Write a program that simulates a checkout line at a supermarket. The line is a queue object. Customers (i.e., customer objects) arrive at random integer intervals of from 1 to 4 minutes. Also, each customer is serviced at random integer intervals of from 1 to 4 minutes.

Obviously, the rates need to be balanced. If the average arrival rate is larger than the average service rate, the queue will grow infinitely. Even with “balanced” rates, randomness can still cause long lines. Run the supermarket simulation for a 12-hour day (720 minutes), using the algorithm in Fig. 21.21. Then answer each of the following:

a) What is the maximum number of customers in the queue at any time?

b) What is the longest wait any one customer experiences?

c) What happens if the arrival interval is changed from 1 to 4 minutes to 1 to 3 minutes?

Fig. 21.21

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I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 18 Choose a random integer between 1 and 4 to determine the minute at which the first customer arrives. At the first customer's arrival time, do the following: Determine customer's service time (random integer from 1 to 4). Begin servicing the customer. Schedule arrival time of next customer (random integer 1 to 4 added to the current time). For each simulated minute of the day, consider the following: If the next customer arrives, proceed as follows: Say so. Enqueue the customer. Schedule the arrival time of the next customer. If service was completed for the last customer, do the following: Say so. Dequeue next customer to be serviced. Determine customer's service completion time (random integer from 1 to 4 added to the current time).