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Stationary state probabilities of the stochastic process

Question:

Consider a two-server loss system. Customers arrive according to a homogeneous Poisson process with intensity A customer is always served by server 1 when λ. this server is idle, i.e. an arriving customer goes only then to server 2, when server 1 is busy. The service times of both servers are idd exponential random variables with parameter Let be the number of customers in the system at time μ. X(t) t.

Determine the stationary state probabilities of the stochastic process {X(t), t ≥ 0}.

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## Q : Suitable homogeneous markov chain

Model the situation by a suitable homogeneous Markov chain {X(t), t = 0} and draw he transition graph.