(A) Sal's International is a popular haircutting and styling salon near the campus of the University of New Orleans. Four barbers work full-time and spend an average of 15 minutes per customer. Customers arrive throughout the day at an average rate of 12 each hour. All arriving customers are assigned a waiting number. Arrivals tend to follow the Poisson distribution, while service time is exponentially distributed. Assuming an infinite population source, determine the following:

1. What is the average number of customers in the salon?

2. What is the average time that a customer spends in the salon?

3. What is the average time a customer spends waiting to be attended?

4. What is the average number of customers waiting to be attended?

(B) Sal is now considering changing the queuing characteristics of his salon. Upon arrival, instead of being assigned waiting numbers, customers will be able to choose the barbers they prefer. Assuming this selection does not change while the customers are waiting for their barbers to become available and the requests for each of the four barbers are evenly distributed, answer the following:

What is the average number of customers in the salon?

What is the average time that a customer spends in the salon?

What is the average time a customer spends waiting to be attended?

What is the average number of customers waiting to be attended?

(C) Explain why the results from parts (A) and (B) are different.

1. What is the average number of customers in the salon?

2. What is the average time that a customer spends in the salon?

3. What is the average time a customer spends waiting to be attended?

4. What is the average number of customers waiting to be attended?

(B) Sal is now considering changing the queuing characteristics of his salon. Upon arrival, instead of being assigned waiting numbers, customers will be able to choose the barbers they prefer. Assuming this selection does not change while the customers are waiting for their barbers to become available and the requests for each of the four barbers are evenly distributed, answer the following:

What is the average number of customers in the salon?

What is the average time that a customer spends in the salon?

What is the average time a customer spends waiting to be attended?

What is the average number of customers waiting to be attended?

(C) Explain why the results from parts (A) and (B) are different.

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