Willow Brook National Bank operates a drive-up teller window that allows customers to complete…

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Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up teller window occur at random, with an arrival rate of 18 customers per hour or 0.3 customers per minute. In the same bank waiting line system, assume that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 24 customers per hour, or 0.4 customers per minute. Determine the following operating characteristics for the system:

a. What is the mean or expected number of customers that will arrive in a ?ve-minute
period?
b. Assume that the Poisson probability distribution can be used to describe the arrival
process. Use the arrival rate in part (a) and compute the probabilities that exactly 0, 1,
2, and 3 customers will arrive during a ?ve-minute period.
c. Delays are expected if more than three customers arrive during any ?ve-minute
period. What is the probability that delays will occur? The probability that no customers are in the system. If required, round your answer to four decimal places.
P0 = The average number of customers waiting. If required, round your answer to four decimal places.
Lq = The average number of customers in the system. If required, round your answer to nearest whole number.
L = The average time a customer spends waiting. If required, round your answer to four decimal places.
Wq = min The average time a customer spends in the system. If required, round your answer to nearest whole number.
W = min The probability that arriving customers will have to wait for service. If required, round your answer to four decimal places.
Pw =

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