The M/M/1 queue is Bernoulli

• Autorzy: Michael Keane , Neil O'Connell
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 37A50: Relations with probability theory and stochastic processes
• 37H99: None of the above, but in this section
• 60J25: Continuous-time Markov processes on general state spaces
• 60K25: Queueing theory
• 60J65: Brownian motion

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2008
• Tom: 110
• Numer: 1
• Strony: 205-210

Daty

wydano

2008

Twórcy

autor

Michael Keane

• Department of Mathematics and Computer Science, Wesleyan University, Middletown, CT 06459, U.S.A.

autor

Neil O'Connell

• Department of Mathematics and BCRI, University College Cork, Cork, Ireland

Identyfikatory

DOI

10.4064/cm110-1-9