Customers arrive at a waiting system of type M/M/1/∞ with intensity λ. As long as there are less than n customers in the system, the server remains idle. As soon as the nth customer arrives, the...

Customers arrive at a waiting system of type M/M/1/∞ with intensity λ. As long as there are less than n customers in the system, the server remains idle. As soon as the nth customer arrives, the server resumes its work and stops working only then, when all customers (including newcomers) have been served. After that the server again waits until the waiting queue has reached length n and so on. Let 1/μ be the mean service time of a customer and X(t) be the number of customers in the system at time t.

(1) Draw the transition graph of the Markov chain {X(t), t ≥ 0}.

(2) Given that n = 2, compute the stationary state probabilities. (Make sure that they exist.)