IEEE Systems, Man and Cybernetics Magazine - April 2021 - 26

not adjacent (like seats 1 and 3 in row 1 in Figure 4), only
the psychological repulsive force is calculated. If two seats
are adjacent (like seats 1 and 2 in row 1 in Figure 4), both
the psychological repulsive force and the contact force
should be calculated. The parameters are set as follows:
A = 450 N, B = 0.08 m, k = 819.62 kg/s 2, l = 510.49 kg/m.s,
v = 1.64 m/s, average body mass m = 60 kg, and x = 0.5 s.
To facilitate the calculations, we made the following adjustments. If a seat is in a student's favorite area,
drv
drv
f i = 1 N; otherwise, f i = 0.8 N. The direction of
drv
f i is opposite to n ij . f iz = 0.5 N, and the direction of
f iz is the same as n ij .
The new social force f i loaded on student i is

w=1

z= 0

f i = f i + | f ij + | f iw + | f iz . (8)
drv

j (≠ i)

Students would like to choose a seat with the greatest resultant force in the direction of the driving force. If the resultant forces of several seats are the same, one of them is
picked randomly.

Direction 2

Direction 3

Case Study
There are six instructional buildings on the campus of a
university in Guangdong Province, China. Classrooms in
instructional buildings 1-5 can be used by students for selfstudy in the evenings when there are no lectures and events.
On campus, there are 68 lecture halls (223 seats per room),
94 large classrooms (108 seats per room), and 43 small classrooms (51 or 70 seats per room).
As demonstrated in Figure 5, the students enter the classrooms in the instructional buildings from four directions
(directions 1-4 in Figure 5). The students' preferences for a
classroom are as follows. A student may go to the instructional building from any one of the entry directions depicted

in Figure 5. Most students go to the instructional building
closer to their entry directions and are satisfied with the
classroom environment decreasingly from the lower floors
to the upper ones.
Figures 4, 6, and 7 illustrate the layout of a lecture hall, a
large classroom, and a small classroom, respectively. If a
seat is near an aisle, it is called an aisle seat. The aisle seats
are listed as follows: 1) the seats in columns 1, 2, 4-7, 13-16,
18, and 19 in Figure 4; 2) the seats in columns 1, 2, 6-9, 13,
and 14 in rows 1-6 and the seats in columns 1, 2, 6-9, 11, and
12 of rows 7 and 8 in Figure 6; and 3) all of the seats in Figure 7 excluding the seats in columns 1, 6, and 11.
If every seat were occupied by one student, the comfort
of all of the students in a classroom would inevitably be
greatly degraded. In this work, the occupied-seat rate refers
to what percentage of the seats in a classroom are occupied
by students. Thus, it is necessary to discuss the relationship
between the occupied-seat rate and occupant comfort in a
classroom. When the occupied-seat rate in a classroom is
very low, the occupant comfort will be relatively high, nearly
100%. As the occupied-seat rate in a classroom increases to
20%, the students' comfort begins to decline. When the occupied-seat rate in a classroom is high enough, the students'
comfort approaches zero.
As illustrated in Figure 4, aisles 2 and 3 separate each
row of seats (excluding row 12) into three zones with five,
nine, and five adjoining seats, respectively. Similarly, in
Figure 6, aisle 2 separates each row of seats (excluding
rows 7 and 8) into two zones: seven adjoining seats and
another seven adjoining ones. In Figure 7, aisles 1 and 2
separate all seats in a small classroom into three zones. If
an aisle seat in a given row is occupied, some students are
reluctant to take a seat in the middle of the row because
they may bother the adjacent occupants when going in
and out.

Direction 1

Instructional
Building
Number 6

Instructional
Building
Number 4

Instructional
Building
Number 2

Instructional
Building
Number 5

Instructional
Building
Number 3

Instructional
Building
Number 1

Direction 4
Figure 5. The layout of the instructional buildings.
26

IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE Apri l 2021

IEEE Systems, Man and Cybernetics Magazine - April 2021

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