A crew of mechanics at the Transylvania Department of Motor Vehicles garage make minor repairs to snowplows during the winter.  The snowplows break down at an average rate of  4 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 7 vehicles per day with a repair time distribution that approximates a negative exponential distribution.  Assume an 8 hour day. Approximately how many vehicles are in the garage, waiting for or being repaired?

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 21P
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A crew of mechanics at the Transylvania Department of Motor Vehicles garage make minor repairs to snowplows during the winter.  The snowplows break down at an average rate of  4 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 7 vehicles per day with a repair time distribution that approximates a negative exponential distribution.  Assume an 8 hour day. Approximately how many vehicles are in the garage, waiting for or being repaired?

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