3 not only reduces the time for evacuation but also guarantees the safety for the people in hospital and improves the capability of rescue. IV. SUMMARY We integrate Intelligent Agent into a reformed lattice gas model. Taking the particularity of the crowd behaviors into consideration, we study the crowd evacuation in in-patient department when fire happens. Moreover, we set the rules of conduct for the agent behaviors according to fish school algorithm. The process of evacuation is divided into two stages and we built a model that could simulate the process of rescue and evacuation simultaneously. Using Anylogic to simulate the situation, we find that the crowd behaviors are often blocked during evacuation and also come up with three initial solutions. By re-simulating, we manage to work out the best solution and this solution is proved by the experiment to have the highest efficiency. Although the passage introduce a hybrid model with rescue and evacuation and two crowd’s intelligent parameters (understanding of the hospital’ structure and reasonable degree during emergency), the rules of the Agents’ behaviors are pre-set. With the improvement of the hardware, the future research can regard the crowd as Multi-Agent, in order to simulate the environment much closer to the real world fire conditions. ACKNOWLEDGMENT We thank two anonymous reviewers for their constructive comments. This work is supported by national innovation experiment program for university students. (No. 081028628)
1547
