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

22. 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 probabilityI mage. That is, with probabilityI mage such an arrival will not join the system. Show that the limiting distribution of the number of customers in the system is Poisson with meanI mage.
Assume that the service distribution is exponential with rate μ.