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

Customers arrive at a single-server queue in accordance with a Poisson process

having rate .However, an arrival that finds n customers already in the systemwill

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 /.

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