Question: 4. (M/M/1 Queue) Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars.

4. (M/M/1 Queue) Willow Brook National Bank

4. (M/M/1 Queue) 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 a mean arrival rate of 24 customers per hour or 0.4 customers per minute. Assume that the service times for the drive-up teller follow an exponential probability distribution with a mean service rate of 36 customers per hour or 0.6 customers per minute. What is the probability that no customers are in the system? b. What is the average number of customers waiting in line? What is the average number of customers in the system? d. What is the average time a customer spends waiting in line? What is the average time a customer spends in the system? f. What is the probability that arriving customers will have to wait for service (hint: An arriving customer has to wait except when no customers are in the system upon their arrival)? a. c

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