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The M/M/1 queue is Bernoulli

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Keane M., O'Connell N.

Colloquium Mathematicum

2008

tom 110

nr 1

205-210

The classical output theorem for the M/M/1 queue, due to Burke (1956), states that the departure process from a stationary M/M/1 queue, in equilibrium, has the same law as the arrivals process, that is, it is a Poisson process. We show that the associated measure-preserving transformation is metrically isomorphic to a two-sided Bernoulli shift. We also discuss some extensions of Burke's theorem where it remains an open problem to determine if, or under what conditions, the analogue of this result holds.

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1 Colloquium Mathematicum

1 Keane M.

1 O'Connell N.

1 2008

Wyniki wyszukiwania

The M/M/1 queue is Bernoulli