Determine the average time customers spend at the machine, including waiting in line and completing transactions. Determine the probability that a customer will not have to wait upon arrival at the ABM. Determine the utilization of the ABM.

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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Many of a bank’s customers use its automated banking machine (ABM). During the early evening
hours in the summer months, customers arrive at an ABM at the rate of one every other minute
(assume Poisson). Each customer spends an average of 99 seconds completing the transaction.
Transaction times are exponentially distributed. Assume that the length of the queue is not a
constraint.

  1. Determine the average time customers spend at the machine, including waiting in line and completing transactions.
  2. Determine the probability that a customer will not have to wait upon arrival at the ABM.
  3. Determine the utilization of the ABM.

 

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