5 Suppose customers arrive to a two server system according to a Poisson process with rate , and suppose that each arrival is, independently, sent either to server 1 with probability or to server 2 with probability Suppose the service time at server i is exponential with rateI mage, (a) Find , the average amount of time a customer spends in the system (b) If Image and Image, , find the value of that minimizes

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Question: 5. Suppose customers arrive to a two server system according to a Poisson process with rate , and suppose that each arrival is, independently, sent

5. Suppose customers arrive to a two server system according to a Poisson process with rate λ, and suppose that each arrival is, independently, sent either to server 1 with probability α or to server 2 with probability . Suppose the service time at server i is exponential with rateI mage, .

(a) Find , the average amount of time a customer spends in the system.

(b) If Image and Image, , find the value of α that minimizes .

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