Customers arrive randomly at a product returns counter at a department store, which meets the assumptions of the Single-Server, Single-Phase waiting line model (i.e., the arrival rate is Poisson distributed and service rate is exponentially distributed). There is only one returns employee, and the time required for returns varies from customer to customer. There is a single waiting line. The average arrival rate is 16 customers per hour. The average time to serve a customer is 2.52 minutes. Respond to the following questions:
a. What is the utilization factor?
b. How long can a customer expect to wait in line?
c. How many customers are expected to wait to be serviced?
d. How many customers are expected to be in the system?
e. How long can a customer expect to wait to be serviced and be serviced?
f. What is the probability that there are exactly 2 customers in the system?
g. What is the probability that there are exactly 5 customers in the system?