Question

For the next 7 questions, please refer to the following information.

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.).

f. What is the utilization of the pumps?

• A. 0.63
• B. 0.83
• C. 0.53
• D. 0.73

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. 6
• B. 2
• C. 4
• D. 8

Answer 1

f.

IN QUEING THEORY UTILIZATION RATE OF SERVERS   ρ = λ/Cµ

WHERE   λ=MEAN ARRIVAL RATE OF CUSTOMERS

                µ = AVERAGE SERVICE RATE

             C= NO OF SERVERS

In the given problem arrival rate λ is 30 per hour

Service rate µ is 15 per hour as it takes 4 minutes in all activities

While C = 3

So UTILIZATION RATE OF SERVERs here PUMPS is   ρ = 30/15x3 = 2/3 or .66

g.

Now 98% business is expected to cater by the filling stations

Utilization factor or rate is ρ .66

Mean arrival rate λ = 30 per hour

Expected service rate µ = 30* .98= 29.4 per hour

So value of C i.e. number of servers required will be C = λ / ρ µ

                                     = 30 /.66 x 29.4

                                     = 1.54 or 2 pumps are enough to cater 98% of demand