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Queueing Systems

, Volume 67, Issue 1, pp 33–45 | Cite as

Time-dependent properties of symmetric queues

  • Brian Fralix
  • Bert Zwart
Article

Abstract

We settle a conjecture of Kella et al. (J. Appl. Probab. 42:223–234, 2005): the distribution of the number of jobs in the system of a symmetric M/G/1 queue at a fixed time is independent of the service discipline if the system starts empty. Our derivations are based on a time-reversal argument for regenerative processes and a connection with a clearing model.

Keywords

Regenerative processes Symmetric queues Time-reversal 

Mathematics Subject Classification (2000)

60K25 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Mathematical SciencesClemson UniversityClemsonUSA
  2. 2.CWIGB AmsterdamThe Netherlands

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