2 (5 points). A gas station has 4 gasoline pumps. Cars stop for gasoline according to a Poisson process at a mean rate of 20 per hour. However, if all pumps are being used, the next customer will simply drive to a gas station across the street. The time required to service a car has an exponential distribution with a mean of 5 minutes. (a What is the state space of this queueing system? (b Construct the rate diagram for this queueing system. ) l (0) Develop the balance equations. ) (d Solve these equations to nd the steady-state probability distribution of the number of cars at the station. (e) What is the waiting time in the queue, W