Question

PA 17-1 Mr. Cherry owns a gas station on a highway in Erlang Loss Table m 6 1 2. 3 5 7 10 r= pla 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 Enter a value for 'r' in the green cell above. Vermont station that would like to refuel. However, since there are several other gas stations Mr. Ch 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. station on a highway afternoon hours, ther 30 cars per hour passing by the average 4 minutes parked at a pump (filling up their tank, paying, etc.) used for fueling vehicles and cars spend The gas station has 3 pumps that can

a. What is the offered load?

b. What is the implied utilization? (Round your answer to 2 decimal places.)

c. What is the capacity of the gas station (cars per hour)? table above to determine the probability that all 3 pumps are being used by d. (Round your answer to 4 decimal places.)

e. How many customers are served every hour? (Round your answer to 1 decimal place.)

f. What is the utilization of the pumps? (Round your answer to 2 decimal places.) Use the table above to determine how many pumps are required to capture at least 98% of the demand that drives by the station.

Answer 1

(a.) Since there are 30 cars passing by on an avg. of 4 Minutes hence,

offered load as per erlang's formula = cars passing by * avg minutes / 60

= 30*4/60 = 2 cars.

(B) Implied utilization = Demand / Capacity

= 3/30 = 0.001

(C) Capacity of the station = 3 pumps

(D.) Round off to 4 decimal places = 0.0003

(e.) customer served every hour = 30.00

(F.) The utilisation of the pump = 0.004

Hence around 12 pumps are required to capture around 90 percent of the market