Question

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.).

d. What is the probability that all three pumps are being used by vehicles?

• A. 0.1458
• B. 0.2105
• C. 0.1650
• D. 0.1895

e. How many customers are served every hour?

• A. 16.7
• B. 23.7
• C. 25.6
• D. 12.7

f. What is the utilization of the pumps? A. 0.73 B. 0.83 C. 0.53 D. 0.63

g. How many pumps should it have to ensure that it captures at least 98 percent of the demand that drives by the station? A. 2 B. 6 C. 4 D. 8

Answer 1

d. What is the probability that all three pumps are being used by vehicles?

• Number of cars passing by the gas station that would like to refuel = demand = 30 cars/hour,
• Each car arrives on an average every a = 1 hour/ 30 cars = 60 minutes /30 cars = 2 minutes
• The number of pumps in the gas station =
• It take a car, on an average minutes to refuel,
• 
  
  Using the Erlang Loss table,
  
  

Answer d. Option B) 0.2105

e. How many customers are served every hour?

A car will be served when the gas station is not full
P(A car is served) = P(gas station is not full) = 1 - P(gas station is full) = 1 - 0.2105 = 0.7895
Total number of cars served = Number of cars arriving in 1 hour * P(A car is served) = 30*0.7895 = 23.7 cars/hour

This is also the flow rate = 23.7 cars/ hour

Answer e. Option B) 23.7 cars/hour

f. What is the utilization of the pumps?

Utilization: The utilization is how well a resource is being used. It is calculated as flow rate divided by capacity, where

capacity = m/processing time

Utilization = flowrate/​​​​capacity = 23.7/45 = 0.53

Answer f. Option C) 0.53

g. How many pumps should it have to ensure that it captures at least 98 percent of the demand that drives by the station?

Let m be the number of pumps

So we want the probability that a car is served to be atleast 0.98

Probability that a car is served =

using the Erlan loss table, we have

Since

so this is satisfied for m \geq 6 pumps

Answer g. Option B) 6

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