Practical Management Science, Loose-leaf Version
5th Edition
ISBN: 9781305631540
Author: WINSTON, Wayne L.; Albright, S. Christian
Publisher: Cengage Learning
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Chapter 13.5, Problem 15P
Summary Introduction
To estimate: The arrival rate.
Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.
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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
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(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
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(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.)
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 24 customers per hour or 0.4 customers per minute.
What is the mean or expected number of customers that will arrive in a five-minute period?λ = fill in the blank 1 per five minute period
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 five-minute period. If required, round your answers to four decimal places.
x
P(x)
0
fill in the blank 2
1
fill in the blank 3
2
fill in the blank 4
3
fill in the blank 5
Delays are expected if more than three customers arrive during any five-minute period. What is the probability that delays will occur? If required, round your…
The following data has been collected on the number of customers seen to arrive to a museum in a succession of 5-minute intervals: 5, 1, 3, 7, 5, 5, 6, 7, 5, 7, 4, 8, 1, 5, 2, 3, and 5. Estimate the squared coefficient of variation of the arrival process. If this data was known to come from a Poisson process, what would be your estimate of λ, the rate of customer arrivals?
Chapter 13 Solutions
Practical Management Science, Loose-leaf Version
Ch. 13.3 - Prob. 1PCh. 13.3 - Prob. 2PCh. 13.3 - Prob. 3PCh. 13.3 - Prob. 4PCh. 13.4 - Prob. 5PCh. 13.4 - Prob. 6PCh. 13.4 - Prob. 7PCh. 13.4 - Prob. 8PCh. 13.5 - Prob. 9PCh. 13.5 - Prob. 10P
Ch. 13.5 - Prob. 11PCh. 13.5 - Prob. 12PCh. 13.5 - Prob. 13PCh. 13.5 - Prob. 14PCh. 13.5 - Prob. 15PCh. 13.5 - Prob. 16PCh. 13.5 - Prob. 17PCh. 13.5 - Prob. 18PCh. 13.5 - Prob. 19PCh. 13.5 - Prob. 20PCh. 13.5 - Prob. 21PCh. 13.5 - Prob. 22PCh. 13.5 - Prob. 23PCh. 13.5 - Prob. 24PCh. 13.5 - Prob. 25PCh. 13.5 - Prob. 26PCh. 13.5 - Prob. 27PCh. 13.5 - Prob. 28PCh. 13.5 - Prob. 29PCh. 13.5 - Prob. 30PCh. 13.5 - Prob. 31PCh. 13.5 - Prob. 32PCh. 13.5 - Prob. 33PCh. 13.5 - Prob. 34PCh. 13.5 - Prob. 35PCh. 13.5 - Prob. 36PCh. 13.5 - Prob. 37PCh. 13 - Prob. 46PCh. 13 - Prob. 47PCh. 13 - Prob. 48PCh. 13 - Prob. 49PCh. 13 - Prob. 50PCh. 13 - Prob. 51PCh. 13 - Prob. 52PCh. 13 - Prob. 54PCh. 13 - Prob. 58PCh. 13 - Prob. 59P
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