The average of gas refueling time is 1 minute, 2minute, 5minute for each machine. How long does it take on average for my car to finish refueling? Pls explain in detail

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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At a gas station with three gas systems, we want to put oil in the car. However, all three refueling machines are being used.

 

The time it takes to refuel follows an individual independent exponential distribution for each refueling machine.

 

My plan is to use gas machine as soon as there is an empty machine.

 

The average of gas refueling time is 1 minute, 2minute, 5minute for each machine. How long does it take on average for my car to finish refueling?

Pls explain in detail

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