# 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.

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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)=