Question: During peak time, customers arrive at a bank teller window (with a single teller) at a rate of 18 per hour, where the teller can

During peak time, customers arrive at a bank teller window (with a single teller) at a rate of 18 per hour, where the teller can serve 24 per hour. This problem will allow you to investigate (via a simple extension of the mean queue size formula) the effect of highly-variable service times on our familiar queuing metrics. The diagram below stylizes the queuing system:

What is the distribution of the total waiting time (that is, the total time a customer spends in the bank)? Calculate the marginal probability of a customer spending longer than 12 minutes (0.2 hours) in the bank, P (W > 0.2).

9. What is the average number of customers at the bank (in line and at the window)?

10. On average, how long does a customer spend in line waiting (in minutes) for the teller to become available?

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