Mr. Cherry owns a gas station on a highway in Vermont. In the afternoon hours, thereare, on average, 30 cars per hour passing by the gas station that would like to refuel.However, because there are several other gas stations with similar prices on the highway, potential customers are not willing to wait—if they see that all of the pumps areoccupied, they continue on down the road.The gas station has three pumps that can be used for fueling vehicles, and cars spendfour minutes, on average, parked at a pump (filling up their tank, paying, etc.).a. What is the offered load?b. What is the implied utilization?c. What is the capacity of the gas station (cars per hour)?d. What is the probability that all three pumps are being used by vehicles?e. How many customers are served every hour?f. What is the utilization of the pumps?g. How many pumps should it have to ensure that it captures at least 98 percent of thedemand that drives by the station?

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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Mr. Cherry owns a gas station on a highway in Vermont. In the afternoon hours, there
are, on average, 30 cars per hour passing by the gas station that would like to refuel.
However, because there are several other gas stations with similar prices on the highway, potential customers are not willing to wait—if they see that all of the pumps are
occupied, they continue on down the road.
The gas station has three pumps that can be used for fueling vehicles, and cars spend
four minutes, on average, parked at a pump (filling up their tank, paying, etc.).
a. What is the offered load?
b. What is the implied utilization?
c. What is the capacity of the gas station (cars per hour)?
d. What is the probability that all three pumps are being used by vehicles?
e. How many customers are served every hour?
f. What is the utilization of the pumps?
g. How many pumps should it have to ensure that it captures at least 98 percent of the
demand that drives by the station?

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ISBN:
9781337406659
Author:
WINSTON, Wayne L.
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Cengage,