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Stochastic Processes : M/M/s Queue, Stationary Distribution and Long-Run Proportion

Consider the M/M/s queue, with arrival rate...

5. Consider the M/M/s queue, with arrival rate λ >0 and service rate μ >0.
(a) Find the condition involving λ, μ and s that is necessary for there to exist a stationary distribution. Why does this condition makes sense?
(b) Find the long-run proportion of time that there are k customers in the system, for k = 0,1,...

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M/M/s Queue, Stationary Distribution and Long-Run Proportion are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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