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In: Statistics and Probability

Customers arrive at a two-server system according to a Poisson process having rate λ = 5....

Customers arrive at a two-server system according to a Poisson process having rate λ = 5. An arrival finding server 1 free will begin service with that server. An arrival finding server 1 busy and server 2 free will enter service with server 2. An arrival finding both servers busy goes away. Once a customer is served by either server, he departs the system. The service times at server i are exponential with rates μi, where μ1 = 4, μ2 = 2.

(a) Find the long-run proportion of time that there is only one customer in the system.
(b) What proportion of time is server 2 busy?
(c) What is the average time an entering customer spends in the system?

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orchestra answered 1 year ago
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