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 Cumulative Probability Random Number Interval

30 seconds 0.45

60 seconds 0.25

90 seconds 0.15

120 seconds 0.10

150 seconds 0.05

Mode of Payment

Payment Mode Probability Cumulative Probability Random Number Interval

Cash 0.6

Credit Card 0.4

Cash Service Time

Service Time Probability Cumulative Probability Random Number Interval

20 seconds 0.35

40 seconds 0.30

60 seconds 0.25

80 seconds 0.10

Credit Card Service Time

Service Time Probability Cumulative Probability Random Number Interval

30 seconds 0.20

60 seconds 0.45

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

Complete the table below to show the results of the simulation.

Customer Random Number Arrival Time Random Number Mode of Payment Random Number Service Time Service Time Waiting Time

Begins Ends Cash Credit

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)=

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## This question was asked on Jun 03, 2013 and answered on Jun 03, 2013.

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