4.10 "Output" of a M/M/1 system In this problem you are asked to prove the important theorem of Section 4.10 for the case of a M/M/1 queueing system. Let a queueing system with a single server have Poisson arrivals at a rate , infinite queue capacity, and negative exponential service time with mean 1/ ( > ). Show that in the steady state the "output" stream leaving this queueing system is also Poisson at a rate .

Hint: What is the pdf for the time between service completions when the server is continually busy?