Burke's theorem

In queueing theory, a discipline within the mathematical theory of probability, Burke's theorem (sometimes the Burke's output theorem) is a theorem (stated and demonstrated by Paul J. Burke while working at Bell Telephone Laboratories) asserting that, for the M/M/1 queue, M/M/c queue or M/M/∞ queue in the steady state with arrivals is a Poisson process with rate parameter λ:

1. The departure process is a Poisson process with rate parameter λ.
2. At time t the number of customers in the queue is independent of the departure process prior to time t.