Problem:
At a border, vehicles arrive at the rate of 9 pr minute in a poisson distribution. For simplicity in this problem assume that there is only one lane and one inspector who can inspect vehicles at the rate of 12 per minute in an exponentially distribution fashion.
Required:
Question 1) what is the average length of the waiting line?
Question 2) what is the percentage of the time the inspector is idle?
Question 3) what is the probability that when you arrive there will be four or more vehicles (include the one being inspected ahead of you?
Provide correct solution of the given problem with complete calculations.