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Problem: Customers wait in a single queue to be served by the first bank teller that is available to serve them. There are four bank tellers, and each takes on average 60 seconds to serve a customer, with a standard deviation of service time of 40 seconds. Customers arrive on average every 20 seconds, with the standard deviation of the time between arrivals of 18 seconds. From the above, we can see that the arrival rate is 180 customers/hour and the utilization is 75%. What is the coefficient of variation of inter-arrival times? What is the coefficient of variation of service times? On average, how long does a customer wait in line before they can talk to a teller? Express your answer in seconds. How many customers are waiting in the queue, on average, at any given point in time?
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