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

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Abstract

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.

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Authors and Affiliations

  1. Carnegie Mellon University, Pittsburgh, PA, USA

    Varun Gupta

  2. IBM Research—Tokyo, Kanagawa, Japan

    Takayuki Osogami

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  1. Varun Gupta
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  2. Takayuki Osogami
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Correspondence to Varun Gupta.

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Gupta, V., Osogami, T. On Markov–Krein characterization of the mean waiting time in M/G/K and other queueing systems. Queueing Syst 68, 339–352 (2011). https://doi.org/10.1007/s11134-011-9248-8

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  • DOI: https://doi.org/10.1007/s11134-011-9248-8

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