Long-parkers and short-parkers arrive at a parking place for cars according to indepen- dent Poisson processes with respective rates of L = 4 and S =...

Long-parkers and short-parkers arrive at a parking place for cars according to indepen- dent 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. Specify clearly what the states represent and what the transition probabilities are.

b. What is the probability that the parking lot is empty at any given time?

c. What is the probability that an arriving car is going elsewhere to park?