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Multi-Server Queueing Systems with Multiple Priority Classes

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A Correction to this article was published on 27 September 2021

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Abstract

We present the first near-exact analysis of an M/PH/k queue with m > 2 preemptive-resume priority classes. Our analysis introduces a new technique, which we refer to as Recursive Dimensionality Reduction (RDR). The key idea in RDR is that the m-dimensionally infinite Markov chain, representing the m class state space, is recursively reduced to a 1-dimensionally infinite Markov chain, that is easily and quickly solved. RDR involves no truncation and results in only small inaccuracy when compared with simulation, for a wide range of loads and variability in the job size distribution.

Our analytic methods are then used to derive insights on how multi-server systems with prioritization compare with their single server counterparts with respect to response time. Multi-server systems are also compared with single server systems with respect to the effect of different prioritization schemes—“smart” prioritization (giving priority to the smaller jobs) versus “stupid” prioritization (giving priority to the larger jobs). We also study the effect of approximating m class performance by collapsing the m classes into just two classes.

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Authors and Affiliations

  1. Department of Computer Science, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, PA, 15213

    Mor Harchol-Balter, Takayuki Osogami & Adam Wierman

  2. Tepper School of Business, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, PA, 15213

    Alan Scheller-Wolf

Authors
  1. Mor Harchol-Balter
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  2. Takayuki Osogami
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  3. Alan Scheller-Wolf
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  4. Adam Wierman
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Corresponding author

Correspondence to Mor Harchol-Balter.

Additional information

Supported by NSF Career Grant CCR-0133077, NSF Theory CCR-0311383, NSF ITR CCR-0313148, and IBM Corporation via Pittsburgh Digital Greenhouse Grant 2003.

AMS subject classification: 60K25, 68M20, 90B22, 90B36

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Harchol-Balter, M., Osogami, T., Scheller-Wolf, A. et al. Multi-Server Queueing Systems with Multiple Priority Classes. Queueing Syst 51, 331–360 (2005). https://doi.org/10.1007/s11134-005-2898-7

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  • DOI: https://doi.org/10.1007/s11134-005-2898-7

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