Consider a single-server queuing system where customers arrive according to a Poisson process with rate , service

Consider a single-server queuing system where customers arrive according to a Poisson process with rate λ, service times are exponential with rate μ, and customers are served in the order of their arrival. Suppose that a customer arrives and finds (n-1) others in the system. Let X denote the number of customers in the system at the moment that customer departs. Find the probability mass function of X, i.e., P[X=k], k=0,1,2.

 

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