Burke's theorem

In queueing theory, a discipline within the mathematical theory of probability, Burke's theorem (sometimes the Burke's output theorem[1]) 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.
  1. ^ Walrand, J. (1983). "A probabilistic look at networks of quasi-reversible queues". IEEE Transactions on Information Theory. 29 (6): 825–831. doi:10.1109/TIT.1983.1056762. S2CID 216943.