Question: Customers arrive at a single-server queue according to a Poisson process of rate . However, an arrival that finds n customers already in the system

Customers arrive at a single-server queue according to a Poisson process of rate λ. However, an arrival that finds n customers already in the system will only join the system with probability 1/(n+1). The service rates are exponential with parameter μ. Derive the long time limiting distribution of the number of customers in the system and show that it is Poisson with mean λ/μ.

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