A gas station with only one gas pump employs the following policy: If a customer has to wait, the price is $3.50 per gallon; if she does not have to wait, the price is $4.00 per gallon. Customers arrive according to a Poisson process with a mean rate of 15 per hour. Service times at the pump have an exponential distribution with a mean of 3 minutes. Arriving customers always wait until they can eventually buy gasoline. Determine the expected price of gasoline per gallon.
A gas station with only one gas pump employs the following policy: If a customer has to wait, the price is $3.50 per gallon; if she does not have to wait, the price is $4.00 per gallon. Customers arrive according to a Poisson process with a mean rate of 15 per hour. Service times at the pump have an exponential distribution with a mean of 3 minutes. Arriving customers always wait until they can eventually buy gasoline. Determine the expected price of gasoline per gallon.
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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![9. A gas station with only one gas pump employs the following policy: If a customer has to wait, the price is $3.50
per gallon; if she does not have to wait, the price is $4.00 per gallon. Customers arrive according to a Poisson
process with a mean rate of 15 per hour. Service times at the pump have an exponential distribution with a
mean of 3 minutes. Arriving customers always wait until they can eventually buy gasoline. Determine the
expected price of gasoline per gallon.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd83c3ce1-cd72-4e3b-8702-f62923bac270%2Fc5522d95-2464-44d4-90a2-c9ace3a67276%2Fpk9n652_processed.png&w=3840&q=75)
Transcribed Image Text:9. A gas station with only one gas pump employs the following policy: If a customer has to wait, the price is $3.50
per gallon; if she does not have to wait, the price is $4.00 per gallon. Customers arrive according to a Poisson
process with a mean rate of 15 per hour. Service times at the pump have an exponential distribution with a
mean of 3 minutes. Arriving customers always wait until they can eventually buy gasoline. Determine the
expected price of gasoline per gallon.
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