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3. Cars of type i = 1,2 arrive to a one-way street at random time instants with expected interarrival times of 6, minutes (61 = 3, 62 = 10). The street has one parking space. If an arriving car finds the space vacant, the car parks there immediately. Otherwise the car drives away. A car of type i remains parked for an expected duration of m, minutes (mi = 5, my = 20). The interarrival times and parking times of type-i cars are mutually independent and exponentially distributed. In addition, type-1 cars behave independently of type-2 cars. Currently the parking space is vacant. (a) Model the state of the parking space as a continuous-time Markov chain. Draw the transition diagram and write down the generator matrix of the chain. (2 p) (b) Determine the probability that the parking space is vacant in steady state. (2 p) (c) Explain how you can compute with the help of a computer the probability that the parking space is vacant after 30 minutes from now. (1 p) (d) What is the probability that at least 2 cars arrive to the street during the 5-minute time interval starting after one hour? (1 p)