Many of a bank’s customers use its automatic teller machine to transact business after normal banking hours. During the early evening hours in the summer months, customers arrive at a certain location at the rate of one every other minute. This can be modeled using a Poisson distribution. Each customer spends an average of 87 seconds completing his or her transactions. Transaction time is exponentially distributed. Determine the following: a. The average time customers spend at the machine, including waiting in line and completing transactions b. The probability that a customer will not have to wait upon arriving at the automatic teller machine c. The average number waiting to use the machine

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
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Many of a bank’s customers use its automatic teller machine to transact business after normal banking hours. During the early evening hours in the summer months, customers arrive at a certain location at the rate of one every other minute. This can be modeled using a Poisson distribution. Each

customer spends an average of 87 seconds completing his or her transactions. Transaction time is

exponentially distributed. Determine the following:

a. The average time customers spend at the machine, including waiting in line and completing

transactions

b. The probability that a customer will not have to wait upon arriving at the automatic teller

machine

c. The average number waiting to use the machine

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