QSO510 Module 10
QSO 510: Module 10
Notes: Before doing this assignment, do the practice problem posted under Apply and Discover. Word-process 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
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Inter-arrival Time |
Probability |
Cumulative Probability |
Random Number Interval |
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30 seconds |
0.45 |
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60 seconds |
0.25 |
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90 seconds |
0.15 |
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120 seconds |
0.10 |
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150 seconds |
0.05 |
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Mode of Payment
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Payment Mode |
Probability |
Cumulative Probability |
Random Number Interval |
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Cash |
0.6 |
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Credit Card |
0.4 |
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Cash Service Time
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Service Time |
Probability |
Cumulative Probability |
Random Number Interval |
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20 seconds |
0.35 |
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40 seconds |
0.30 |
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60 seconds |
0.25 |
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80 seconds |
0.10 |
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Credit Card Service Time
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Service Time |
Probability |
Cumulative Probability |
Random Number Interval |
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30 seconds |
0.20 |
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60 seconds |
0.45 |
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90 seconds |
0.25 |
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120 seconds |
0.10 |
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Random Numbers |
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(A) |
(B) |
(C) |
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6320 |
1094 |
1995 |
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4630 |
7371 |
7971 |
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8657 |
2809 |
3554 |
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0030 |
5148 |
6300 |
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5624 |
9115 |
5495 |
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6728 |
1469 |
5165 |
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5925 |
6480 |
9339 |
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2829 |
2447 |
6997 |
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7939 |
7031 |
1443 |
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6476 |
8442 |
3574 |
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3319 |
7387 |
0150 |
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8134 |
1788 |
0933 |
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1712 |
4891 |
7082 |
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6317 |
1149 |
5025 |
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6605 |
8822 |
4081 |
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2734 |
9451 |
4100 |
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0432 |
2990 |
7190 |
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3441 |
8314 |
6822 |
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0726 |
7176 |
5053 |
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6969 |
2766 |
8284 |
Complete the table below to show the results of the simulation.
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Customer |
Random Number |
Arrival Time |
Random Number |
Mode of Payment |
Random Number |
Service Time |
Service Time |
Waiting Time |
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Begins |
Ends |
Cash |
Credit |
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1 |
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2 |
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8 |
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9 |
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10 |
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11 |
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12 |
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14 |
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15 |
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16 |
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18 |
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19 |
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20 |
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Average Waiting Time (Cash)= |
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Average Waiting Time (Credit)= |
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