Simulation Problem

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. For the arrival time, please start at 0 seconds, and increments in seconds from the results you get from decoding of the random numbers. As an example, the first random number is 6320, which equates to 60 seconds of inter-arrival time. So, your first customer arrival time is 60 seconds. For your second customer, the random number is 4630, which also equates to 60 seconds of inter-arrival time. As a result, your second customer arrival time will be 120 seconds, and so on. Please keep your results in seconds for all customers.

Use 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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