A. Grid-Base Environment Models
We use grids to represent environment of the emporium.
Each grid denotes 0.2 × 0.2 square meters in a real world.
The width and height of the scene is 500 grids and 300 grids,
which equal 100 meter and 60 meter in the real emporium. We
build coordinates in the grid-based environment models. The
origin point in the coordinates is top left point in the scene. The
top line is selected as X coordinate whose positive direction is
from left to right. The left line is selected as Y coordinate
whose positive direction is from top to bottom. Besides, we
assume the length and width of any objects is the number of
multiple 0.2 × 0.2 square meters in the emporium.
We need to compute the distance from any grids to doors.
We set values for a grid to denote distances from the grid to
doors. We assume two grids G1(x1, y1) and G2(x2, y2) in the
emporium or any room. Besides, we assume distance between
two grids connecting together in vertically and horizontally
line is 2. The distance between two girds connecting together
in diagonal line is 3. The value here is not real distance in a
real world. We just use it to plan evacuation path for agents.
Then we could compute distance between G1 and G2 by (1).
= 3 + 2( −) (1)
= [| 1 − 2|, | 1 − 2|]
= [| 1 − 2|, | 1 − 2|]
We need to consider the situation that there is an object in
the evacuation path. Agents should round over a barrier when
they move in the emporium. The values of grids occupied by a
barrier are set as “-1” to denote that the grid can’t be passed.
Then the shortest evacuation path may be cut. We use recursive
arithmetic to update the value denoting the distance from the
grids to doors. The recursive arithmetic is presented as fig. 1.
The function1 updates the values of grids adjoining to a barrier.
The parameters, nTop, nLeft, nBottom, and nRight, denote the
coordinates of two grids at top left point and bottom right point
in a barrier. In function2, when the value of any grid is
changed, the value of its 8 neighbor grids will be update in
fuction2 as a recursive process. The update process is to find
the minimal value in its neighbor girds, and add 2 or 3 to the
minimal value to be the new value of the grid.
The distances from any grids to a door in a room are
computed as fig. 2. We set the value of grids occupied by door
as 0. The blue grids denote a door. The red grids denote a
barrier in a room. The yellow grids are the neighbors of the
barrier.
(a) Fuction1(nTop, nLeft, nBottom, nRight)
(b) Fuction2(nX, nY)
Figure 1. Recursive arithmetic for computing distance
Figure 2. Distance from girds to a door in a room
B. Heterogeneous Agents Models
In a real world, each person may occupy 0.4 × 0.4 square
meters approximately when he stands and moves forward. So
we design an agent as a squire occupying 4 girds in the scene
of the emporium. We divide agents into three age groups
=
( , − 1),
( +
1, −1,
+1, ,
+1, +1,
,
+1,
−1, +1,
−1, ,
−1, −
1
If
( , ) >
+ 2
Then
( , ) =
+ 2
Else If
( , ) >
+ 3
Then
( , ) =
+ 3
Fuction2(nX,nY-1); Fuction2(nX+1,nY-1);
Frandomly, including children, adults, and oldsters. Agents in
different age groups have various travelling speeds. The
variables, , , and , denote the maximum travelling
speeds of children, adults, and oldsters respectively. As shown
in fig. 3, green points denote children, red points denote adults,
and blue points denote oldsters. Agents’ travelling speeds are
influenced by the population density of crowds. We use (2) to
compute agents’ travelling speeds [10].
( ) = ( + + ) (2)
= 1.32 − 0.82 ( ), = 3.0 − 0.76
While, the variable is the impact factor denoting the
influence from neighbor agents at front and back; the variable
is the impact factor denoting the influence from neighbor
agents at left and right; the variable is the factor
representing agents’ physic characteristics; the variable
is agents’ maximum travelling speed in emergency evacuation.
Besides, the range of variable is in an interval [0.25, 0.44];
the range of variable is in an interval [0.014, 0.088]; the
range of variable is in an interval [0.15, 0.26].
In the emporium, agents could move at 8 directions. Before
moving, they could observe the environment and select
appropriate evacuation path. We set agents’ visual field is 5
grids adjoining them. Agents could choose any 4 grids as their
destinations, which could be passed and nearest to the door.
Then we use average value (
) of the 4 grids to
evacuate the distance from a destination to a door, just
described as (3). The variables,
,
,
,
, respectively denote the values of grids at the top left
point, left bottom point, top right point, and bottom right point
for a destination.
=
+
+
+
4 (3)
In a simulation tick, the distance that agents could travel is
calculated by multiplying simulation time in a tick with agents’
travelling speeds. Beside, agents could select a door as
evacuation exit according to the shortest distance from its
position to the doors.
SIMULATION EXPERIMENTS
A. Design Simulation Experiments
We create agents in three age groups and set agents’
maximum travelling speed ( ) as 1.0m/s for children,
1.7m/s for adults, and 1.3m/s for oldsters. Besides, we set the
variable as 0.42 and the variable as 0.027. We set the
variable as 0.15 for children, 0.24 for adults, and 0.2 for
oldsters. The numbers of agents in the emporium and 8 rooms
are set as table II.
In fig. 4 (a), we observe agents are blocked at front of the
right door of supermarket, and at top right corner of book store.
Besides, we discover desks near to the right door of the
emporium cut the evacuation route of agents. So we change the
position of desks, and move book store at the right direction to
generate a new path through which agents in sport store could
evacuate by the left door of the emporium directly. The
optimized interior layout of the emporium is represented as fig.
4 (b). Moreover, in order to keep agents to evacuate faster, and
mitigate blocks near doors, we broaden the width of doors in
the emporium. The widths of doors in initial scene (I) and
optimized scene (O) are represented in table
NUMBER OF AGENTS IN THE EMPORIUM
Room name Number of
agents Room name Number of
agents
Emporium 100 Supermarket 50
KFC 50 WC 5
Book Store 15 Sport Store 15
Cafes 15 Furniture Store 20
Clothing store 25
TABLE III. THE WIDTH OF DOORS
Door name Width (I/O)
(meter) Door name Width (I/O)
(meter)
EL_Door, 1.6/4 SL_Door 1.6/2.4
ER_Door 1.6/4 SR_Door 1.6/2.4
KFC_Door 1.6/3.2 WC_Door 1.6/1.6
BS_Door 1.6/2.4 SSL_Door 1.6/1.6
C_Door 1.6/2.4 SSR_Door 1.6/1.6
CS_Door 1.6/2.4 FS_Door 1.6/2.4
B. Analyze results
We conduct 50 experiments with the initial scene and
optimized scene respectively. Then we collect data of all
agents’ evacuation time and travelling speed at the doors. We
use average evacuation time of agents to evaluate the
performance of two scenes for emergency evacuation, and use
average travelling speed of agents at the doors to evaluate the
width of doors for emergency evacuation.
We assume a variable as the number of all agents in
different rooms or the emporium. The average evacuation time
of agents in different rooms and the emporium are computed
by (4). The average travelling speeds of agents at different
doors when they get out of rooms and the emporium are
computed by (5).
!"
= ∑ $
%"
=1
(4)
! !
$&'
* = ∑ $
% !
$&'
*
=1
(5)
Through observing emergency scene in fig. 3, we discover
agents could avoid blocks at the place where we improve the
layout of rooms and objects. We plot the average value and
standard deviation of evacuation time in two scenes as fig. 4
(a), and plot the average value and standard deviation of
travelling speeds at doors in two scenes as fig. 4 (b).
In fig. 4 (a), we discover the average evacuation time in
optimized scene equals 22.47 second, and the average
evacuation time in initial scene equals 44.34 second. Besides,
after broadening the width of doors in rooms, the average
evacuation time in each room are shorter. In fig. 4 (b), we find that agents’ average travelling speeds at two doors of the
emporium both are accelerated about 0.3 (m/s) after
broadening the width of doors, as well as the door of KFC. The
average travelling speeds at others doors also be accelerated
accordingly. So we conclude the performance of optimized
scene for emergency evacuation is better than the one of initial
scene.
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