Question: Customers arrive at a single server queue in accordance with a Poisson process having rate A. However, an arrival that finds n customers already in

Customers arrive at a single server queue in accordance with a Poisson process having rate A. However, an arrival that finds n customers already in the system will only join the system with probability 1/(n + 1). That is, with probability n/(n + 1) such an arrival will not join the system. Show that the limiting distribution of the number of customers in the system is Poisson with mean A/.

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