Long-parkers and short-parkers arrive at a parking place for cars according to independent Poisson processes with respective rates of λL = 4 and λS = 6 cars per hour. The parking place has room for only 2 cars. Each arriving car which finds both places occupied goes elsewhere. The parking time for long-parkers is exponentially distributed with a mean of 1 hour, while the parking time for short-parkers is exponentially distributed with a mean of 20 minutes.
(a) Model this situation as a continuous time Markov Chain
(b) What is the probability that the parking lot is empty?
(c) What is the probability that an arriving car is going elsewhere to park?