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For a queuing system with Poisson input, a single waiting line without defections, and identically distributed independent (negative) exponential service times, the equilibrium distribution of the number of service completions in an arbitrary time interval is shown to be the same as the input distribution, for any number of servers. This result has applications in problems of tandem queuing. The essence of the proof is the demonstration of the independence of an interdeparture interval and the state of the system at the end of the interval.
Paul J. Burke (Sat,) studied this question.