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)=