Burke's theorem

Burke's theorem

Burke's theorem is a theorem in queueing theory by Paul J. Burke while working at Bell Telephone Laboratories that states for an M/M/1, M/M/m or M/M/∞ queue in the steady state with arrivals a Poisson process with rate parameter λ then:

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

Burke first published this theorem along with a proof in "The Output of a Queuing System", Operations Research, Vol. 4, No. 6 (December, 1956), pp. 699-704 ( [http://www.jstor.org/pss/166919 Available on JSTOR] ).


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