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Large-scale parallel server system with multi-component jobs

Author

Listed:
  • Seva Shneer

    (Heriot-Watt University)

  • Alexander L. Stolyar

    (University of Illinois at Urbana-Champaign)

Abstract

A broad class of parallel server systems is considered, for which we prove the steady-state asymptotic independence of server workloads, as the number of servers goes to infinity, while the system load remains sub-critical. Arriving jobs consist of multiple components. There are multiple job classes, and each class may be of one of two types, which determines the rule according to which the job components add workloads to the servers. The model is broad enough to include as special cases some popular queueing models with redundancy, such as cancel-on-start and cancel-on-completion redundancy. Our analysis uses mean-field process representation and the corresponding mean-field limits. In essence, our approach relies almost exclusively on three fundamental properties of the model: (a) monotonicity, (b) work conservation and (c) the property that, on average, “new arriving workload prefers to go to servers with lower workloads.”

Suggested Citation

  • Seva Shneer & Alexander L. Stolyar, 2021. "Large-scale parallel server system with multi-component jobs," Queueing Systems: Theory and Applications, Springer, vol. 98(1), pages 21-48, June.
    • Handle: RePEc:spr:queues:v:98:y:2021:i:1:d:10.1007_s11134-021-09686-y
    DOI: 10.1007/s11134-021-09686-y
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    References listed on IDEAS

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    1. Kristen Gardner & Mor Harchol-Balter & Alan Scheller-Wolf & Mark Velednitsky & Samuel Zbarsky, 2017. "Redundancy-d: The Power of d Choices for Redundancy," Operations Research, INFORMS, vol. 65(4), pages 1078-1094, August.
    2. Alexander L. Stolyar, 2017. "Pull-based load distribution among heterogeneous parallel servers: the case of multiple routers," Queueing Systems: Theory and Applications, Springer, vol. 85(1), pages 31-65, February.
    Full references (including those not matched with items on IDEAS)

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