(Supermarket Simulation) Write a program that simulates a check-out line at a supermarket. The line is a queue. Customers arrive in random integer intervals of 1 to 4 minutes. Also, each customer is serviced in random integer intervals of 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 in-finitely. Even with balanced rates, randomness can still cause long lines. Run the supermarket simulation for a 12-hour day (720 minutes) using the following algorithm:
1) Choose a random integer between 1 and 4 to determine the minute at which the first customer arrives.
2) At the first customer's arrival time:
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).
3) For each minute of the day:
If the next customer arrives, Say so;
Enqueue the customer;
Schedule the arrival time of the next customer. If service was completed for the last customer, 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) .
Now run your simulation for 720 minutes and answer each of the following:
a) What's the maximum number of customers in the queue at any time?
b) What's the longest wait any one customer experienced?
c) What happens if the arrival interval is changed from 1 to 4 minutes to 1 to 3 minutes?
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