# IEEE Systems, Man and Cybernetics Magazine - April 2021 - 25

```Modified Social Force Model
We introduce a new resistance f iz for the traditional social
force model. When a student wants to reach a certain seat
and needs other students' cooperation, it gets a little bit difficult to reach it. As demonstrated in Figure 4, there are five
seats between aisles 1 and 2, where seats 1 and 5 are occupied. Now, if student i wants to arrive at seat 3, he/she will
need help from the students in seats 1 or  5. Consequently,
student i gets a resistance f iz . If student i arrives at a
certain seat and needs the help of person z ^z = 0, 1, 2, f, Z h,
he/she will receive R Zz = 1 f iz . Most students think that if it is
not convenient to walk across two students to reach the destination seat, they will not go to such a seat. It is reasonable
to suppose that Z is zero or a positive integer.
When students walk into a classroom and move toward a
seat without going through obstacles, it is supposed that
there is no repulsion among them, and they can always
maintain the desired speed. The driving force to a location is
related to personal seating preference. If the selected seat is
in an ideal area, the driving force is large; otherwise, the
driving force is relatively small. We can then calculate the
repulsive force to a certain seat. If two occupied seats are

Force f ij between students i and j contains psysoc
phy
chological force f ij and physical force f ij , as listed in
the following:

soc

phy

f ij = f ij + f ij , (3)
rij - d ij
D n ij, (4)
Bi
x, x > 0
g^ xh = (
, (5)
0, x ≤ 0
f ij = A i exp :
soc

f ij = k # g ^ rij - d ij h n ij + l # g ^ rij - d ij h 9v ji t ij . (6)
phy

t

In (3)-(6), A i, B i, k , and l denote the coefficients.
rij = ri + r j represents the sum of comfortable radius
between two students; d ij = ri - r j represents the distance between the centers of two students, as illustrated in
Figure 3; and n ij = (ri - r j ) /d ij represents a unit vector from
student j to student i . The function g (x) is a switch triggered by collisions to exert strong repulsive forces; t ij is a
unit vector perpendicular to the line between students i
t
and j ; and 9v ji t ij = ^v j - v i h t ij represents the rate difference between students i and j in the direction t ij .
Force f iw between student i and obstacle w is calculated by (7). Let d iw stand for the distance between the centers of student i and obstacle w , as depicted in Figure 3;
n iw for a unit vector from obstacle w to student i ; and
t iw for a unit vector perpendicular to the line between student i and obstacle w .

w
i

diw

ri - d iw D
+ k # g ^ ri - d iw h0 n iw
Bi

+ l # g (rij - d iw) (v i t iw) t iw .

f iw = & A i exp :

rj

ri

j

dij

Figure 3. The radius and distance.

(7)

Platform
Front
Door

Front
Door

1

Row 1

2

3

4

5

6

7

8

9

10 11 12 13 14

15 16 17 18 19

...

Aisle 4

...

Aisle 3

Aisle 2

...

Aisle 1

Row 2

...

Row 11
Column
15-19
Back
Door

Row 12
Column
1-5

Column
6-14

Figure 4. The layout of a lecture hall.

Ap ri l 2021

IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE

25

```

# IEEE Systems, Man and Cybernetics Magazine - April 2021

## Table of Contents for the Digital Edition of IEEE Systems, Man and Cybernetics Magazine - April 2021

contents
IEEE Systems, Man and Cybernetics Magazine - April 2021 - Cover1
IEEE Systems, Man and Cybernetics Magazine - April 2021 - Cover2
IEEE Systems, Man and Cybernetics Magazine - April 2021 - contents
IEEE Systems, Man and Cybernetics Magazine - April 2021 - 2
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IEEE Systems, Man and Cybernetics Magazine - April 2021 - 63
IEEE Systems, Man and Cybernetics Magazine - April 2021 - 64
IEEE Systems, Man and Cybernetics Magazine - April 2021 - Cover3
IEEE Systems, Man and Cybernetics Magazine - April 2021 - Cover4
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