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)

Answer 1

8 cars visit every hour                  
=> 8/60 = 0.1333 cars visit every minute                  
                  
Let X be the number of cars visiting every minute                  
Then X follows Poisson distribution with λ = 0.1333 cars per minute                  
λ = 0.1333                  
Let Y be the service time (time for fueling)                  
Y follows Exponential Distribution with mean = 5 minutes                  
μ = service rate = 1/5 = 0.2 cars per minute                  
           
Average number of cars waiting in the queue                  

Average number of cars waiting in the queue = 1.332