38. Consider an n server system where the service times of server i are exponentially distributed with
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38. Consider an n server system where the service times of server i are exponentially distributed with rate . Suppose customers arrive in accordance with a Poisson process with rate λ, and that an arrival who finds all servers busy does not enter but goes elsewhere. Suppose that an arriving customer who finds at least one idle server is served by a randomly chosen one of that group; that is, an arrival finding k idle servers is equally likely to be served by any of these k.
(a) Define states so as to analyze the preceding as a continuous-time Markov chain.
(b) Show that this chain is time reversible.
(c) Find the limiting probabilities.
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