It follows from Exercise 4 that if, in the M/M/1 model, W Q is the amount of
Question:
It follows from Exercise 4 that if, in the M/M/1 model, W∗
Q is the amount of time that a customer spends waiting in queue, then W∗
Q =
0, with probability 1 − λ/μ
Exp(μ − λ), with probability λ/μ
where Exp(μ − λ) is an exponential random variable with rate μ − λ. Using this, find Var(W∗
Q).
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