Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekdaymornings, arrivals to the drive-up teller window occur at random, with an arrival rate of 15 customers per hour or 0.25 customers per minute.Let's assume that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 21 customers per hour, or 0.35customers per minute.Determine the following operating characteristics for the system. (Round your answers to four decimal places.)(a) The probability that no customers are in the system(b) The average number of customers waiting(c) The average number of customers in the system(d) The average time (in min) a customer spends waitingmin(e) The average time (in min) a customer spends in the systemmin(f) The probability that arriving customers will have to wait for service

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Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 9P

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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 30 customers per hour or 0.5 customers per minute. Assume the Poisson probability distribution can be used to describe the arrival process. (a) What is the mean or expected number of customers that will arrive in a six-minute period? (b) Use the arrival rate in part (a) and compute the probabilities that exactly 0, 1, 2, and 3 customers will arrive during a six-minute period. (Round your answers to four decimal places.) X 0 1 2 3 P(x) (c) Delays are expected if more than three customers arrive during any six-minute period. What is the probability that delays will occur? (Round your answer to four decimal places.)

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