cellular automata evacuation simulation

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Procedia Engineering 31 (2012) 1066 – 1071

1877-7058 © 2011 Published by Elsevier Ltd.

doi:10.1016/j.proeng.2012.01.1143

Available online at www.sciencedirect.com

International Conference on Advances in Computational Modeling and Simulation

Simulation of Evacuation Processes in a Large Classroom

Using an Improved Cellular Automaton Model for Pedestrian

Dynamics

Ling Fua,b

, Jixiong Luoa,b

, Minyi Denga, Lingjiang Kong

a, Hua Kuang

a*

a

College of Physical Science and Technology, Guangxi Normal University, Guilin 541004, Chinab Department of Physics and Information Technology, Guilin Normal College, Guilin 541002,China

Abstract

An improved cellular automaton model is proposed to simulate the evacuation processes in a large classroom by

considering the different exit choosing and movement rules. The effects of the different influence coefficients on the

evacuation time are investigated, and the typical characteristics of space-time dynamics are analyzed. The numerical

simulations show that the model can better reproduce realistic evacuation phenomena, such as route-choice behaviors

and bottleneck effects at the exits. Especially, when the distance to exit and the local density distribution of

pedestrians are considered synthetically, the evacuation time can be reduced apparently, which is more reasonable

and realistic.

© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Kunming

University of Science and Technology

Keywords: Cellular automaton model; Pedestrian evacuation; Computer simulation;

1. Introduction

In recent years, various accidents caused by pedestrian jams and trample of crowd have happenedfrequently. Great attention has been paid to pedestrian evacuation from the different buildings, which has

become the most exciting topic on the pedestrian flow. Especially, the safety evacuation of students in

classroom has attracted considerable attention. Several models, such as social force model, hydrodynamic

model [1], lattice gas model and cellular automata model [2-14], have already been applied to simulate

* Corresponding author. Tel.:+86-15207738132.

E-mail address: [email protected].


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1067 Ling Fu et al. / Procedia Engineering 31 (2012) 1066 – 1071

the evacuation process. Since the cellular automaton model is conceptually simpler and can be easily

implemented on computers for numerical investigations, it has become a particularly interesting choice

for the most scholars. Yang et al [3] proposed a new cellular automata model to simulate pedestrian

evacuation by considering the position danger grade and the fire danger grade so as to determine the rules

of the pedestrian movement. The simulation shows that the model is good at simulating evacuation

behaviours such as the arching and clogging around the exit. Varas et al [4] have studied the process of

pedestrian evacuation in a room with fixed obstacles by using a bi-dimensional cellular automaton andfound that replacing the double door by two single doors does not improve evacuation times noticeable.

However, the above researches can not simulate the evacuation process accurately enough when the

pedestrians are distributed heterogeneously. For example, some people assemble densely in a specified

zone of a building.

For this consideration, we presented an improved cellular automaton model to simulate pedestrian

evacuation from a large classroom with obstacles by considering the exit choosing behaviors and

movement rules, and focused on studying the influences of the local density distribution of pedestrians.

This paper is organized as follows. In section 2, an improved cellular automaton model is proposed, and

the sets of the exit choosing and movement rules are described. Numerical simulation and results analysis

are shown in section 3. Finally, conclusions are drawn.

2. Model

The classroom is described by a two-dimensional grid. The underlying structure is the square lattice of

31 20 cells. The size of a cell corresponds to 0.5 0.5m m . Each cell can be empty or occupied by an

obstacle (or a pedestrian). The pedestrian can move to eight directions and arrive to an adjacent empty

cell in one time-step (see Fig.1 (a)). The average speed of pedestrian is around 1m/s under normal state

and is around 1.5 /m s or faster under emergency state. In our model, 1.0 /v m s or 2 /v m s , and one

time-step corresponds to 0.5 s. The classroom has two exits: one is on the left and the other is on the right.

Each exit occupies 3 cells. The dais also occupies 3 cells. There are 168 seats in the classroom. A desk

and a chair occupied 1 cell, respectively. When the students stand up, the chair will be folded

automatically and does not occupy the space except the backrests of the last row of chairs, whichresemble a “wall” and prohibit anyone through it. The detailed layout of the classroom is shown Fig. 1(b).

Fig. 1 Sketch of the model. (a) the possible directions of motion for a pedestrian; (b) the layout of the classroom.


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2.1. C hoosing exit rules

When the pedestrian chooses the exit rationally, two main factors should be considered: (1) the spatial

distance between the exit and the pedestrian; (2) the crowd degree of the pedestrians around the exit. Here,

the attraction degree of the left ( L) and right ( R) exit is defined as follows:

( )( ) ( )

1

( , ) ( , ) ( , )(1 )

( , ) ( , ) ( , ) ( , )

L R L R L R

L R L R

F i j G i j M i j

G i j G i j M i j M i j

where,( ) ( , ) L RG i j is the value of the floor field to the left ( L) and right ( R) exit at lattice site ( , )i j . The

definition and value of,( ) ( , ) L RG i j are the same as in Ref. [4]. ( , ) L R M i j is the number of the pedestrian,

where value of the floor field (see Ref. [4] for a detailed discussion of this point) is lower than that of

the , ( , ) L RG i j . is the influence coefficient of the choosing exit, and 0 1.0 ．The pedestrian

usually choose the exit with higher attraction degree. When the attraction degrees of two exits are same, both of them can be chosen with the same probability.

2.2. Movement rules

Several aisles are composed of desks and chairs in the classroom. When the pedestrian choose the aim

cell, they may consider the value of the floor field of the aim cell and the local density distribution in the

classroom. Here, the total danger degree is defined as follows:

( ) ( )

( )

( ) ( )

1,0 1,0 1,0 1,0

( , ) ( , )( , ) (1 )

( , ) ( , )

L R L R

L R

L R L R

i j i j

G i i j j N i i j j D i i j j

G i i j j N i i j j

where the subscripts of L and R denote the left and right exit, respectively. ( ) ( , ) L R N i i j j denotes

the number of the pedestrian in the aisles, where the pedestrian of the lattice ( , )i j passes the cell

( , )i i j j and arrives the left (right) exit, here, 1,0, 1,0i j . If the neighbouring lattice

occupied by a desk or a pedestrian, the values of L RG and L R N are 0, and the value of L R D is . is

the influence coefficient reflecting the strength of choosing exit after the local density distribution is

considered, and 0 1.0 . The pedestrian movement obeys the following rules:

(1) In the region of aisle occupied by desks and chairs, the total danger degree L R D of the

neighbouring lattices will be compared and the lattice with the lowest value of L R D will be chosen as the

aim lattice. If L R D of the aim lattice is lower than that of the lattice where the pedestrian locates, the

pedestrian will move to this lattice. If L R D are equal, the pedestrian may move to the aim lattice or

remain the original lattice with the same probability. Here, it should be noted that if L R D of the aim

lattice is higher than that of the original lattice, the pedestrian still move to the aim lattice with 20%

probability in order to reflect the unreasonable action induced by panic in the emergent evacuation. When

pedestrian can choose several aim lattices, only one of them can be chosen with the same probability.

(2) In the region of the exits (see region A and region B in Fig.1 (b)), the aim lattice will only be

chosen by the value of the floor field, and the choosing rules of the aim lattice are mentioned above.


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2.3. Avoiding conflicting rules

All pedestrian obey the above rules to move, but when several pedestrians intend to move towards the

same lattice, the confliction will occur inevitably. Here, as the same method in Ref. [4], the pedestrians of

vertical and horizontal direction movement have a priority to move towards the aim lattice earlier than

those of diagonal directions.

3. Simulation results and analysis

There are 168 pedestrians in a large classroom, and the process of pedestrian evacuation is simulated

100 times by the computer. The result is averaged over them.

Fig.2. Plot of evacuation time t against influence coefficients (a) and (b), respectively.

Figure 2 shows the plot of evacuation time t against influence coefficients and , respectively.

From Fig.2 (a), we can see clearly that for 0.0 , the evacuation time decreases with the increase of

as 0.6 , and has the minimum value as 0.6 ; while as 0.6 , the evacuation time increases withthe increase of .This means when is small (see. Eq. (1)), pedestrian consider the floor field too much,

i.e., the pedestrian prefers to escape classroom from the nearest exit to them, and ignores whether the exitis crowded. This behaviour directly leads to lower utilization efficiency of exit, and the evacuation time

increase. On the other hand, when is larger, the pedestrian considers the local density distribution so

much as to hesitate and wander between two exits, and the evacuation time increase inevitably. In

addition, When the is appropriate (e.g., 0.6 ), the floor field and the local density distribution of

pedestrians are considered synthetically, the evacuation time is the smallest, and the evacuation efficiency

is the highest.

In Fig.2 (b), we can see clearly that when 0.4 , the evacuation time is larger, with the increase of

, the evacuation time almost tends to constant. When 0.4 , the pedestrian focus on the floor field,

and ignore the distribution of pedestrians in classroom. However, when 0.4 1.0 , the pedestrians

consider the floor field and the distribution of pedestrians, they can select the appropriate aisle and exit to

escape, and then the evacuation time become smaller.Figs.3-6 give the snapshots of a simulation with different and , where the full circle represents the

pedestrian. From Fig.3 and Fig.4, it can be found when 0.0 , the jam would occur more easily

between desks and chairs. Because the pedestrian have not considered the distribution of local density at

different aisles, and only selected the shortest route to exit, the aisles have not been utilized adequately,

which results in the increase of the evacuation time. Compared with Fig.3, Fig.4 is more reasonable and

realistic about the distribution of pedestrians at exits.


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Fig.3. Snapshots of a simulation at different times (a) t =10, (b) t=40, (c) t=60, where 0.0, 0.0 .

Fig.4. Snapshots of a simulation at different times (a) t =10, (b) t =40, (c) t =60, where 0.6, 0.0 .

Fig.5. Snapshots of a simulation at different times with (a) t =10, (b) t =40, (c) t =60, where 0.0, 0.5 .

Fig.6. Snapshots of a simulation at different times with (a) t =10, (b) t =40, (c) t =60, where 0.6, 0.5 .

Comparing Fig.5 with Fig.6, we find that when 0.6, 0.5 , i.e., the floor field and the local

density distribution of pedestrians are considered synthetically (see Fig.6), the aisles and free space in

classroom are utilized adequately, and the jams obviously decrease. In such case, the evacuation time is

the shortest, and the evacuation efficiency is the highest.

4.

Conclusions

To explore the typical characteristics of the evacuation processes, we have presented a modified

cellular automaton model to investigate pedestrian evacuation in a large classroom with obstacles. The


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exit choosing mechanisms, movement rules and avoiding conflicting rules are illustrated, respectively.

Through the numerical simulation, a shortest evacuation time can be obtained when the distance to exit

and the local density distribution of pedestrians are considered synthetically. We hope that our model can

be extended to investigate emergency evacuation from other common buildings with obstacles.

Acknowledgements

The authors would like to thank Dr. Xingli Li for helpful discussions and suggestions. This work was

supported by the National Natural Science Foundation of China (Grant Nos. 10962002, 10902076 and

81060307), the Natural Science Foundation of Shanxi Province (Grant No.2010011004) and the Program

for the Top Young Academic Leaders of Higher Learning Institutions of Shanxi.

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