Question: Tiger Cut is a small barber shop which has a single server, where the service time is an exponential random variable with rate . The

Tiger Cut is a small barber shop which has a single server, where the service time is an exponential random variable with rate . The arrivals to Tiger Cut can be modeled by a Poisson process with arrival rate . Suppose that the barber shop has a capacity of 3 (2 waiting + 1 in service), and an arrival is rejected if the capacity is reached. (a) Model this stochastic process as a CTMC. Clearly define the state space, transition rates, and transition probability matrix. (b) In the long run, what is the expected number of customers in the shop?

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