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Consider a two-server queue with Exponential arrival rate λ. Suppose servers 1 and 2 have exponential...

Consider a two-server queue with Exponential arrival rate λ. Suppose servers 1 and 2 have exponential rates μ1 and μ2, with μ1 > μ2. If server 1 becomes idle, then the customer being served by server 2 switches to server 1.

a) Identify a condition on λ,μ1,μ2 for this system to be stable, i.e., the queue does not grow indefinitely long.

b) Under that condition, and the long-run proportion of time that server 2 is busy.

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