Question: Consider a two-server queue with Exponential arrival rate . Suppose servers 1 and 2 have exponential rates 1 and 2, with 1 > 2. If

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

a)Identify a condition on ,1,2 for this system to be stable, i.e., the queue does not grow indefinitely long.

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

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