Queueing Systems

, 68:339

On Markov–Krein characterization of the mean waiting time in M/G/K and other queueing systems



We propose a new research direction to reinvigorate research into better understanding of the M/G/K and other queueing systems—via obtaining tight bounds on the mean waiting time as functions of the moments of the service distribution. Analogous to the classical Markov–Krein theorem, we conjecture that the bounds on the mean waiting time are achieved by service distributions corresponding to the upper/lower principal representations of the moment sequence. We present analytical, numerical, and simulation evidence in support of our conjectures.


M/G/K Moments Bounds Multi-server systems Markov-Krein theorem Tchebycheff system 

Mathematics Subject Classification (2000)



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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Carnegie Mellon UniversityPittsburghUSA
  2. 2.IBM Research—TokyoKanagawaJapan

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