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In: Statistics and Probability

2. Consider an N = 1 server queue with arrival rate λ > 0 and service...

2. Consider an N = 1 server queue with arrival rate λ > 0 and service rate µ = 1.

(a) Under what conditions will the process be (i) transient, (ii) positive recurrent, and (iii) null recurrent?

(b) If the process is positive recurrent, find the stationary distribution, say π(x). What is the name of this distribution?

(c) If the process is transient, find ρx0 for x ≥ 1.

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