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Multi-Server Queueing Systems with Multiple Priority Classes

Author

Listed:
  • Mor Harchol-Balter

    (Carnegie Mellon University)

  • Takayuki Osogami

    (Carnegie Mellon University)

  • Alan Scheller-Wolf

    (Carnegie Mellon University)

  • Adam Wierman

    (Carnegie Mellon University)

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.

Suggested Citation

  • Mor Harchol-Balter & Takayuki Osogami & Alan Scheller-Wolf & Adam Wierman, 2005. "Multi-Server Queueing Systems with Multiple Priority Classes," Queueing Systems: Theory and Applications, Springer, vol. 51(3), pages 331-360, December.
    • Handle: RePEc:spr:queues:v:51:y:2005:i:3:d:10.1007_s11134-005-2898-7
    DOI: 10.1007/s11134-005-2898-7
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    References listed on IDEAS

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    1. Dimitris Bertsimas & Daisuke Nakazato, 1995. "The Distributional Little's Law and Its Applications," Operations Research, INFORMS, vol. 43(2), pages 298-310, April.
    2. Richard H. Davis, 1966. "Waiting-Time Distribution of a Multi-Server, Priority Queuing System," Operations Research, INFORMS, vol. 14(1), pages 133-136, February.
    3. Edward P. C. Kao & Kumar S. Narayanan, 1990. "Computing Steady-State Probabilities of a Nonpreemptive Priority Multiserver Queue," INFORMS Journal on Computing, INFORMS, vol. 2(3), pages 211-218, August.
    4. Kao, Edward P. C. & Wilson, Sandra D., 1999. "Analysis of nonpreemptive priority queues with multiple servers and two priority classes," European Journal of Operational Research, Elsevier, vol. 118(1), pages 181-193, October.
    5. J. P. Buzen & A. B. Bondi, 1983. "The Response Times of Priority Classes under Preemptive Resume in M / M / m Queues," Operations Research, INFORMS, vol. 31(3), pages 456-465, June.
    6. Alan Cobham, 1954. "Priority Assignment in Waiting Line Problems," Operations Research, INFORMS, vol. 2(1), pages 70-76, February.
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    Cited by:

    1. Yacov Satin & Rostislav Razumchik & Ivan Kovalev & Alexander Zeifman, 2023. "Ergodicity and Related Bounds for One Particular Class of Markovian Time—Varying Queues with Heterogeneous Servers and Customer’s Impatience," Mathematics, MDPI, vol. 11(9), pages 1-15, April.
    2. Elvin Coban & Aliza Heching & Alan Scheller‐Wolf, 2019. "Service Center Staffing with Cross‐Trained Agents and Heterogeneous Customers," Production and Operations Management, Production and Operations Management Society, vol. 28(4), pages 788-809, April.
    3. Jianfu Wang & Opher Baron & Alan Scheller-Wolf, 2015. "M/M/c Queue with Two Priority Classes," Operations Research, INFORMS, vol. 63(3), pages 733-749, June.
    4. Andrei Sleptchenko & M. Eric Johnson, 2015. "Maintaining Secure and Reliable Distributed Control Systems," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 103-117, February.
    5. Jori Selen & Brian Fralix, 2017. "Time-dependent analysis of an M / M / c preemptive priority system with two priority classes," Queueing Systems: Theory and Applications, Springer, vol. 87(3), pages 379-415, December.
    6. Walraevens, Joris & Fiems, Dieter & Wittevrongel, Sabine & Bruneel, Herwig, 2009. "Calculation of output characteristics of a priority queue through a busy period analysis," European Journal of Operational Research, Elsevier, vol. 198(3), pages 891-898, November.
    7. Przemysław Korytkowski & Tomasz Wiśniewski, 2011. "Performance analysis of commercial offset printing under dynamic priority rules," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 21(1), pages 53-64.

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