Question: Consider a sequential queueing model with three servers, where customers arrive at server 1 in accordance with a Poisson process with rate . After completion

Consider a sequential queueing model with three servers, where customers arrive at server 1 in accordance with a Poisson process with rate λ. After completion at server 1 the customer then moves to server 2; after a service completion at server 2 the customer moves to server 3; after a service completion at server 3 the customer departs the system. Assuming that the service times at server i are exponential with rate μi, i = 1, 2, 3, find the limiting probabilities of this system by guessing at the reverse chain and then verifying that your guess is correct.

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