Question

A new gas station has only one pump for gasoline. Cars take on an average 5 minutes to fuel up. The gas station manager calculated that the pump has an average of 8 cars visiting it every hour. On an average, how many cars will be waiting in the queue for refueling? (3 decimals)

The answer is suppose to be 1.333.

I need help figuring out how my professor got this answer. Please only reply if you know a step-by-step solution.

Answer 1

Arrival rate = = 8 cars per hour

Service rate = = 1 car per 5 minute = 1 * 12 per 5 * 12 minute = 12 per 60 minute = 12 cars per hour

Utilization rate = = / = 8/12 = 2/3

Average number of cars will be waiting in the queue for refueling = / (1 - )

= (2/3)² / (1 - 2/3)

= (4/9) / (1/3)

= (4 * 3) / 9

= 1.333