MATH3801 Probability & Stochastic Proc

4. Consider a two-server queue with Exponential arrival rate A. Suppose servers 1 and 2 have exponential rates /1 and M2, with M1 > /2. If server 1 becomes idle, then the customer being served by server 2 switches to server 1. a) Identify a condition on A, /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