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Math Help - Markov Process:Poisson Queue with exponential services

  1. #1
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    Markov Process:Poisson Queue with exponential services

    A single-server queue has Poisson arrivals at finite rate \lambda > 0 and exponential services at finite rate \mu > 0. When there are n customers in the system an arrival joins the queue with probability \frac{1}{(n+1)} and decides not to join with probability \frac{n}{(n+1)}. Let X_t be the number of customers in the system at time t.

    What are the transition rates for the Markov process (X_t).

    Under what condition(s) does the limiting distribution exist? What is the limiting distribution of the number of customers in the system?
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  2. #2
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    I can't do the second two questions until I have calculated the transition rates, and I am unsure how to calculate them in this question. Can anyone please help me to understand this?
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