4) [18 pts.] At a railway station only one train is handled at a time. The railway station is sufficient only for two trains to wait while the other is given signal to leave the station. Trains arrive at the station at an average rate of 6 per hour and the railway station can handle them on an average of 12 per hour. Assuming Poisson arrivals and exponential service distribution, a) find the steady state probabilities for the various number of trains in the system. b) Also, find average waiting time of a new train coming into the yard.