During the campus Spring Fling, the bumper car amusement attraction has a problem with cars becoming disabled and in need of repair.  One repairer can fix cars in an average time of 25 minutes.  While a car is out of service either disabled and waiting to be repaired or being repaired, cars tend to break down at the rate of two per hour.  Assume that there is only one repair person, the arrival rate follows a Poisson distribution and the service time follows an exponential distribution.   a) On average, how long is a disabled bumper car out of service waiting to be repaired?   b)  On average, how many disabled bumper cars are out of service and not able to take riders on the bumper car attraction?   c)  When a bumper car becomes disabled, what is the probability that it will find that there is at least one other bumper car already waiting to be 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
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During the campus Spring Fling, the bumper car amusement attraction has a problem with cars becoming disabled and in need of repair.  One repairer can fix cars in an average time of 25 minutes.  While a car is out of service either disabled and waiting to be repaired or being repaired, cars tend to break down at the rate of two per hour.  Assume that there is only one repair person, the arrival rate follows a Poisson distribution and the service time follows an exponential distribution.

 

a) On average, how long is a disabled bumper car out of service waiting to be repaired?

 

b)  On average, how many disabled bumper cars are out of service and not able to take riders on the bumper car attraction?

 

c)  When a bumper car becomes disabled, what is the probability that it will find that there is at least one other bumper car already waiting to be repaired? 

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