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For an M/M/1 queueing system with arrival rate λ and the service rate μ (λ < μ), let {Ns(t),

t ≥ 0} be the number of customers in the server. (Clearly, Ns(t) is always either 1 or 0.) Is Ns(t) a Markov chain? If yes, show that it is a Markov chain and find the transition rates between states 0 and 1. If not, carefully explain why. How about Nq(t), the number of customers in the queue only? Is this Markov? Justify your answer.Screen Shot 2019-10-15 at 12.08.17 PM.png

Screen Shot 2019-10-15 at 12.08.17 PM.png

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