This document simulates customer arrivals and service times at a grocery store. It contains a table tracking 100 customers with columns showing arrival times, service times, wait times, time in system, and server idle time. Key findings are that about half of customers waited, with an average wait time of 0.76 minutes. The server was busy 76% of the time and idle 24% of the time. The simulation could be run for longer to increase accuracy.

1. Grocery Store Example
[Simulation of Queueing Systems]
[Simulation of Queueing Systems]
For manual simulation, Simulation tables are designed for the
problem at hand, with columns added to answer questions
problem at hand, with columns added to answer questions
posed: 2nd customer was in the
system for 5 minutes.
Time Waiting Time Time
Customer
Interarrival
Time (min)
Arrival
Time
(clock)
Service
Time
(min)
Time
Service
Begins
(clock)
Waiting
Time in
Queue
(min)
Time
Service
Ends
(clock)
Time
customer
spends in
system (min)
Idle time
of server
(min)
1 0 4 0 0 4 4
2 1 1 2 4 3 6 5 0
2 1 1 2 4 3 6 5 0
3 1 2 5 5 4 11 9 0
4 6 8 4 11 3 15 7 0
5 3 11 1 15 4 16 5 0
6 7 18 5 18 0 23 5 2
Service could not begin
Service ends at time 16, but
… … … … … … … … …
100 5 415 2 416 1 418 3
Totals 415 317 174 491 0
13
Service could not begin
until time 4 (server was
busy until that time)
Service ends at time 16, but
the 6th customer did not arrival
until time 18. Hence, server
was idle for 2 minutes

2. Grocery Store Example
[Simulation of Queueing Systems]
[Simulation of Queueing Systems]
Tentative inferences:
About half of the customers have to wait, however, the average waiting
About half of the customers have to wait, however, the average waiting
time is not excessive.
The server does not have an undue amount of idle time.
Longer simulation would increase the accuracy of findings.
Note: The entire table can be generated using the Excel spreadsheet
14
Note: The entire table can be generated using the Excel spreadsheet
for Example 2.1 at www.bcnn.net

3. Grocery Store Example
[Simulation of Queueing Systems]
[Simulation of Queueing Systems]
A histogram of the 50 average waiting times for the 50 trials:
15

4. Grocery Store Example
[Simulation of Queueing Systems]
[Simulation of Queueing Systems]
Key findings from the simulation table:
waiting
Average
46
.
0
100
46
customers
of
number
total
wait
who
customers
of
numbers
y(wait)
Probabilit
min
74
.
1
100
174
customers
of
number
total
(min)
queue
in
wait
time
total
(min)
time
waiting
Average
0.76
0.24
-
1
server
busy
of
y
Probabilit
:
Hence
24
.
0
418
101
(min)
simulation
of
run time
total
(min)
server
of
time
idle
total
server
idle
of
y
Probabilit
46
.
0
100
customers
of
number
total
y(wait)
Probabilit
time
service
Expected
:
Check
min
17
.
3
100
317
customers
of
number
total
(min)
time
service
total
(min)
time
service
Average
0.76
0.24
-
1
server
busy
of
y
Probabilit
:
Hence
415
(min)
times
al
interarriv
all
of
sum
al
interarriv
Average
min
2
.
3
)
05
.
0
(
6
)
1
.
0
(
5
)
25
.
0
(
4
3
.
0
(
3
)
2
.
0
(
2
)
1
.
0
(
1
time
service
Expected
:
Check
16
min
2
.
3
2
/
)
8
1
(
time
al
interarriv
Expected
:
Check
min
19
.
4
99
415
1
arrivals
of
number
(min)
times
al
interarriv
all
of
sum
(min)
Times
al
interarriv
Average