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

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 infinitely long.

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

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