Customers arrive at a single-server queue in accordance with a Poisson process having rate . However, an

Customers arrive at a single-server queue in accordance with a Poisson process having rate λ. 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 λ/μ.

Assume that the service distribution is exponential with rate μ.