A Simulation Model for Guiding Refugees in an Emergency

Copyright © IFAC Control Science and Technology (8th Triennial World Congress) Kyoto. Japan . 1981

CONTROL OF BUILDING AND SAFETY SYSTEMS

A SIMULATION MODEL FOR GUIDING REFUGEES IN AN EMERGENCY S. Tamura*, M. Arai* and K. Suzuki** ·Toshiba R esearch and Developm ent Cent er, Toshiba Corporation, Saiwaiku, Kawasaki, Japan "Industrial Power System Engineering Department, H eavy Apparatus Division, Toshiba Corporation, Minato-ku , Tokyo , Japan

Abstract . In this pape r, a model is presented which describes the behavior of peop le and the effect of escape guidance when a fire breaks out in a building . The transient movement of the people is modeled by equations which are modifications of those for continuous fluid dynamics. Multi - attribute utility theory is used to express the path selection prefe r ence of the escaping peop le. Some simulation results are obtained, which are useful for designing the building structure and planning the escape guidance procedure Keywords. Modeling; computer software; human factor; escape guidance; multiattribute utility function.

INTRODUCTION There are many factors in a building which aggravate troubles when a fire breaks out. The higher o r the lar ger the buildings are, the more people cou ld be killed or injured, and it becomes more difficult to predict the aftermath of accidents. Therefore, many people have come t o recognize the importance of fire prevention and escape guidance systems in an emergency . However, the re are still many obstacles to providing buildings with these systems . For example 1) Safety systems are not productive , and the occurren ce of accidents is very rare. 2) The reliability and effecti veness of the safety systems are not confirmative . 3) Skillful experts are needed to operate safety systems in an emergency. The objectives of the escape guidance simulator a r e to support the development of the safety equipment, to establish the operation p rocedure for the equipment and to construct safer buildings by solving the above - mentioned problems . It will be used for designing the building , planning the layout of furniture, planning escape guidance p rocedure and educat ing system operators . Such simulators have been developed at many places since about 1970. They are divided into two groups, according to their model structures. One is the model in which the kinetic equations are made individually for each escaping person. (Hirai, 1970) The models can simulate the motion of an escaping c r owd p r ecisely. However , the y require large computer memory capacity , long compu tation time and more accurate data to run programs. In another model, escaping pe rsons are not distinguished from each other.

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These models are further divided into network model and fluid model. In a network model , the paths for escape and their capac ity are fixed p reviously, and they are described as a network. (Nakasaki, 1977) Contrary to the network model , in a fluid model , it is not necessary to fix the paths for escape . The fluid mechanic equations are made , and they are solved as if the escaping crowd is a fluid . (Yoshihara, 1978) The simulator , which is p r esented in this paper , is a fluid model. It has the following characteristics. 1) The escaping crowd is treated as a fluid . 2) The decision criteria for a person to use in selecting the safest exit among all the exits from a room is modeled by using mul ti-attribute utili ty function . (Keeney, 1976; Dewispelare, 1 979) 3) The simulator can be run on a minicomputer. So, it is possible to accom pl is h a simulation in a bu ilding con trol system and to designate the escape gu iding conditions interactively by investigating the simulation results. 4) Programs and data are separated , so it is possible to simulate for any kind of building immediately .

SIMULATION MODEL In this simulator, the behavior of an escaping crowd is described as a fluid. An escaping crowd is subject to the influence of the smoke , the building structure and the escape guidance . Equation (1) and (2) de scribe the motion of a crowd .

S . Tamura , M. Arai and K. Suzuki

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div (pV)

aV at

grad(F +G+C) Igrad(F + G + C)

{M(X , y)

I

+ grad (P) + A (p) V }

t : y: p: P:

( 2)

time x : space x co-ordinate space y co-ordinate crowd density crowd velocity V: crowd pressure

Equation (1) is for continuity and means that the increment of the crowd density at any place equals to the difference between the number of persons who come to that place and those who leave during the considered duration . Equation (2) is for the crowd motion , the left hand term means the acceleration of a crowd and the right hand term means the force which acts on a person in a crowd. F , G , and Care the po tential functions of external force , corresponding to influence of the smoke, the building structure and the escape guidance, respectively . These functions are described precisely in later section . M (x, y) is the magnitude of external force and is a decreasing function of the distance between a point (x , y) and a fire , as shown in Eq . (3) . M(x,y) = max { Fmin , Fmax (Fmax - Fmin) . £ (x , y) L

( 3)

Fmin: minimum external force magnitude Fmax: maximum external force magnitude £( x , y) ; distance between a point (x , y) and a fire L constant P is crowd p ressure , which is an increasing function of crowd density, and grad(p) in Eq . (2) means the effect causing a crowd to move to a place where the crowd density is lower. It is assumed that P is proportional to p~ as in Eq. (4) , and the constant kp is determined by simulation results . p = k p . p2

EXTERNAL FORCE WHICH ACTS ON A CROWD

(1)

kp:

constant

(4)

The last term of Eq . (2) is resistance . A(p) is determined so that the magnitude of the stationary velocity of a crowd equals the experimentalily measured speed vv( p) , when the magnitude of external force takes the maximum value Fmax . The relation between crowd speed vo(p) and density is represented by Eq . (5) experimentalily. (Kimura , 1937) From Eqs . (2) and (5), A(p) is determined as Eq . (6).

In the previons section , three kinds of external force were introduced. They were influences of smoke, building structure and escape guidance . In this section, these individual forces are considered more p re cisely .

Smoke Influence The fear of a fire is too severe to allow a person to move toward smoke. A crowd moves with the smoke expansion. So, it is possible to consider that, in a smoky area there is only influence of the smoke . Because a crowd moves toward a place where the smoke density is lower , the smoke influence can be expressed by the smoke potent i al function F(x , y , t), which is p ro po rtional to smoke density . Out of a smoke area, influence of the smoke does not act , because smoke density is constant there . However , in a real situation, influence of the smoke acts on a person , even if he is out of the smoke area. This effect will be contained in influence of the building structure . The smoke behavior is simulated as a mixture of two homogeneous compressible fluids. (Horibata , 1981)

Building Structure Influence A person who has escaped from a smoke area moves to safer places and finally reaches an exit. Therefore , if the function G' (x , y) is defined which represents the safety degree of each point in a building, it is possible to consider that a person moves to a p lac e where G' (x,y) is higher. Let's call the function G(x , y) = - G ' (x,y) building structure potential function. G(x,y) is determined primarily by the building structure, and modified by the distribution of the crowd and the smoke. If the exit's utility of each point (x,y) , which means the read iness of escaping through that exit from a po int (x , y) to a po int outside of the room , is defined , the p roblem of determining G(x,y) resolves itself into one to determine the exit ' s utility. Namely , the safety degree of a point (x,y) is cons idered to be the safest exit ' s utility for a pe rson at a po int (x , y) . G(x,y) can be calculated by Eq . (7). G(x , y)

Ui vo (P) A(p)=

min { 2 , 1.1 p - o . 7954 } Fmax VD (p)

(5) N

(x , y) ;

max [ ui (x,y) i = 1 , 2 , - -- , N

( 7)

the i ' th ex it's utility at a point (x,y) number of exits in a room

(6)

In computer p rograms, the area of the building is divided by a mesh. These equations are approximated by difference equations.

The following factors are considered in calcula ting Eq . (7) . 1) The exit ' s influence rang e The effect of an exit varies from exit

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A Simulation Model for Guiding Refugees

to exit . For example, an exit from a room is useful only for the people in that room . To express these facts , let an area accompany each exit. The exit is useful only in this area . The area ac companying an exit , which is usually used , may be larger than the one which accom panies a rarely used exit . 2) The exit status The exit's utility is not constant in time . If a fire covers the exit , a fire breaks out through the exit or the sign or symbol indicating the exit is danger ous is presented , then the exit will not be useful any longer. So , for each exit, the exit status ac companies and Eq . (7) is calculated by considering the exit status . These two factors are effective only for persons who have information about the fire . So, it must be considered the information flow as in later .

Exit ' s Utility. To determine the exit ' s utility U(x , y) for each point (x , y) , the following three quantities are considered . 1) Distance between the exit and a point (x , y) . (£) The greater the distance to the exit be comes, the more difficult for a person to escape through that exit . So , U(x,y) is a decreasing function of £ . Howeve r, £ must be measured along the shortest path to the exit which avoids a smo k e area , as shown in Fig . 1 . I f £ is measured without avoiding a smoke a r ea , points may appear where the effect of the smoke potential and the building structure potential balance and the motion of a c r owd stops , as also shown in Fig . 1 . Distance between the exit and the place 2) where smoke has spread . (r) U(x,y) is an increasing function of r , because it is dangerous for a pe rson to escape through an exit which is near a fire . 3) Congestion degree near the exit . (d) Because it is difficult for a person to pass through a crowded exit, U(x , y) is a decreasing function of d. d is defined as Eq . (8) . d

=

pe: w:

pe / w

(8)

crowd density near the exit effective width of the exit

Exit ' s utility U(x , y) is a function in which the above - mentioned quantities are combined . According to the multi - attribute utility theo r y , it is not difficult to show that £ , r , and d are mutually preference independ en t and U(x,y) can be expressed as Eq . (9). Coefficients and functions in Eq . (9) are determined by asking some questions about exit's utility . U(x,y; £ , r , d) = K ~ . UQ. (Q.) + Kr . Ur (r) + Kd . Ud (d) + K { KQ. Kr UQ. (£) Ur (r) +KrKd Ur(r)Ud(d) + KdKQ.Ud(d)UQ.( £ )} + K2 K£KrKdU£( £) Ur(r)Ud(d) (9)

constants utility function when r and d are the worst level utili ty function when £ and dare the worst level utili ty function when £ and r are the worst level

K, KQ"Kr , Kd: UQ,(£)

Ur(r)

Ud (d)

of £ , fixed at of r , fixed at of d , fixed at

Escape Guidance Influence People who are in a smoke area will move instinctively , but people who are out of a smoke area will obey the escape guidance . In this simulator , the following two ways are prepared to express the effect of escape guidance . 1) Except i on of the exit from the building structure potential. If it is not desireble for an escaping crowd to move toward some exits , the effect of the corresponding exits will be omitted from the calculation of Eq . (7) .

2)

Escape guidance potential . Escape guiding conditions are expressed by the escape guidance potential func tion, and an escaping crowd moves toward the location where that potential is l ower . The escape guidance potential value at each time C(x,y , t) , is calculated by Eq . (10) . Where m(k , x , y) (k = 1, 2 ,---, M) is the guiding pattern f o r k ' th escape guidance controller , and has a similar meaning as for the escape guidance potential function . M

C(x , y , t) = L m(k , x , y) i(k,t) k= l i(k , t):

M

(10)

magnitude of the control of k ' th escape guidance controller at time t number of escape guidance controllers

Informat i on Flow The behavior of an escaping crowd differs with the information about a fire. For example, a person who knows about the outbreak of a fire will escape , but a person who has no information will not be able to escape . A person who knows that a fire has broken out beyond some exit will not move toward that exit . However, if that information is not known, escapees will move toward that exit. In this simulator, the fire infor mation level is divided into three classes . The building structure and the escape guid ance potential functions are calculated according to these information levels . Level A; People have no information about a fire, so all kinds of influence are invalid. Level B; People know only about the out -

S . Tamura, M. Arai and K. Suzuki

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break of a fire, but do not know where the fire broke out . So , the behavior of the people will not be changed by the fire condition . Level C; People know the place where a fire has broken out and the direction to follow in their escape. The building floor is divided into several blocks , which a person can look out over , and the information level is the same in each block . The information flows block to block , when the distance between the people who are in neighboring blocks is less than a particular value . The information level for a block changes A ~ B ~ C or A ~ C , and does not change in reverse order .

asked, according to the procedure , by R. L. Keeney. (Keeney, 1976) . Fifteen persons answered these questions. They were divided into two groups, I and II, by clustering their answers. There were 8 persons in group I and 7 persons in group IL Coefficients K, K£, Kr and Kd and functions Ut , Ur and Ud in Eq. (9) for each group are calculatec as follows: Group I K - 0 . 97889 K£ = 0 . 2611 Kr 0.9 Kd = 0 .77 809 U£ 1.41396[l-exp{0 . 094491(£- IS)} 1 Ur 1.00959[l-exp{ - 0 . 38806(r- 3) } 1 Ud 1 . 09574[l - exp{0 . 4875(d - 5) } 1 Group II K -0.80978 K£ = 0 . 24833 Kr 0.8 Kd = 0 . 4 U£ 0 . 036653[exp{0.2571(15 - £)} - ll Ur 1.02819[exp{0.056612(r-3)}-ll Ud 0.38583[exp{0.25573(5 -d )} - ll

SIMULATION RESULTS Figure 2 shows the floor of the building used for the simulation. SW, NW, SE and NE are room indicators . People who are in those rooms will go through adequate exit to a corridor and finally escape to staircase 1 or 2 . The hatched areas are for elevators and for storerooms and are never used in an eme rgenc y . 1 to 10 are smoke exhaust ports and a to dare hanging walls which prevent the smoke spread . In this simulation, the floor is divided by a mesh which has 3 . 05 meter width in the xdirection and 3.85 meter width in the y-direction . Motions of the escaping crowd and the smoke are calculated at every second . Figure 3 shows the time transition of crowd density near exit 11. It is assumed that, initially, crowd density is 0.5 person/m 2 and uniformly distributed in each room. A fire breaks out in room SW. A dashed line corresponds to the case where kp in Eq . (4) equals O. Namely , the case where the crowd pressure effect is omitted . 30 seconds after a fire broke out , crowd density reaches 10 persons/m 2 . People who are in rooms SE and NE do not know about the accident until escape g~~uance is made 6 seconds after a fire broke out, so crowd density does not change at an early point in time. The solid line corresponds to the case where kp equals 0.071. The chained line corresponds to the case where kp equals 0.142 . According to Eq . (5) and the fact that the maximum number of persons who can cross the unit width during one second is 1.5 persons/m' sec, the maximum crowd density becomes 4.55 persons/m 2 . So, in the following re sults, kp was set at 0.071 . To calculate the building structure poten tial, at first the best and the worst values of £ , rand d in Eq. (9) are selected as follows .

r

d

Best Value

Worst Value

2 m 15 m 0 person/m2 .m

15 m 3 m 5 persons/m 2 'm

Some questions about the exit's utility were

Figure 4(a) shows the building structure potential in room SW and NW for a person in group I . Figure 4(b) shows the building structure potential for a person in group II. A fire broke out at the black painted section in room NW. People were uniformly distributed at 0 . 125 person/m 2 density . Numbers in the figure show the potential. For persons in group I, {G(13 ,4) - G(13,5)}/{G(13 , 4) - G( 14,4) } = 20/11,

where G(i,j) means the potential value of (i,j) section. However, for persons in group II, this ratio is 15/22 . This means that smoke influence is more important for persons in group II than for persons in group 1.

Persons in group I, if they are at (5 ,3) section, will escape to exit 1, but persons in group II will escape also to exit 2 . Considering that the effective width of ex it 1 is 1 meter and that of exit 2 is 2 meters, this means that crowd density influence is more important for persons in group II than for persons in group I. Figures 5, 6 and 7 show the distribution of crowd and smoke, 12 seconds and 40 seconds after a fire broke out at exit 1. Initially, the people were uniformly distributed in each room at density 0 . 125 person/m 2, and the outbreak of a fire was announced 6 seconds after the fire broke out . In Fig . 5 and 6, crowd and smoke density at each place are expressed by dot patterns . In Fig. 7, smoky areas are dotted, and nu merals on each section show the number of persons who were left at that place. Nu merals without parentheses correspond to the case where no escape guidance was made , so the persons near staircase 1 are very dangerous and move toward staircase 2. Parenthe sized numerals correspond to the case where escape guidance was made . To prevent the crowd concentration at exit 7, persons in room SW and SE were guided to exit 3 or exit 12, so that they became safe.

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A Simulation Model for Guiding Refugees

CONCLUSION In this simulator , it is assumed that a person does not make a mistake in determining the circumstances and the mob psychology effect is not considered . Accurately dealing with these facts is very difficult, and it is impossible to describe the motion of a crowd completely . Therefore, in this research, it is attempted to avoid unreasonable accidents by examining and learning the average behavior of people in an emergency and recognizing the functions of escape guidance by all the persons in a building. It is also known that a crowd cannot cross the exit if the crowd density is over some certain value . However, because only a few data are available about that, this effect is omitted from the simulator too.

exit

.~---

( x,

y ) (b)

(a ) Shortest path to the exit (b) Sho r test path which avoids a smoke are a (c)

Influence of the building structure along the path (a )

(d) Smoke influence

Fi g . 1. Di s ta nce f r om a po i nt (x , y) to t h e exit .

REFERENCES Dewispelare, A. R. , and A. P . Sage (1979). IEEE Trans. Syst., Man & Cybern., Vol . SMC - 9, no. 8 , pp. 442 - 445. Hirai , K., and K. Tarui (1970). 2nd symposium on modeling and simulation in system con trol (JAACE), pp. 1-4 . (in Japanese) Horibata , Y., M. Arai, and T . Tsuda (1981). IFAC congress VIII, Kyoto , Japan. Keeney, R. L. , and H. Raiffa (1976). Decisions with Multiple Objectives. Wiley , New York . Kimura (1937). The transaction of AIJ. , Vol. 5 , pp. 307 . (in Japanese) Nakasaki , K. , and I . Nakabori (1977) . 1977 Joint convention record of lEE . Japan , pp . 2232 . (in Japanese) Yoshihara , K. , M. Nakao , and M. Ohnari (1978) . The transaction of lEE. Japan, Vol. 98 - C, no . 4 , pp. 111 - 118. (in Japanese)

10

20

60

80

F i g . 3. Cr owd den s i t y t ime t r a nsition.

67. 2 m

I

Room SW

Room NW

a)

I I I I

1

L8J

2

~xi t

E

4

3

Il:I Exi t 3

I

Il:I

I'8J Exit 4

Exi

00

'" Ex I t 12 7

Ex iLl)

8

Il:I

Il:I Room SF. Cl

Exit 14

I

I 10 I ~

9

Il:I

I

I I

Room NE

d

I

F ig . 2. A floo r in th e building used f o r s imul at ion .

S. Tamur a , M. Arai and K. Suzuki

36 .',6 9

10

1111 13

14 15 16

17 18

19 20

(a)

for

the people

1n group 1.

Exit 1

Exit 2

Exit 4

Exit 5

Cb)

f o r th p

~ co ple

In qr o u~ 11.

Ex i t 1

Ex i t

2

~)(

t

4

Fig. 4. Building structure potential example.

Fig. 5.

Distribution of smoke.

Fig. 6.

(12 seconds after a fire broke out)

Distribution of crowd.

(12 seconds after a fire broke out)

Ex i t

B

r-----

/

Ex i t

-

--

-- -

11

----t---, - ,----+--

Room SE

Room NE

Fig . 7 . Distribution of crowd and smoke. (40 seconds after a fire broke out)