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. Assume that Poisson probability distribution with an arrival rate of 24 customers per hour or 0.4 customer per minute can be used to describe the arrival pattern. Assume further that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 36 customers per hour, or 0.6 customer per minute. a. Use the single-channel drive-up bank teller operation to determine the average time a customer spends waiting b. Use the single-channel drive-up bank teller operation to determine the average time a customer spends in the system c. Use the single-channel drive-up bank teller operation to determine the probability that arriving customers will have to wait for service d.Use the single-channel drive-up bank teller operation to determine the probability of 4 customers in the system e.Use the single-channel drive-up bank teller operation to determine the average service time in minutes of the drive-up teller.
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. Assume that Poisson probability distribution with an arrival rate of 24 customers per hour or 0.4 customer per minute can be used to describe the arrival pattern. Assume further that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 36 customers per hour, or 0.6 customer per minute.
a. Use the single-channel drive-up bank teller operation to determine the average time a customer spends waiting
b. Use the single-channel drive-up bank teller operation to determine the average time a customer spends in the system
c. Use the single-channel drive-up bank teller operation to determine the probability that arriving customers will have to wait for service
d.Use the single-channel drive-up bank teller operation to determine the probability of 4 customers in the system
e.Use the single-channel drive-up bank teller operation to determine the average service time in minutes of the drive-up teller.
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