QSO 510: Module 10
Notes: Before doing this assignment, do the practice problem posted under Apply and Discover. Wordprocess your answers within this document. Do not create a new file. Show all steps used in arriving at
the final answers. Incomplete solutions will receive partial credit.
Problem
During the dinner hour, the distribution of the inter-arrival time of customers at a restaurant is estimated
to be as shown below. The mode of payment and the service times of the cash and credit card
customers are shown in the following tables. Complete the tables and simulate the system for 20
customer arrivals and determine the average time a cash and credit card customer must wait in line
before paying the cashier. Use Column A of the given random number table to determine the customer
inter-arrival time, Column B to determine whether the customer pays with cash or credit, and Column C
to determine the service time.
Inter-arrival time
Inter-arrival Time
Probability
30 seconds
60 seconds
0.15
120 seconds
0.10
150 seconds
Random Number
Interval
0.45
90 seconds
Cumulative
Probability
0.05
0.25
Mode of Payment
Payment
Mode
Probability
Cash
0.6
Credit Card
Cumulative
Probability
Random Number
Interval
0.4
Cash Service Time
Service Time
Probability
20 seconds
40 seconds
0.35
0.30
60 seconds
0.25
80 seconds
0.10
Cumulative
Probability
Random Number
Interval
Credit Card Service Time
Service Time
Probability
30 seconds
60 seconds
0.20
90 seconds
0.25
120 seconds
0.10
Random Numbers
(A)
(B)
(C)
6320
1094
1995
4630
7371
7971
8657
2809
3554
0030
5148
6300
5624
9115
5495
6728
1469
5165
5925
6480
9339
2829
2447
6997
7939
7031
1443
6476
8442
3574
3319
7387
0150
8134
1788
0933
1712
4891
7082
6317
1149
5025
6605
8822
4081
2734
9451
4100
0432
2990
7190
3441
8314
6822
0726
7176
5053
6969
2766
8284
0.45
Cumulative
Probability
Random Number
Interval
Complete the table below to show the results of the simulation.
Custome
r
Rando
m
Numbe
r
Arriva
l
Time
Rando
m
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Average Waiting Time (Cash)=
Average Waiting Time (Credit)=
Mode of
Payment
Rando
m
Numbe
r
Servic
e
Time
Service Time
Begin End
s
s
Waiting Time
Cash
Credit
4
QSO 510: Module 10