Waiting Lines
What appears below =
is the
first model in the book (from Chapter 2, Section 1). This model is very simple; much mo=
re
elaborate models are possible. The
goal here is just to give you a feel for how SimQuick works. Explanations of the details (inclu=
ding
an introduction to simulation) can be found in the book. Example: A bank Consider the follow=
ing
process within a small bank: Customers enter the bank, get into a single li=
ne,
are served by a teller, and finally leave the bank. Currently, this bank has one teller
working from 9 a.m. to 11 <=
span
style=3D'text-transform:uppercase'>a.m. Management is concerned that the w=
ait in
line seems to be too long. Therefore, they are considering two process
improvement ideas: adding an additional teller during these hours or instal=
ling
a new automated check-reading machine that can help the single teller serve
customers more quickly.
What should managem=
ent do?
To answer this ques=
tion,
management has collected and summarized some data:
The
amount of time between arrivals of customers can be approximated by an expo=
nential
distribution with a mean of 2 minutes.&nbs=
p;
The line in this bank can only hold 8 people and if a person arrives
when the line is full, he/she does not get in line. The service time by the teller can=
be
approximated by a normal distribution with a mean of 2.4 minutes and a stan=
dard
deviation of .5 minutes.
Building the model
Next we see how to =
build a
SimQuick model for the current process with a single teller.
SimQuick provides f=
ive
building blocks, called Elements, which can be combined in a huge number of
ways. The elements are Entran=
ces,
Exits, Buffers, Workstations, and Decision Points.
The first step in u=
sing
SimQuick is to draw a flow map of the real-world process using these buildi=
ng
blocks. Here’s what the=
model
looks like for the bank:
![](3D"SimQuickExample-Web_files/image002.jpg")
The next step is to=
input
the model into SimQuick in Excel.
You first open the Excel file SimQuick-v2.xls. What you see is the Control Panel,=
which
is copied below. For each ele=
ment
in the model, you click on the element’s button on the Control Panel =
and
fill in a table with the details about the element. You also fill in, on the Control P=
anel,
how many simulations you want to do and how long each simulation should las=
t. (In this example, we are doing 50
simulations, each for 120 time units, which corresponds to two hours.) The filled-in Control Panel and ta=
bles
look like this:
![](3D"SimQuickExample-Web_files/image004.jpg")
![](3D"SimQuickExample-Web_files/image006.jpg")
Running and analyzing the model
You then click Run
Simulations on the Control Panel.
After a few seconds the 50 simulations of the 9AM to 11AM time perio=
d are
finished. Clicking on View Results brings up the table below. (Here we see only the results of t=
he
first five simulations.)
|
Simulation
Results |
|
|
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
|
Element |
Element |
Statistics |
Overall |
Simulation number(s) |
||||
|
types |
names |
|
means |
1 |
2 |
3 |
4 |
5 |
|
|
|
|
|
|
|
|
|
|
|
Entrance(s) |
Door |
Objects entering process |
53.88 |
58 |
56 |
55 |
57 |
48 |
|
|
|
Objects unable to enter |
6.70 |
7 |
3 |
6 |
18 |
0 |
|
|
|
Service level |
0.90 |
0.89 |
0.95 |
0.90 |
0.76 |
1.00 |
|
|
|
|
|
|
|
|
|
|
|
Work Station(s) |
Teller |
Final status |
NA |
Working |
Working |
Working |
Working |
Not Working |
|
|
|
Final inventory (int. buff.) |
0.00 |
0 |
0 |
0 |
0 |
0 |
|
|
|
Mean inventory (int. buff.) |
0.00 |
0.00 |
0.00 |
0.00 |
0.00 |
0.00 |
|
|
|
Mean cycle time (int. buff.) |
0.00 |
0.00 |
0.00 |
0.00 |
0.00 |
0.00 |
|
|
|
Work cycles started |
48.43 |
51 |
49 |
49 |
50 |
48 |
|
|
|
Fraction time working |
0.96 |
0.98 |
1.00 |
0.97 |
0.97 |
0.96 |
|
|
|
Fraction time blocked |
0.00 |
0.00 |
0.00 |
0.00 |
0.00 |
0.00 |
|
|
|
|
|
|
|
|
|
|
|
Buffer(s) |
Line |
Objects leaving |
48.43 |
51 |
49 |
49 |
50 |
48 |
|
|
|
Final inventory |
5.45 |
7 |
7 |
6 |
7 |
0 |
|
|
|
Minimum inventory |
0.00 |
0 |
0 |
0 |
0 |
0 |
|
|
|
Maximum inventory |
7.77 |
8 |
8 |
8 |
8 |
7 |
|
|
|
Mean inventory |
4.47 |
5.03 |
4.64 |
3.05 |
6.43 |
3.42 |
|
|
|
Mean cycle time |
11.04 |
11.83 |
11.36 |
7.46 |
15.43 |
8.54 |
|
|
|
|
|
|
|
|
|
|
|
|
End |
Objects leaving |
0.00 |
0 |
0 |
0 |
0 |
0 |
|
|
|
Final inventory |
47.44 |
50 |
48 |
48 |
49 |
48 |
|
|
|
Minimum inventory |
0.00 |
0 |
0 |
0 |
0 |
0 |
|
|
|
Maximum inventory |
47.44 |
50 |
48 |
48 |
49 |
48 |
|
|
|
Mean inventory |
22.75 |
22.84 |
24.19 |
22.71 |
23.29 |
22.89 |
|
|
|
Mean cycle time |
Infinite |
Infinite |
Infinite |
Infinite |
Infinite |
Infinite |
From this table yo=
u can
see two key performance measures: Our simulated customers were waiting in l=
ine
for 11.04 minutes, on average (see the “Mean cycle time” row un=
der
“Buffer(s), Line”), and there were 4.47 customers in line, on
average (see the “Mean inventory” row under “Buffer(s),
Line”).
From here it’=
;s easy
to change the model for the case of two tellers and the case of a single te=
ller
who can work faster due to some automation. We can then see the effect of these
changes on the waiting time and number of customers in line. This can help management decide wh=
at to
do.
See the book for t=
he
details.